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aqua_rat__K8ybjoyhzWsuRWfS | When 22 is divided by the positive integer k, the remainder is 2, for how many different values of k is this true?
Options: A) 1 B) 2 C) 3 D) 4 E) 5 | When 22 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2. It also means that 20 is completely divisible by k. Factors of 20 are 1, 2, 4, 5, 10, 20 Out of these, k can be 4, 5, 10 and 20. Answer (4)
<result>D</result> | D | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | When 22 is divided by the positive integer k, the remainder is 2, for how many different values of k is this true? |
aqua_rat__koMSd5k4MtYbgLmx | 7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country. Choose the correct choice
A) 200 B) 300 C) 400 D) 500 E) 600 | Let x be the total grown quantity of wheat. According to the question (7%of x)+ 64 31 %of x)+3 7x 31x => 100+ 6 = 400 + 3 1200 x = β 400 million tonnes rice grown 400
<result>C</result> | C | {
"A": "200",
"B": "300",
"C": "400",
"D": "500",
"E": "600"
} | 7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country. |
aqua_rat__LcKa5ewAFtXoWVr6 | In a sequence, each term is obtained by adding 2 to the preceding one. If the sum of the first 20 terms is equal to 140, what is the result of the addition of the first 40 terms? Answers
A) 1020 B) 1080 C) 1160 D) 1240 E) 1280 | a is first term and d = 2 since the preceding number is always greater than the previous one.. Now 20th term is a+19(2). Sum of n terms is n/2(first term + last term)and here we have to get sum of 20 terms , we get 20/2 ( a + a+38) = 140 ( given sum of 20 terms is 140) => 10(2a+38) = 140 => 2a+38 = 14 => a = -12 Now to get sum of first 40 terms , we need to get 40th term value i.e. -12+39(2) = 66. Sum of first 40 terms = 40/2( -12 + 66) = 1080. Hence option 1080 is correct answer..
<result>B</result> | B | {
"A": "1020",
"B": "1080",
"C": "1160",
"D": "1240",
"E": "1280"
} | In a sequence, each term is obtained by adding 2 to the preceding one. If the sum of the first 20 terms is equal to 140, what is the result of the addition of the first 40 terms? |
aqua_rat__vGC96K0LVCvoPmRc | One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,75,000 as total savings, how much has he saved in Public Provident Fund ?
Choose the correct choice from the following:
A) 80000 B) 60000 C) 50000 D) 70000 E) 90000 | Let savings in N.S.C and P.P.F. be Rs. x and Rs. (175000 - x) respectively. Then, =1/3 x = 1/2 (175000 - x) =x/3 + x/2 = 87500 =5x/6 = 87500 =x = 87500 x 6 /5 = 105000 Savings in Public Provident Fund = Rs. (175000 - 105000) = Rs. 70000 Answer is 70000.
<result>D</result> | D | {
"A": "80000",
"B": "60000",
"C": "50000",
"D": "70000",
"E": "90000"
} | One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,75,000 as total savings, how much has he saved in Public Provident Fund ? |
aqua_rat__waW2aS9SErw0IMS4 | Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 30% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease? Choose the correct answer.
A) $20 B) $40 C) $50 D) $70 E) $100 | Deargoodyear2013, I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s. Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100. They had this same selling price, $100, before they made the change, and had a profit of 30%, so the manufacturing must have been $70. Answer = ($70).
<result>D</result> | D | {
"A": "$20",
"B": "$40",
"C": "$50",
"D": "$70",
"E": "$100"
} | Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 30% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease? |
aqua_rat__hu2Lq9ki7EVRBQ46 | A class has 6 boys and x girls. Average score of boys and girls is 50 and 60 respectively. the average of the whole class is 55, what is the value of x? Choose the correct choice from the following choices:
A) 5
B) 6
C) 10
D) 12
E) 15 | After you have got : 6(50)+60x/6+x=55 6*50 + 60x = 6*55 + 55x x=6 Answer is 6
<result>B</result> | B | {
"A": "5",
"B": "6",
"C": "10",
"D": "12",
"E": "15"
} | A class has 6 boys and x girls. Average score of boys and girls is 50 and 60 respectively. the average of the whole class is 55, what is the value of x? |
aqua_rat__rf589oWpwz4VkBnz | If 2x^2 + y^2 = 2xy, then (x - y)^2 = Select the correct option.
A) -x^2 B) 3x^2 C) 4xy D) 2y^2 E) β y^2 | (x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2-2x^2-y^2 = -x^2 Correct option : -x^2
<result>A</result> | A | {
"A": "-x^2",
"B": "3x^2",
"C": "4xy",
"D": "2y^2",
"E": "β y^2"
} | If 2x^2 + y^2 = 2xy, then (x - y)^2 = |
aqua_rat__xqJbOLBt2KypMqYQ | Find the least square number which is exactly divisible by 10,12,15 and 18. Choose the most appropriate option: A) 900 B) 120 C) 103 D) 104 E) 217 | L.C.M. of 10, 12, 15, 18 = 180. Now, 180 = 2 * 2 * 3 * 3 *5 = 22 * 32 * 5. To make it a perfect square, it must be multiplied by 5. Required number = (22 * 32 * 52) = 900. 900NSWER 900 900
<result>A</result> | A | {
"A": "900",
"B": "120",
"C": "103",
"D": "104",
"E": "217"
} | Find the least square number which is exactly divisible by 10,12,15 and 18. |
aqua_rat__xgqPtNigdFY5tHC3 | George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 15% of the money for taxi fare and buys 15 mangoes. How many oranges can he buy? Choose one
A) 25 B) 17.5 C) 20 D) 16 E) 12 | Let the amount of money be 200 Let cost of 1 Orange be 4 Let cost of 1 mango be 5 He decides to retain 15% of 200 = 30 for taxi fare, so he is left with 170 He buys 20 mangoes ( @ 5) so he spends 100 Money left is 70 (170 - 100) No of oranges he can buy = 70/4 =>17,5 So, George can buy 15 Oranges. 17.5
<result>B</result> | B | {
"A": "25",
"B": "17.5",
"C": "20",
"D": "16",
"E": "12"
} | George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 15% of the money for taxi fare and buys 15 mangoes. How many oranges can he buy? |
aqua_rat__cBudjQsdSYp58Ata | The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 20% profit?
Choose the correct choice from the following answers:
A) 277 B) 960 C) 277 D) 266 E) 768 | Let C.P. = Rs. x. Then, 832 - x = x - 448 2x = 1280 => x = 640 Required S.P. = 120% of Rs. 640 = 120/100 * 640 = Rs. 768. Answer: 768
<result>E</result> | E | {
"A": "277",
"B": "960",
"C": "277",
"D": "266",
"E": "768"
} | The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 20% profit? |
aqua_rat__rfGX8qtkfR88sOPx | In the interior of a forest, a certain number of apes equal to the square of one-fourth of the total number are playing and having great fun. The remaining four apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? Choose the correct choice from the following answers
A) 48 B) 8 C) 64 D) 80 E) 16 or 48 | Let total number be x No in the interior = (x/4)^2 No outside = 4 So : x - (x/4)^2=4 x^2-16x+64=0 (x-8)^2=0 So x=8 8
<result>B</result> | B | {
"A": "48",
"B": "8",
"C": "64",
"D": "80",
"E": "16 or 48"
} | In the interior of a forest, a certain number of apes equal to the square of one-fourth of the total number are playing and having great fun. The remaining four apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes? |
aqua_rat__B9V8Mxy8I4MqS2Sq | Area of a square is 1/2 hectare. The diagonal of the square is?
Choose the correct option.
A) 250 meter
B) 100 meter
C) 50β 2 meter
D) 50 meter
E) 35 meter | Area = 1/2 hectare = 10000 / 2 m2 = 5000 m2 Again Area = 1/2 x (Diagonal)2 So 1/2 x (Diagonal)2 = 5000m2 Diagonal2= 10000 Diagonal = 100 Answer : 100 meter
<result>B</result> | B | {
"A": "250 meter",
"B": "100 meter",
"C": "50β 2 meter",
"D": "50 meter",
"E": "35 meter"
} | Area of a square is 1/2 hectare. The diagonal of the square is? |
aqua_rat__zFqzM5hsv1hDtQtz | A box contains 9 apples, 8 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n? Choose the correct choice from the following choices:
A) 3 B) 4 C) 5 D) 6 E) 7 | P(choosing a red apple 5 times in a row) = 8/9*7/8*6/7*5/6*4/5 = 4/9 < 0.5 The answer is 5.
<result>C</result> | C | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | A box contains 9 apples, 8 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n? |
aqua_rat__I9d3rwh3MKrrpYgC | How much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? Choose the correct choice from the following answers.
A) 40 sec
B) 50 sec
C) 60 sec
D) 70 sec
E) 80 sec | The distance to be covered = Sum of their lengths = 400 + 300=
<gadget id="calculator">400 + 300</gadget>
<output>700</output>
700 m. Relative speed= 72 -36=
<gadget id="calculator">72 -36</gadget>
<output>36</output>
36 kmph= 36 * 5/18=
<gadget id="calculator">36 * 5/18</gadget>
<output>10</output>
10 mps. Time required= d/s = 700/10=
<gadget id="calculator">700/10</gadget>
<output>70</output>
70 sec. ANSWER:70 sec
<result>D</result> | D | {
"A": "40 sec",
"B": "50 sec",
"C": "60 sec",
"D": "70 sec",
"E": "80 sec"
} | How much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? |
aqua_rat__GEihnCTwutDP0YPD | If k is a non-negative integer and 21^k is a divisor of 435,961 then 7^k - k^7 = Choose the correct option.
A) 0 B) 1 C) 42 D) 118 E) 242 | 4+3+5+9+6+1=
<gadget id="calculator">4+3+5+9+6+1</gadget>
<output>28</output>
28, so this number is not divisible by 3 and thus not divisible by 21. Therefore, k=0 7^k - k^7 =1-0=
<gadget id="calculator">1-0</gadget>
<output>1</output>
1 The answer is 1.
<result>B</result> | B | {
"A": "0",
"B": "1",
"C": "42",
"D": "118",
"E": "242"
} | If k is a non-negative integer and 21^k is a divisor of 435,961 then 7^k - k^7 = |
aqua_rat__kVRY23AFnW8owibx | The Simplastic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic? Choose the correct choice from the following answers
A) 9 B) 12 C) 36 D) 72 E) 108 | The nouns havefixed structureC-V-C-V-C. Now,each Ccan take 3 values (let's say X, Y or Z) andeach Vcan take 2 values (let's say A or E), so there will be 3*2*3*2*3=
<gadget id="calculator">3*2*3*2*3</gadget>
<output>108</output>
108 nouns possible. Answer: E. It's basically the same if it were how many different 5-digit numbers are possible with the following structure odd-even-odd-even-odd, where odd numbers can be only 1, 3 or 5 and even numbers only 2 and 4. It's natural to think that a noun can have for example two same vowels (X-A-Y-A-Z) or 3 same consonants (X-A-X-A-X), so if this was not the case then this would be explicitly mentioned.answer is 108
<result>E</result> | E | {
"A": "9",
"B": "12",
"C": "36",
"D": "72",
"E": "108"
} | The Simplastic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic? |
aqua_rat__jVT8LlPcxDcn7nFo | What distance will be covered by a city bus moving at 72 kmph in 30 seconds? Choose the correct answer: A) 200 m B) 300 m C) 600 m D) 500 m E) 400 m | 72 kmph = 72 * 5/18=
<gadget id="calculator">72 * 5/18</gadget>
<output>20</output>
20 mps Dist= Speed * time = 20 * 30=
<gadget id="calculator">20 * 30</gadget>
<output>600</output>
600 m. ANSWER 600 m
<result>C</result> | C | {
"A": "200 m",
"B": "300 m",
"C": "600 m",
"D": "500 m",
"E": "400 m"
} | What distance will be covered by a city bus moving at 72 kmph in 30 seconds? |
aqua_rat__qLq1uW5PhqwjvtaV | In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 25 p coins are there? Choose the correct choice from the following answers:
A) 155 B) 100 C) 125 D) 150 E) 120 | Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively. Then, sum of their values = (25 x/100) + (20 x/100) + (15 x/100) = 60 x /100 30 = 60 x / 100 x = 50 = 25 p coin Hence, the number of 5 p coins = (3 * 50)=
<gadget id="calculator">(3 * 50)</gadget>
<output>150</output>
150. Ans - 150
<result>D</result> | D | {
"A": "155",
"B": "100",
"C": "125",
"D": "150",
"E": "120"
} | In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 25 p coins are there? |
aqua_rat__IbnGko2Ho6FYR08l | What number has a 5:1 ratio to the number 11?
Choose the correct choice
A) 22 B) 50 C) 55 D) 52 E) 12 | 5:1 = x: 10 x = 55 Answer: 55
<result>C</result> | C | {
"A": "22",
"B": "50",
"C": "55",
"D": "52",
"E": "12"
} | What number has a 5:1 ratio to the number 11? |
aqua_rat__cbyD4Wj9t8qzITQx | In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls? Choose the correct answer:
A) 80 B) 81 C) 64 D) 63 E) 82 | Stage 1: Select a box for the 1st ball to go into. There are 3 available boxes, so we can complete stage 1 in 3 ways Stage 2: Select a box for the 2nd ball to go into. There are 3 available boxes, so we can complete stage 2 in 3 ways Stage 3: Select a box for the 3rd ball to go into. There are 3 available boxes, so we can complete stage 3 in 3 ways Stage 4: Select a box for the 4th ball to go into. There are 3 available boxes, so we can complete stage 4 in 3 ways 81y the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus distribute all 4 balls) in (3)(3)(3)(3)(4) ways (= 81 ways) Answer:81
<result>B</result> | B | {
"A": "80",
"B": "81",
"C": "64",
"D": "63",
"E": "82"
} | In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls? |
aqua_rat__U78RtQj4oz0pvVzg | There are two numbers. If 50% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? Choose the correct answer
A) 5/9
B) 5/7
C) 5/3
D) 5/8
E) 2/1 | Let the two numbers be x and y. 50/100 * x + y = 5/4y => 1/2 x = 1/4 y => x/y = 2/1 Answer: 2/1
<result>E</result> | E | {
"A": "5/9",
"B": "5/7",
"C": "5/3",
"D": "5/8",
"E": "2/1"
} | There are two numbers. If 50% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? |
aqua_rat__9owmCSi59ASkr3g4 | What is the HCF of 2/3, 4/9 and 6/18
Select the correct option:
A) 7/45 B) 2/45 C) 1/9 D) 8/45 E) 9/45 | Explanation: H1/9F of Fractions = H1/9F of Numerators/L1/9M of Denominators = (H1/9F of 2, 4, 6)/(L1/9M of 3, 9, 18) = 2/18 = 1/9 Answer: Option 1/9
<result>C</result> | C | {
"A": "7/45",
"B": "2/45",
"C": "1/9",
"D": "8/45",
"E": "9/45"
} | What is the HCF of 2/3, 4/9 and 6/18 |
aqua_rat__92XYXt9BswZJi8m4 | A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? Select the correct option:
A) 300 B) 350 C) 450 D) 470 E) 500 | Explanation: 10 * 150=
<gadget id="calculator">10 * 150</gadget>
<output>1_500</output>
1500 3 * 100 + 5 * 150=
<gadget id="calculator">3 * 100 + 5 * 150</gadget>
<output>1_050</output>
1050 1500 β 1050= 450 450
<result>C</result> | C | {
"A": "300",
"B": "350",
"C": "450",
"D": "470",
"E": "500"
} | A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? |
aqua_rat__dz39ekRVGvLFkcYu | If x and y are odd integers, which of the following must always be a non-integer Choose the correct answer.
A) -x^2y B) y/x C) xy/4 D) x/y E) x^2y^2 | as X and Y are odd, multiplication of x and y would result in odd integer (Odd Integer)/4 will always be non integer. xy/4
<result>C</result> | C | {
"A": "-x^2y",
"B": "y/x",
"C": "xy/4",
"D": "x/y",
"E": "x^2y^2"
} | If x and y are odd integers, which of the following must always be a non-integer |
aqua_rat__07FZyrGAV5qysjgy | David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
Choose the correct choice from the following choices.
A) 19
B) 28
C) 30
D) 37
E) None | EXPLANATION Suppose their paths cross after x minutes. Then, 11 + 57x = 51 β 63x <=> 120x = 40 x= 1/3 Number of floors covered by david in (1/3) min = (1/3 x 57) = 19 So, their paths cross at (11 +19) i.e., 30th floor. Answer 30
<result>C</result> | C | {
"A": "19",
"B": "28",
"C": "30",
"D": "37",
"E": "None"
} | David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ? |
aqua_rat__9y8Ec6SUheYLTc6x | From below option 48 is divisible by which one? Choose the correct option:
A) A)3
B) B)5
C) C)9
D) D)7
E) E)11 | 48/3=
<gadget id="calculator">48/3</gadget>
<output>16</output>
16 3
<result>A</result> | A | {
"A": "A)3",
"B": "B)5",
"C": "C)9",
"D": "D)7",
"E": "E)11"
} | From below option 48 is divisible by which one? |
aqua_rat__LkYxD7FkEyn5kfns | A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 60 as remainder. Find the no. is? Select the correct option:
A) 145646 B) 236578 C) 645353 D) 456546 E) 220060 | (555 + 445) * 2 * 110 + 60 = 220000 + 60=
<gadget id="calculator">220000 + 60</gadget>
<output>220_060</output>
220060 220060
<result>E</result> | E | {
"A": "145646",
"B": "236578",
"C": "645353",
"D": "456546",
"E": "220060"
} | A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 60 as remainder. Find the no. is? |
aqua_rat__K4ixJelnsovtv6tv | Find the odd man out. 12, 24, 34, 48, 64, 84 Choose the correct choice from the following choices:
A) 48 B) 34 C) 24 D) 12 E) 11 | Explanation : All numbers except 34 are multiples of 4. Answer : Option 34
<result>B</result> | B | {
"A": "48",
"B": "34",
"C": "24",
"D": "12",
"E": "11"
} | Find the odd man out. 12, 24, 34, 48, 64, 84 |
aqua_rat__4iuTU7aXMBo5OZFt | The ratio of the two natural numbers is 5 : 6. If a certain number is added to both the numbers, the ratio becomes 7 : 8. If the larger number exceeds the smaller number by 10, find the number added? Choose the correct choice from the following: A) 17 B) 14 C) 10 D) 16 E) 20 | Let the two numbers be 5x and 6x. Let the numbers added to both so that their ratio becomes 7 : 8 be k. (5x + k) / (6x + k) = 7/8 => 40x + 8k = 42x + 7k => k = 2x. 6x - 5x = 10 => x = 10 k = 2x = 20. Answer:10
<result>C</result> | C | {
"A": "17",
"B": "14",
"C": "10",
"D": "16",
"E": "20"
} | The ratio of the two natural numbers is 5 : 6. If a certain number is added to both the numbers, the ratio becomes 7 : 8. If the larger number exceeds the smaller number by 10, find the number added? |
aqua_rat__zZJ6gnkFX3leB8l9 | If N = 1/5 + 1/5^2 +1/5^3 , then N is multiplied by 100 , will the product be greater than 100? Select.
A) Less than 100 B) Greater than 100 C) Indeterminate D) Equal to 100 E) Cannot be determined | We need to check if (1/5 + 1/5^2 +1/5^3) > 1 If it is greater than 1 then the product 100 * N will be greater than 1 else not N = 1/5 + 1/5^2 +1/5^3 5^3 * N = 5^3 * 1/5 + 5^3 * 1/5^2 + 5^3 * 1/5 ^3 125 * N = 25 + 5 + 1 125 * N = 31 N = 31/125 N is less than 1 since numerator is less than denominator . Therefore 100 N would be less than 100 Less than 100ns: Less than 100
<result>A</result> | A | {
"A": "Less than 100",
"B": "Greater than 100",
"C": "Indeterminate",
"D": "Equal to 100",
"E": "Cannot be determined"
} | If N = 1/5 + 1/5^2 +1/5^3 , then N is multiplied by 100 , will the product be greater than 100? |
aqua_rat__kJPCMXyN3LNeP2r2 | If x/4 + 24/x = 5, what are the values of 4x - 7? Choose the correct choice
A) 8 and 9
B) 8 and 24
C) 25 and 41
D) 12 and 29
E) 17 and 29 | I got the same thing 25 and 41 is the answer 25 or 41
<result>C</result> | C | {
"A": "8 and 9",
"B": "8 and 24",
"C": "25 and 41",
"D": "12 and 29",
"E": "17 and 29"
} | If x/4 + 24/x = 5, what are the values of 4x - 7? |
aqua_rat__3NMHSvx8UFieS2DX | A thief goes away with a SANTRO car at a speed of 22 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 72 kmph when will the owner over take the thief from the start? Choose the correct choice from the following answers:
A) 5/3 hours
B) 11/25 hours
C) 2/3 hours
D) 1/3 hours
E) 2/5 hours | -----------22--------------------| 72 22 D = 22 RS = 72 Γ’β¬β 22 = 50 T = 22/50 = 11/25 hours ANSWER:11/25 hours
<result>B</result> | B | {
"A": "5/3 hours",
"B": "11/25 hours",
"C": "2/3 hours",
"D": "1/3 hours",
"E": "2/5 hours"
} | A thief goes away with a SANTRO car at a speed of 22 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 72 kmph when will the owner over take the thief from the start? |
aqua_rat__jyXAfv2znBYeDhpJ | A 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar? Choose the correct choice from the following answers:
A) 1/4 B) 2/5 C) 1/2 D) 3/5 E) 2/3 | you can simply use this formula to avoid confusion: w1/w2 = (A2 - Aavg)/(Avg - A1) Here is how you will find the values of A1 an A2. We have an overall loss (average loss). The average loss is 3 kg when 30 kg alloy is immersed. This is a loss of (3/30)*100=
<gadget id="calculator">(3/30)*100</gadget>
<output>10</output>
10%. This is Aavg The loss of tin is 1.375 kg for every 10 kg. This means it loses (1.375/10)*100=
<gadget id="calculator"> (1.375/10)*100</gadget>
<output>13.75</output>
13.75% of its weight in water. This is A1. The loss of silver is .375 kg for every 5 kg. This means it loses (.375/5)* 100=
<gadget id="calculator"> (.375/5)* 100</gadget>
<output>7.5</output>
7.5% of its weight in water. This is A2. Weight of Tin/Weight of Silver= (Silver's loss - Avg loss)/(Avg loss - Tin's loss) X/Y = (7.5 - 10)/(10 - 13.75) = 2/3 2/3
<result>E</result> | E | {
"A": "1/4",
"B": "2/5",
"C": "1/2",
"D": "3/5",
"E": "2/3"
} | A 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar? |
aqua_rat__N4DG9VD3Bj4VwOaQ | A tour group of 25 people paid a total of $1050 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
Choose the correct choice from the following answers
A) $22 B) $23.94 C) $40 D) $25.20 E) $30 | Soln:- 1050/25=x+0.05x 1050/25=1.05x x=40 ANSWER:$40
<result>C</result> | C | {
"A": "$22",
"B": "$23.94",
"C": "$40",
"D": "$25.20",
"E": "$30"
} | A tour group of 25 people paid a total of $1050 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices |
aqua_rat__fprvQaHCdlScbVyg | A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? Select:
A) 220 metre
B) 230 metre
C) 250 metre
D) 260 metre
E) 270 metre | Distance covered in 26 seconds = 26Γβ72Γβ5/18=520 meter Length of the train = 520-250=
<gadget id="calculator">520-250</gadget>
<output>270</output>
270 meter ANSW270 metreR: 270 metre
<result>E</result> | E | {
"A": "220 metre",
"B": "230 metre",
"C": "250 metre",
"D": "260 metre",
"E": "270 metre"
} | A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ? |
aqua_rat__SJya75yUTzL4OdRi | John borrowed 3 soccer boots from Jake, and forgot them on the field, if peter came across a total of 15 boots on the field Jake's boots inclusive, and he took 4 boots at random, what is the probability that Jake's boots were not amongst the 4 taken?. Choices:
A) 12/91 B) 3/15 C) 12/15 D) 33/91 E) 3/91 | Since Jake owns 3 of the boots, the subset from which the 4 boots should be chosen are the 12 boots not owned by Jake from the universe of 15. The first boot can be one of the 12 from the 15 with probability 12/15. The second boot can be one of the 11 from the 14 remaining with probability 11/14. The third boot can be one of the 10 from the 13 remaining with probability 10/13. The fourth boot can be one of the 9 from the 12 remaining with probability 9/12. The total probability will be 12/15 Γ 11/14 Γ 10/13 Γ 9/12 . On cancellation, this comes to 33/91. Thus, the answer is 33/91 - 33/91
<result>D</result> | D | {
"A": "12/91",
"B": "3/15",
"C": "12/15",
"D": "33/91",
"E": "3/91"
} | John borrowed 3 soccer boots from Jake, and forgot them on the field, if peter came across a total of 15 boots on the field Jake's boots inclusive, and he took 4 boots at random, what is the probability that Jake's boots were not amongst the 4 taken?. |
aqua_rat__LaAIWWVgxjBEbQjQ | Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin? Choose the correct choice from the following choices:
A) 24.8 years B) 28.5 years C) 84.5 years D) 34.5 years E) 24.5 years | Let Rahul's age be x years. Then, Sachin's age = (x - 7) years. (x - 7)/x = 7/9 2x = 63 => x = 31.5 Hence, Sachin's age = (x - 7) = 24.5 years. Answer:24.5 years
<result>E</result> | E | {
"A": "24.8 years",
"B": "28.5 years",
"C": "84.5 years",
"D": "34.5 years",
"E": "24.5 years"
} | Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin? |
aqua_rat__26OM4O2qo3niimJA | What will be the difference between simple and compound interest at 16% per annum on a sum of Rs. 1000 after 4 years?
Select
A) 164.19 B) 164.12 C) 170.6 D) 167.1 E) 165.11 | S.I. = (1000 * 16 * 4)/100 = Rs. 640 C.I. = [1000 * (1 + 16/100)4 - 1000] = Rs. 810.6 Difference = (810.6-640) = Rs. 170.6 Answer: 170.6
<result>C</result> | C | {
"A": "164.19",
"B": "164.12",
"C": "170.6",
"D": "167.1",
"E": "165.11"
} | What will be the difference between simple and compound interest at 16% per annum on a sum of Rs. 1000 after 4 years? |
aqua_rat__Dg00cMNgcNpG1BDA | If paint costs $3.20 per quart, and a quart covers 1200 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge? Choose the correct choice from the following options: A) $ 1.60 B) $ 16.00 C) $ 96.00 D) $108.00 E) $196.00 | total surface area = 6a^2 = 6*10*10=
<gadget id="calculator">6*10*10</gadget>
<output>600</output>
600 each quart covers 20 sqr ft thus total number of quarts= 600/1200=
<gadget id="calculator">600/1200</gadget>
<output>1/2 = around 0.5</output>
0.5 cost will be 0.5*3.2=
<gadget id="calculator"> 0.5*3.2</gadget>
<output>1.6</output>
$1.6 $ 1.60ns: $ 1.60
<result>A</result> | A | {
"A": "$ 1.60",
"B": "$ 16.00",
"C": "$ 96.00",
"D": "$108.00",
"E": "$196.00"
} | If paint costs $3.20 per quart, and a quart covers 1200 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge? |
aqua_rat__4wyN93M9SqcgIuJQ | An empty bottle weighs 1/6th of the full bottle. When a certain percent of water was removed and the bottle was weighed, the weight of the bottle turned out to be 1/3rd of the bottle when it was full. What is the percent of water removed? Choose the correct choice
A) 89% B) 82% C) 81% D) 50% E) 80% | Explanation: Let the weight of full bottle be 6kg. Therefore, weight of empty bottle is 1kg and that of water is 5kg. If x% of water is removed, the weight of the bottle becomes 2kg. Therefore, the amount of water removed is 4kg. % of water removed = 4/5 *100=
<gadget id="calculator">4/5 *100</gadget>
<output>80</output>
80% ANSW80%R: 80%
<result>E</result> | E | {
"A": "89%",
"B": "82%",
"C": "81%",
"D": "50%",
"E": "80%"
} | An empty bottle weighs 1/6th of the full bottle. When a certain percent of water was removed and the bottle was weighed, the weight of the bottle turned out to be 1/3rd of the bottle when it was full. What is the percent of water removed? |
aqua_rat__qQqYgxqhNvZov0T4 | A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 20 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)
Choose the correct choice from the following: A) 4200 B) 5400 C) 6600 D) 7800 E) 8900 | The distance the sound traveled to the man is 20*330=
<gadget id="calculator">20*330</gadget>
<output>6_600</output>
6600 meters The answer is 6600.
<result>C</result> | C | {
"A": "4200",
"B": "5400",
"C": "6600",
"D": "7800",
"E": "8900"
} | A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 20 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s) |
aqua_rat__2funm30NrD4hHpjk | a school has 6 maths 5 physics and 5 chemistry teachers each teacher can teach 4 subjects max what is he minimum number of teachers required
Choose one: A) 2 B) 4 C) 5 D) 6 E) 7 | Total subjects = 6+5+5=
<gadget id="calculator">6+5+5</gadget>
<output>16</output>
16 Max subjects by 1 teacher= 4 So, min of teachers required = 16/4=
<gadget id="calculator">16/4</gadget>
<output>4</output>
4 ANSWER:4
<result>B</result> | B | {
"A": "2",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | a school has 6 maths 5 physics and 5 chemistry teachers each teacher can teach 4 subjects max what is he minimum number of teachers required |
aqua_rat__CqyjTJq6SLJnxE2k | A person, who decided to go to weakened trip should not exceed 8 hours driving in a day. Average speed of forward journey is 40 m/h. Due to traffic in Sundays, the return journey average speed is 30 m/h. How far he can select a picnic spot? Choose the correct answer:
A) 120 miles B) between 120 and 140 miles C) 160 miles D) 180 miles E) 260 miles | let dist travelled be 2x. hence destination is at dist x x/40+x/30=8 x=137.14 ANSWER:between 120 and 140 miles
<result>B</result> | B | {
"A": "120 miles",
"B": "between 120 and 140 miles",
"C": "160 miles",
"D": "180 miles",
"E": "260 miles"
} | A person, who decided to go to weakened trip should not exceed 8 hours driving in a day. Average speed of forward journey is 40 m/h. Due to traffic in Sundays, the return journey average speed is 30 m/h. How far he can select a picnic spot? |
aqua_rat__hNpkd5mOmTMI2vco | Taequan is playing a dice game where he rolls two, fair, six-sided dice twice. If he gets the same roll on his second try as his first, he wins. If he rolled an 8 on his first try, what is the probability that he will win with his second roll? Select the correct option:
A) 1/18 B) 1/12 C) 1/9 D) 1/6 E) 5/36 | There are 5 ways to roll an 8: 2 and 6, 6 and 2, 3 and 5, 5 and 3, 4 and 4 (4 and 4 is counted just once). There are 6*6=
<gadget id="calculator"> 6*6</gadget>
<output>36</output>
36 ways to roll two six-sided dice. The dice are fair, so the probability of rolling an 8 is 5/36. 5/36
<result>E</result> | E | {
"A": "1/18",
"B": "1/12",
"C": "1/9",
"D": "1/6",
"E": "5/36"
} | Taequan is playing a dice game where he rolls two, fair, six-sided dice twice. If he gets the same roll on his second try as his first, he wins. If he rolled an 8 on his first try, what is the probability that he will win with his second roll? |
aqua_rat__ONK2H24wgyr4ltLh | A thief is spotted by a policeman from a distance of 100 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken? Select the correct option
A) 100 m B) 200 m C) 400 m D) 500 m E) 300 m | Relative speed of the policeman = (10-8) km/hr =2 km/hr. Time taken by police man to cover 100m 100/1000 x 1/2 hr = 1/20 hr. In 1/20 hrs, the thief covers a distance of 8x 1/20km =2/5km = 400 m ANSWER 400 m
<result>C</result> | C | {
"A": "100 m",
"B": "200 m",
"C": "400 m",
"D": "500 m",
"E": "300 m"
} | A thief is spotted by a policeman from a distance of 100 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken? |
aqua_rat__5iSfrCTtBgTVwBjN | Mangala completes a piece of work in 18 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is Choose one:
A) 6 days B) 7 days C) 15 days D) 9 days E) 11 days | If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 18 Γβ 40/48 = 15 days. 15 days
<result>C</result> | C | {
"A": "6 days",
"B": "7 days",
"C": "15 days",
"D": "9 days",
"E": "11 days"
} | Mangala completes a piece of work in 18 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is |
aqua_rat__dtxwv4nZkDtOs7mE | The average weight of 8 person's increases by 5 kg when a new person comes in place of one of them weighing 35 kg. What might be the weight of the new person? Select the correct option.
A) 80 kg
B) 85 kg
C) 75 kg
D) 100 kg
E) 110 kg | Total weight increased = (8 x 5) kg = 40 kg. Weight of new person = (35 + 40)=
<gadget id="calculator">(35 + 40)</gadget>
<output>75</output>
75 kg. Answer : 75 kg
<result>C</result> | C | {
"A": "80 kg",
"B": "85 kg",
"C": "75 kg",
"D": "100 kg",
"E": "110 kg"
} | The average weight of 8 person's increases by 5 kg when a new person comes in place of one of them weighing 35 kg. What might be the weight of the new person? |
aqua_rat__Oubmt1S5tOwclStR | What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?
Answers.
A) 20 18 48 61 B) 50 18 48 62 C) 10 18 48 68 D) 30 18 48 66 E) 40 18 48 69 | D 30 18 48 66. Starting at the top, add pairs of numbers in each column to arrive at the next number.
<result>D</result> | D | {
"A": "20 18 48 61",
"B": "50 18 48 62",
"C": "10 18 48 68",
"D": "30 18 48 66",
"E": "40 18 48 69"
} | What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ? |
aqua_rat__hVAHylxM0OKx7c8T | A tradesman sold an article at a loss of 20%. If the selling price had been increased by $100, there would have been a gain of 5%. What was the cost price of the article ? Answers
A) $400 B) $150 C) $300 D) $550 E) $610 | Let C.P. be $x Then 105% of x - 80% of x = 100 25% of x = 100 x/4 = 100 x = 400 $400nswer is $400
<result>A</result> | A | {
"A": "$400",
"B": "$150",
"C": "$300",
"D": "$550",
"E": "$610"
} | A tradesman sold an article at a loss of 20%. If the selling price had been increased by $100, there would have been a gain of 5%. What was the cost price of the article ? |
aqua_rat__BHvzG0yjrzjDilF4 | On January 1, 2011, James invests 80% of his retirement savings in Antarctic largecap stocks, 10% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 5% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013,James has the same total amount of retirement savings as he did two years before, then x is between Pick one.
A) 10 and 20 B) 20 and 30 C) 30 and 40 D) 40 and 50 E) 50 and 60 | Pick a smart number for the total retirement savings James starts withβsay, $1,000. (If you pick $100, youβll wind up needing to track decimals, so give yourself more zeros to start with.) Here are the starting values: L = $800 M = $100 S = $100 Apply the first yearβs changes, so that you have these numbers on 1/1/2012: Newer L = $800 + 10% = $880 Newer M = $100 + 10=
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
$110 Newer S= $100 + 20=
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
$120 Now apply the second yearβs changes to L and M: Newest L= $880 β 5% = $880 β $44 = $836 Newest M = $110 β 10% = $110 β $11 = $99 Add these to get $935. So the newest S must be $1,000 (the target final total of Jamesβs retirement savings) minus $935, $65 The dollar change in S from 1/1/12 to 1/1/13 is $120 β $55 = $65. So the question is this: what percent change does $65 represent, from a starting point of $120? Since $120 is a nasty divisor, switch to benchmarks: 20% of $120 = $24. So 40% is just double that, or $48. And 50% is equal to or $60. From this $55 lies between $48 and $60 The correct answer is 40 and 50.
<result>D</result> | D | {
"A": "10 and 20",
"B": "20 and 30",
"C": "30 and 40",
"D": "40 and 50",
"E": "50 and 60"
} | On January 1, 2011, James invests 80% of his retirement savings in Antarctic largecap stocks, 10% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 5% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013,James has the same total amount of retirement savings as he did two years before, then x is between |
aqua_rat__THda5Wg3yixIPwkG | β{(3.5)(10^9)} is closest to which of the following?
Select the correct option
A) 60,000 B) 75,000 C) 140,000 D) 220,000 E) 250,000 | β{(3.5)(10^9)} = β{(35)(10^8)} = β(35)β(10^8) = (β35) * 10,000 which is almost 60,000. The answer is 60,000.
<result>A</result> | A | {
"A": "60,000",
"B": "75,000",
"C": "140,000",
"D": "220,000",
"E": "250,000"
} | β{(3.5)(10^9)} is closest to which of the following? |
aqua_rat__V9LX3jPsYbVnP6s7 | The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? Choose the correct choice
A) 2:5 B) 2:7 C) 4:3 D) 2:4 E) 2:9 | The volume of the cone = (1/3)Οr2h Only radius (r) and height (h) are varying. Hence, (1/3)Ο may be ignored. V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2 => h1/h2 = 2/5 i.e. h1 : h2 = 2 : 5 2:5nswer:2:5
<result>A</result> | A | {
"A": "2:5",
"B": "2:7",
"C": "4:3",
"D": "2:4",
"E": "2:9"
} | The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? |
aqua_rat__ZWwmmNYqW9pNRjZS | A tank is filled by 3 pipes A,B,C in 5 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
Choose one.
A) 25hr B) 35hr C) 40hr D) 20hr E) 50hr | Suppose pipe A alone take x hours to fill the tank Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank. 1/x + 2/x + 4/x = 1/5 7/x = 1/5 x = 35 hours Answer is 35hr
<result>B</result> | B | {
"A": "25hr",
"B": "35hr",
"C": "40hr",
"D": "20hr",
"E": "50hr"
} | A tank is filled by 3 pipes A,B,C in 5 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ? |
aqua_rat__VhaUiCDLxsnTOoR6 | A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? Choose the correct choice from the following.
A) 200 m B) 700 m C) 800 m D) 100 metre E) 1050 m | Explanation: A can give B (5 min - 4 1/2 min) = 30 sec start. The distance covered by B in 5 min = 1000 m. Distance covered in 30 sec = (1000 * 30)/300=
<gadget id="calculator">(1000 * 30)/300</gadget>
<output>100</output>
100 m. A can give B 100m start. Answer:100 metre
<result>D</result> | D | {
"A": "200 m",
"B": "700 m",
"C": "800 m",
"D": "100 metre",
"E": "1050 m"
} | A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? |
aqua_rat__e6FmF3SUrUq1ulQZ | In a certain province in Russia there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
Choose the correct choice.
A) 30
B) 105
C) 330
D) 14!
E) 15! | Method-1: Russia has Total Cities = 15 and each city should be connected with every other city So Total Roads required to connect 1st City with other 14 cities = 14 Now 1st City is connected with all other cities so, So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13 Now 1st and 2nd Cities are connected with all other cities so, So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12 ......and so on... Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1=
<gadget id="calculator">14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1</gadget>
<output>105</output>
105=105
<result>B</result> | B | {
"A": "30",
"B": "105",
"C": "330",
"D": "14!",
"E": "15!"
} | In a certain province in Russia there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment? |
aqua_rat__KiGKCVICoTuZX1ix | In an apartment building that has 441 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
Choose one: A) 45 B) 70 C) 100 D) 105 E) 140 | rented = 4/7*441=
<gadget id="calculator">4/7*441</gadget>
<output>252</output>
252. Rented two-bedroom= 6/7*252=
<gadget id="calculator">6/7*252</gadget>
<output>216</output>
216; Rented one-bedroom= 1/7*252=
<gadget id="calculator">1/7*252</gadget>
<output>36</output>
36or 252-216=
<gadget id="calculator">252-216</gadget>
<output>36</output>
36). Rented one-bedroom units are 1/5 of all one-bedroom: 1/5*{All one bedroom}= 36 --> {All one-bedroom} = 180. {All two-bedroom} = 441 - 180=
<gadget id="calculator">441 - 180</gadget>
<output>261</output>
261. Two-bedroom not rented= 261 - 216=
<gadget id="calculator">261 - 216</gadget>
<output>45</output>
45. 45nswer: 45.
<result>A</result> | A | {
"A": "45",
"B": "70",
"C": "100",
"D": "105",
"E": "140"
} | In an apartment building that has 441 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented? |
aqua_rat__50x5FK3eaw3rWmi7 | How many minutes does it take Dhoni to type 64 words if he types at the rate of 16 words per minute? Choose the correct answer.
A) 10
B) 15
C) 12
D) 16
E) 14 | time*rate=job --> time*16=64 --> time=64/4=
<gadget id="calculator">64/4</gadget>
<output>16</output>
16. Answer: 16.
<result>D</result> | D | {
"A": "10",
"B": "15",
"C": "12",
"D": "16",
"E": "14"
} | How many minutes does it take Dhoni to type 64 words if he types at the rate of 16 words per minute? |
aqua_rat__25mT8kGKmneAZkam | A and B start walking towards each other at 6pm at speed of 6kmph and 4kmph. They were initially 50km apart. At what time do they meet? Choose the correct answer
A) 8pm B) 6pm C) 11pm D) 10pm E) 5pm | Time of meeting = distance / relative speed = 50/4+6 = 50/10=
<gadget id="calculator">50/10</gadget>
<output>5</output>
5 hrs after 6pm= 11pm Answer is 11pm
<result>C</result> | C | {
"A": "8pm",
"B": "6pm",
"C": "11pm",
"D": "10pm",
"E": "5pm"
} | A and B start walking towards each other at 6pm at speed of 6kmph and 4kmph. They were initially 50km apart. At what time do they meet? |
aqua_rat__1s0qh9QCk9DjY6m3 | Manoj borrowed Rs.4200 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu? Select.
A) 22877 B) 5855 C) 2778 D) 6787 E) 1771 | Let the sum lent by Manoj to Ramu be Rs.P. Amount gained by Manoj = P. 3.9 /100 = 4200.3.6/100 = Rs.824.85 27P = 75600 = 82485 P = (82485 + 75600)/27 = 3055 + 2800 = Rs.5855 Answer: 5855
<result>B</result> | B | {
"A": "22877",
"B": "5855",
"C": "2778",
"D": "6787",
"E": "1771"
} | Manoj borrowed Rs.4200 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu? |
aqua_rat__PsVwFgDC3ooM7epA | Find the remainder of the division (3^50)/7.
Choices: A) 5 B) 3 C) 2 D) 1 E) 7 | Find the pattern of the remainders after each power: (3^1)/7 remainder 3 (3^2)/7 remainder 2 (3^3)/7 remainder 6 (3^4)/7 remainder 4 (3^5)/7 remainder 5 (3^6)/7 remainder 1 -->this is where the cycle ends (3^7)/7 remainder 3 -->this is where the cycle begins again (3^8)/7 remainder 2 2ontinuing the pattern to (3^50)/7 gives us a remainder of 2 Final Answer: 2) 2
<result>C</result> | C | {
"A": "5",
"B": "3",
"C": "2",
"D": "1",
"E": "7"
} | Find the remainder of the division (3^50)/7. |
aqua_rat__3ANKpVGCm8mAju5M | If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Z of the 3 greatest of these temperatures, in degrees Fahrenheit, could be Pick:
A) 6x
B) Z=4x
C) 5x/3
D) 3x/2
E) 3x/5 | OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B) But what about C,D,E? Any ideas why these could be wrong? Note that we have 5positivetemperatures. Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<sum<5x --=""> only option B fits. Answer: Z</sum<5x>=4x.
<result>B</result> | B | {
"A": "6x",
"B": "Z=4x",
"C": "5x/3",
"D": "3x/2",
"E": "3x/5"
} | If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Z of the 3 greatest of these temperatures, in degrees Fahrenheit, could be |
aqua_rat__PWGDtTK7QwfknQxp | The present population of a town is 1000. Population increase rate is 25% p.a. Find the population of town before 1 years? Choose the correct choice from the following choices
A) 800
B) 1500
C) 1000
D) 750
E) 500 | P = 1000 R = 25% Required population of town = P/(1 + R/100)^T = 1000/(1 + 25/100) = 1000/(5/4)=
<gadget id="calculator">1000/(5/4)</gadget>
<output>800</output>
800 800nswer is 800
<result>A</result> | A | {
"A": "800",
"B": "1500",
"C": "1000",
"D": "750",
"E": "500"
} | The present population of a town is 1000. Population increase rate is 25% p.a. Find the population of town before 1 years? |
aqua_rat__7dTe9beSZjd3ItOA | The speed of a boat in still water is 60kmph and the speed of the current is 12kmph. Find the speed downstream and upstream? Choices:
A) 87 kmph
B) 40 kmph
C) 16 kmph
D) 15 kmph
E) 48 kmph | Speed downstream = 60 + 12=
<gadget id="calculator">60 + 12</gadget>
<output>72</output>
72 kmph Speed upstream= 60 - 20 = 48 kmph Answer:48 kmph
<result>E</result> | E | {
"A": "87 kmph",
"B": "40 kmph",
"C": "16 kmph",
"D": "15 kmph",
"E": "48 kmph"
} | The speed of a boat in still water is 60kmph and the speed of the current is 12kmph. Find the speed downstream and upstream? |
aqua_rat__f0Yv0US3DBYaaOpX | A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 104,350,400,000 pounds, how many widgets have been unloaded?
Choices:
A) 2 B) 3 C) 4 D) 5 E) 6 | We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number. When we divide 104,350,400,000 by 100,000, we get 104,350,400,000 = 1,043,504 * 5^5 *2^5. 1,043,504 is not divisible by 5, thus there are 5 widgets. The answer is 5.
<result>D</result> | D | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 104,350,400,000 pounds, how many widgets have been unloaded? |
aqua_rat__VmdScSPi0OQWucKj | How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre? Choose the correct choice
A) 10 litres B) 12 litres C) 15 litres of water D) 18 litres E) 21 litres | C.P. of 1 litre of milk = Rs. 20Γ2/3 = Rs. 40/3. C.P. of 1 litre of water =Rs 0. Mean price = Rs. 32/3. By the rule of alligation, we have : C.P of 1 litre C.P of 1 litre of water of milk (0) (Rs. 40/3) \ / Mean Price (Rs. 32/3) / \ 40/3β32/3 32/(3β0) 8/3 32/3 The ratio of water and milk =8/3:32/3. =8:32=1:4. Thus, Quantity of water to be added to 60 litres of milk: =(1/4)Γ60 litres. =15 litres. ANSWER : 15 litres of water
<result>C</result> | C | {
"A": "10 litres",
"B": "12 litres",
"C": "15 litres of water",
"D": "18 litres",
"E": "21 litres"
} | How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre? |
aqua_rat__G1kEiiJl5orG7jDa | Angelina walked 150 meters from her home to the grocery at a constant speed. She then walked 200 meters to the gym at double the speed. She spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Choose the correct choice from the following: A) 2 B) 3 C) 4 D) 10 E) 12 | let the speed be X... so time taken from home to grocery= 150/x.. the speed to gym = 2x.. so time taken = 200/2=
<gadget id="calculator">200/2</gadget>
<output>100</output>
100/x.. its given 150/x-100/x=10 50/x=10 x=5m/secs.. so grocery to gym=2*5=
<gadget id="calculator">2*5</gadget>
<output>10</output>
10m/s... Answer : 10
<result>D</result> | D | {
"A": "2",
"B": "3",
"C": "4",
"D": "10",
"E": "12"
} | Angelina walked 150 meters from her home to the grocery at a constant speed. She then walked 200 meters to the gym at double the speed. She spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym? |
aqua_rat__zk2IzzGn1XjqM7vq | In a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
Choose the correct choice from the following answers:
A) 100 sec. B) 50 sec C) 25 sec D) Data not sufficient E) None of these | Speed of Shiny = 50/ 10=
<gadget id="calculator">50/ 10</gadget>
<output>5</output>
5m/s Time taken by shiny to complete the race is B= 1000/5=
<gadget id="calculator">1000/5</gadget>
<output>200</output>
200 sec. Time taken by Baley to complete the race is D= 1000/4=
<gadget id="calculator">1000/4</gadget>
<output>250</output>
250 sec. Hence, D-50 sec= 50 sec ANSWER:50 sec
<result>B</result> | B | {
"A": "100 sec.",
"B": "50 sec",
"C": "25 sec",
"D": "Data not sufficient",
"E": "None of these"
} | In a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ? |
aqua_rat__qLNanCJ4EuS7TDNq | If a person walks at 16 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is: Choose the correct choice from the following options
A) 50 km B) 56 km C) 60 km D) 70 km E) 33.3 km | Let the actual distance travelled be x km. x/10 = (x+20)/16 16x = 10x + 200 6x = 200 x = 33.3 km. answer :33.3 km
<result>E</result> | E | {
"A": "50 km",
"B": "56 km",
"C": "60 km",
"D": "70 km",
"E": "33.3 km"
} | If a person walks at 16 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is: |
aqua_rat__RFJ9qgJazYBOO91w | Insert the missing number. 2, 7, 10, 22, 18, 37, 26
Choose the correct option.
A) 26 B) 22 C) 2 D) 52 E) 18 | There are two series here 2, 10, 18, 26, ... (Increase by 8) 7, 22, 37, ... (Increase by 15) Hence, next term is 37+15=
<gadget id="calculator"> 37+15</gadget>
<output>52</output>
52 Answer is 52
<result>D</result> | D | {
"A": "26",
"B": "22",
"C": "2",
"D": "52",
"E": "18"
} | Insert the missing number. 2, 7, 10, 22, 18, 37, 26 |
aqua_rat__CJzQT5XyNrhdUrPb | How many ways are there for 3 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
Choose the correct answer:
A) 6 B) 12 C) 72 D) 100 E) 720 | Lets first sit the 3 man, 2! ways. Now since one position is fixed for women, there are 2 women left and they have 2! ways 2! X 2! = 4 answer is diff this way. or shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, ANS:12
<result>B</result> | B | {
"A": "6",
"B": "12",
"C": "72",
"D": "100",
"E": "720"
} | How many ways are there for 3 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? |
aqua_rat__LbFH5DVHvcfTbWFt | How many different values of positive integer x, for which |x+9|<x, are there? Choose the correct choice from the following options
A) 0
B) 2
C) 3
D) 8
E) 16 | Answer C I opted to put the random value option. i used 0 , 9 , -9 and the the extreme of 10 and -10.. i was able to solve it in 1:09 3
<result>C</result> | C | {
"A": "0",
"B": "2",
"C": "3",
"D": "8",
"E": "16"
} | How many different values of positive integer x, for which |x+9|<x, are there? |
aqua_rat__safyVFiIoiqVOK7Q | A man buys an article for 14% less than its value and sells it for 14% more than its value. His gain or loss percent is: Choose the correct choice from the following answers:
A) no profit, no loss B) 20% profit C) less than 30% profit D) more than 30% profit E) None | Let the article be worth Rs. x. C.P. 86% of Rs. x = Rs. 86x/100 S.P. = 114% of Rs. x = Rs. 114x/100 Gain = (114x/100 - 86x/100) = Rs. 7x/25 Gain % = 7x/25 * 100/86x * 100 = 32 24/43 % > 30% ANSWER:more than 30% profit
<result>D</result> | D | {
"A": "no profit, no loss",
"B": "20% profit",
"C": "less than 30% profit",
"D": "more than 30% profit",
"E": "None"
} | A man buys an article for 14% less than its value and sells it for 14% more than its value. His gain or loss percent is: |
aqua_rat__RHfqrwA9GKDMw8TY | If x is negative and y is positive, which of the following must be positive? Choose the most appropriate option.
A) x/y B) xy C) 2y + x D) (x + y)^2 + 1 E) 3x/y | A. x/y -ve/+ve=-ve will be negative B. xy -ve*+ve= -ve will be negative C. 2y + x might be positive or negative . The sign will be depend on the absolute values of x and y . The expression will be positive if 2y>x D. (x + y)^2 + 1 = (x+y)^2 will be positive irrespective of the absolute values of x and y will be positive always E. 3x/y =- ve/ +ve will be negative Answer (x + y)^2 + 1
<result>D</result> | D | {
"A": "x/y",
"B": "xy",
"C": "2y + x",
"D": "(x + y)^2 + 1",
"E": "3x/y"
} | If x is negative and y is positive, which of the following must be positive? |
aqua_rat__Ip5tcY4h8575ESPd | In an election between 2 candidates, 50% of the voters cast their votes, out of which 10% of the votes were declared invalid. A candidate got 5000 votes which were 50% of the total valid votes. Find the total number of votes enrolled in that election? Choose the correct choice.
A) 16200 B) 18000 C) 17500 D) 15823 E) 15000 | Let the total number of votes enrolled be x. Then, number of votes cast = 50% of x. Valid votes = 90% of (50% of x) 50% of (90% of (50% of x)) = 4050 (50/100)*(90/100)*(50/100)x = 4050 x = 18000 Answer is 18000
<result>B</result> | B | {
"A": "16200",
"B": "18000",
"C": "17500",
"D": "15823",
"E": "15000"
} | In an election between 2 candidates, 50% of the voters cast their votes, out of which 10% of the votes were declared invalid. A candidate got 5000 votes which were 50% of the total valid votes. Find the total number of votes enrolled in that election? |
aqua_rat__IbgecFySYPCxTkCg | A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? Choose the correct choice from the following answers: A) 18/79 B) 1/6 C) 1/45 D) 1/50 E) 1/900 | If it takes 9 minutes to inspect one vehicle, the # of vehicles that can be inspected in 3 hours (180 minutes) = 180/9=
<gadget id="calculator">180/9</gadget>
<output>20</output>
20. Hence, for calculating the probability that the police will find the transmitter within three hours, the favorable cases= 20. Now, we need to figure out the total # of cases. The total # of cases = Total # of such cars possible. The details given about the car is that it starts with 79, which leaves 2 more digits, both of which can be filled by all 10 numbers (0-9). In addition, we have 3 letters, each of which can be filled by any from the set {A,B,C}. Hence the total # of such cars possible = 10*10*3*3=
<gadget id="calculator">10*10*3*3</gadget>
<output>900</output>
900 So, the probability that the police will find the transmitter within three hours= 20/900 = 1/45. Option 1/45
<result>C</result> | C | {
"A": "18/79",
"B": "1/6",
"C": "1/45",
"D": "1/50",
"E": "1/900"
} | A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? |
aqua_rat__LHTBK7ypxAIMWdpz | Prathik purchased 40 shirts for rs 3000.he spends 10% for transportation. What should be the selling price per shirt to earn profit of 20% ?
Answers:
A) 96 rs B) 97 rs C) 98 rs D) 99 rupees E) 100 rs | total CP = 3000 + 3000*10/100=
<gadget id="calculator">3000 + 3000*10/100</gadget>
<output>3_300</output>
3300 to gain 20% profit, SP= (100+20)*3300/100=
<gadget id="calculator">(100+20)*3300/100</gadget>
<output>3_960</output>
3960 selling price per shirt= 3960/40=
<gadget id="calculator">3960/40</gadget>
<output>99</output>
99 rs/shirt ANSWER:99 rupees
<result>D</result> | D | {
"A": "96 rs",
"B": "97 rs",
"C": "98 rs",
"D": "99 rupees",
"E": "100 rs"
} | Prathik purchased 40 shirts for rs 3000.he spends 10% for transportation. What should be the selling price per shirt to earn profit of 20% ? |
aqua_rat__UVfrSewRllxLZ7JF | A can do a certain job in 16 days. B is 60% more efficient than A. How many days does B alone take to do the same job? Choices
A) 11 1/4 days
B) 8 days
C) 5 days
D) 10 days
E) None of them | Ratio of times taken by A and B = 160 : 100 = 8 : 5. Suppose B alone takes x days to do the job. Then, 8 : 5 :: 16 : x = 8x = 5 x 16 =x = 10 days. Answer is 10 days.
<result>D</result> | D | {
"A": "11 1/4 days",
"B": "8 days",
"C": "5 days",
"D": "10 days",
"E": "None of them"
} | A can do a certain job in 16 days. B is 60% more efficient than A. How many days does B alone take to do the same job? |
aqua_rat__SnZJcVMYkNcFhxYe | A can do a work in 22 days. B is 30% more efficient than A. How many days does B alone take to do the same job? Choose the correct choice.
A) 222/13 B) 221/13 C) 220/13 D) 219/13 E) 218/13 | Ratio of times taken by A and B = 130:100 = 13:10 suppose B alone to take x days to do the work then, 13:10::22:x 13x= 10*22=
<gadget id="calculator">10*22</gadget>
<output>220</output>
220/13 days correct option is 220/13
<result>C</result> | C | {
"A": "222/13",
"B": "221/13",
"C": "220/13",
"D": "219/13",
"E": "218/13"
} | A can do a work in 22 days. B is 30% more efficient than A. How many days does B alone take to do the same job? |
aqua_rat__9sq0YtkghzQXK0yG | When Q is divided by X, the quotient is R and the remainder is E. Which of the following expressions is equal to E?
Choose the correct choice from the following choices
A) -RX + Q
B) RX - Q
C) Q + RX
D) QX - R
E) Q/R | Q/X = R + E/W Q -RX = E -RX + Qmswer: -RX + Q
<result>A</result> | A | {
"A": "-RX + Q",
"B": "RX - Q",
"C": "Q + RX",
"D": "QX - R",
"E": "Q/R"
} | When Q is divided by X, the quotient is R and the remainder is E. Which of the following expressions is equal to E? |
aqua_rat__kRKpTDsipsMvREmq | The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? Choose the most appropriate option.
A) 69 B) 78 C) 96 D) 56 E) 48 | let the digits be x,y x + y = 15 x - y = 3 2x = 18, x = 9 so y = 6 hence the number is 96 so the correct answer is option 96) 96.
<result>C</result> | C | {
"A": "69",
"B": "78",
"C": "96",
"D": "56",
"E": "48"
} | The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? |
aqua_rat__k2yyLs8O3UbFhGIf | If n is a natural number, then(6n^2+6n) is always divisible by? Select
A) 6 only B) 6 and 12 C) 12 only D) by 18 only E) None of these | (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Correct Option: 6 and 12
<result>B</result> | B | {
"A": "6 only",
"B": "6 and 12",
"C": "12 only",
"D": "by 18 only",
"E": "None of these"
} | If n is a natural number, then(6n^2+6n) is always divisible by? |
aqua_rat__uf0G2CefT5T3fYAY | In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
Choose the most appropriate option
A) 9/7 B) 5/8 C) 3/7 D) 5/12 E) 4/7 | Here n(S)=(6*6)=
<gadget id="calculator">(6*6)</gadget>
<output>36</output>
36 let E=event of getting a total more than 7 ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)} P(E)=n(E)/n(S)=15/36=5/12. Ans: 5/12
<result>D</result> | D | {
"A": "9/7",
"B": "5/8",
"C": "3/7",
"D": "5/12",
"E": "4/7"
} | In a simultaneous throw of pair of dice .find the probability of getting the total more than 7 |
aqua_rat__DXAyw9X2Zx1O6cFS | Kul is 22 years old and Saras is 33 years. Find the ratio of Saras's age to Kul's age. Choose the correct option: A) 3/1 B) 3/2 C) 5/2 D) 5/3 E) None of these | Explanation : Kul is 22 years old.Saras is 33 years old.Saras's age : Kul's age = 33 : 22 = 3 : 2 Answer : 3/2
<result>B</result> | B | {
"A": "3/1",
"B": "3/2",
"C": "5/2",
"D": "5/3",
"E": "None of these"
} | Kul is 22 years old and Saras is 33 years. Find the ratio of Saras's age to Kul's age. |
aqua_rat__9UjZcSunmIoIU6IP | If 2/a + 3/a + 6/a is an integer, which of the following must also be an integer? Select the correct option
A) 12/a B) 3/a C) 6/a D) 9/a E) 11/a | 2/a + 3/a + 6/a =11/a Answer 11/a
<result>E</result> | E | {
"A": "12/a",
"B": "3/a",
"C": "6/a",
"D": "9/a",
"E": "11/a"
} | If 2/a + 3/a + 6/a is an integer, which of the following must also be an integer? |
aqua_rat__xZptPOpkiYhZDt5e | Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 46800, how much amount per month would he have spent on clothes and transport?
Choose one:
A) 4038 B) 8076 C) 9691.2 D) 4845.6 E) 3900 | β΅ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month β΅ Amount, spent on clothes and transport = 46800β12 = 3900 Answer 3900
<result>E</result> | E | {
"A": "4038",
"B": "8076",
"C": "9691.2",
"D": "4845.6",
"E": "3900"
} | Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 46800, how much amount per month would he have spent on clothes and transport? |
aqua_rat__EDFRSM2r2e8FQz9B | How long does a train 125 m long running at the speed of 78 km/hr takes to cross a bridge 125 m length?
Select: A) 12.7 sec B) 10.1 sec C) 11.5 sec D) 12.1 sec E) 11.7 sec | Speed = 78 * 5/18 = 21.7 m/sec Total distance covered = 125 + 125=
<gadget id="calculator">125 + 125</gadget>
<output>250</output>
250 m. Required time= 250/21.7 ' = 11.5 sec. Answer:11.5 sec
<result>C</result> | C | {
"A": "12.7 sec",
"B": "10.1 sec",
"C": "11.5 sec",
"D": "12.1 sec",
"E": "11.7 sec"
} | How long does a train 125 m long running at the speed of 78 km/hr takes to cross a bridge 125 m length? |
aqua_rat__GExzj2FlRYWC7O7w | The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 23. What is the middle number? Pick: A) 25 B) 27 C) 15 D) 32 E) 34 | The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 23 = 111 So, the middle number is (126 - 111 )=
<gadget id="calculator"> (126 - 111 )</gadget>
<output>15</output>
15 15
<result>C</result> | C | {
"A": "25",
"B": "27",
"C": "15",
"D": "32",
"E": "34"
} | The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 23. What is the middle number? |
aqua_rat__M3YwoXKA6XcQG9te | The compound ratio of 5:6, 5:2 and 4:5?
Options:
A) 1:1 B) 5:3 C) 1:6 D) 1:9 E) 1:2 | 5/6 * 5/2 * 4/5 = 5/3 5:3 Answer: 5:3
<result>B</result> | B | {
"A": "1:1",
"B": "5:3",
"C": "1:6",
"D": "1:9",
"E": "1:2"
} | The compound ratio of 5:6, 5:2 and 4:5? |
aqua_rat__l8S40V5JxcSjlzdB | A car runs at the speed of 40 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 8 hours. How much time will the car take to cover the same distance when not serviced? Select the correct option.
A) 8 hours 12 minutes
B) 12 hours
C) 16 hours
D) 17 hours
E) None | Explanation : Time = 80*8 / 40=
<gadget id="calculator">80*8 / 40</gadget>
<output>16</output>
16 hours Answer Γ’β¬β 16 hours
<result>C</result> | C | {
"A": "8 hours 12 minutes",
"B": "12 hours",
"C": "16 hours",
"D": "17 hours",
"E": "None"
} | A car runs at the speed of 40 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 8 hours. How much time will the car take to cover the same distance when not serviced? |
aqua_rat__OBdbsH4CkbTeqTVj | The Julie's father's age is two more than thrice Julie's age. If Julie will be 15 after 4 years, what is her father's present age? Choose the correct choice from the following
A) 35 years B) 33 years C) 32 years D) 34 years E) 30 years | LET 35 yearsGE OF JULI BE 'J' 35 yearsGE OF HER F35 yearsTHER BE 'F' then given 3J+2=F 35 yearsND J+4=15 ====>J=11 at present then F=3*11+2=
<gadget id="calculator">3*11+2</gadget>
<output>35</output>
35 35 yearsNSWER:35 years
<result>A</result> | A | {
"A": "35 years",
"B": "33 years",
"C": "32 years",
"D": "34 years",
"E": "30 years"
} | The Julie's father's age is two more than thrice Julie's age. If Julie will be 15 after 4 years, what is her father's present age? |
aqua_rat__praY5wLsuOk2c54l | Average score for Virat Kohli in a series of 10 matches is 38.9 runs. If the average for first six matches comes out to be 42 what is his average in the last 4 matches of the series? Choose one:
A) 34.25 B) 34.28 C) 24.252 D) 64.28 E) 34.21 | Explanation: 34.25verage runs scored by Virat Kohli in 10 matches: Total runs scored/10β(1) 34.25verage runs scored by Virat Kohli in 6 matches: (Total runs in 6 matches)/6 => 42 = Runs/6 =>252 runs Using (1): =>38.9 = Runs/10 =>389 runs Runs scored in rest 4 matches: 389 - 252=
<gadget id="calculator"> 389 - 252</gadget>
<output>137</output>
> 137 runs 34.25verage runs scored by Virat Kohli in 4 matches: 137/4=
<gadget id="calculator"> 137/4</gadget>
<output>137/4 = around 34.25</output>
34.25 runs 34.25NSWER: 34.25
<result>A</result> | A | {
"A": "34.25",
"B": "34.28",
"C": "24.252",
"D": "64.28",
"E": "34.21"
} | Average score for Virat Kohli in a series of 10 matches is 38.9 runs. If the average for first six matches comes out to be 42 what is his average in the last 4 matches of the series? |
aqua_rat__a8SBVUmwc0FtbskM | The speed of boat in still water is 20 km/hr. If it travels 26 km downstream and 14 km upstream in same time, what is the speed of the stream? Choose the correct choice from the following answers:
A) 6 B) 7 C) 8 D) 9 E) 2 | Explanation: Let X be speed of stream Speed of boat downstream = (20 + X ) Speed of boat upstream = (20 β X) It is given that boat takes same time to travel 26 km downstream and 14 km upstream [26/(20 +X)] = [14 / (20 β X)] 520 β 26 X = 280 + 14X 40X = 240 X = 6 km/hr 6NSWER: 6
<result>A</result> | A | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "2"
} | The speed of boat in still water is 20 km/hr. If it travels 26 km downstream and 14 km upstream in same time, what is the speed of the stream? |
aqua_rat__Fi3QMQYFtkkzpBso | Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel Q if the median is 10 gallons? Select
A) 1 B) 2 C) 3 D) 4 E) 5 | Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity. (B1+B2+B3+B4)/4 = 8 B1+B2+B3+B4=32 median is 10 ....... as the no. of terms are even i.e 4, median = (22+23)/2 ==> 22+23 = 20 now we have 21+24 = 32-20=
<gadget id="calculator">32-20</gadget>
<output>12</output>
12 Only the following possible cases can be there : 1,9,11,11 1,10,10,11 2,10,10,10 Max value of smallest barrel Q= 2
<result>B</result> | B | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel Q if the median is 10 gallons? |
aqua_rat__1CHzAhqeQAbcQ5ez | Set J consists of 5 consecutive even numbers. If the smallest term in the set is -2, what is the range of the positive integers in set J? Pick one:
A) 0 B) 2 C) 4 D) 6 E) 8 | Since there are only 5 integers, another approach is the just list all 5. We get: -2,0,2, 4, 6 Range of POSITIVE INTEGERS =6 - 2=
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
4 Answer: 4
<result>C</result> | C | {
"A": "0",
"B": "2",
"C": "4",
"D": "6",
"E": "8"
} | Set J consists of 5 consecutive even numbers. If the smallest term in the set is -2, what is the range of the positive integers in set J? |
aqua_rat__77Q8NMQkhrignjyC | What is the measure of the acute angle between the hour and minute hands of a correctly
working clock at 4:18 ?
Select:
A) 12β¦
B) 15β¦
C) 18β¦
D) 21β¦
E) 24β¦ | Consider an axis through the center of the clock with direction, the direction of the hands of the clock at 12:00. At 4:18 the angle between the axis and the hour hand is (4+18/60)*360β¦/12=129β¦ The angle between the axis and the minute hand is 18/60*360β¦(4+18/60)*360 /12=
<gadget id="calculator">(4+18/60)*360 /12</gadget>
<output>129</output>
129β¦ The angle between the axis and the minute hand is 18/60*360=
<gadget id="calculator">18/60*360</gadget>
<output>108</output>
108β¦ correct answer 21β¦
<result>D</result> | D | {
"A": "12β¦",
"B": "15β¦",
"C": "18β¦",
"D": "21β¦",
"E": "24β¦"
} | What is the measure of the acute angle between the hour and minute hands of a correctly
working clock at 4:18 ? |
aqua_rat__qzdHcJ0X43tyoJ9a | A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Choose the correct choice from the following choices.
A) 15.5 days
B) 19.5 days
C) 17.5 days
D) 16.5 days
E) 18.5 days | 17.5 days = 1/5 β 1/7 = 2/35 => 17.5 days ANSWER:17.5 days
<result>C</result> | C | {
"A": "15.5 days",
"B": "19.5 days",
"C": "17.5 days",
"D": "16.5 days",
"E": "18.5 days"
} | A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? |
aqua_rat__lWjRj0tlZwrpmEG6 | A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long?
Pick:
A) 17
B) 18
C) 19
D) 20
E) 21 | Speed = 99 * 5/18 = 55/2 m/sec Total distance covered = 300 + 195=
<gadget id="calculator">300 + 195</gadget>
<output>495</output>
495 m Required time= 495 * 2/55=
<gadget id="calculator">495 * 2/55</gadget>
<output>18</output>
18 sec Answer: 18
<result>B</result> | B | {
"A": "17",
"B": "18",
"C": "19",
"D": "20",
"E": "21"
} | A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long? |
aqua_rat__7XNafaEjw4jOv404 | Of the science books in a certain supply room, 50 are on botany, 75 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? Choose one: A) 81 B) 59 C) 166 D) 285 E) 334 | I solve it using the tough luck technique: According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject. 80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=110>80 Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives. We picked: 50 Botany Books 75 Zoology Books 50 Geology Books Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!! Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick 79*2+1 books Because, we could have picked the books in following order; 1st book picked: Physics 2nd book picked: Chemistry 3rd book picked: Physics Thus, Total= 50+75+50+79*2+1=175+1+158=
<gadget id="calculator">175+1+158</gadget>
<output>334</output>
334 Ans:334
<result>E</result> | E | {
"A": "81",
"B": "59",
"C": "166",
"D": "285",
"E": "334"
} | Of the science books in a certain supply room, 50 are on botany, 75 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? |
aqua_rat__r0d9B9mLIQfujKCi | A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black? Choose the correct answer.
A) 13/213 B) 36/145 C) 25/113 D) 27/137 E) 31/128 | The probability that first ball is white: =12C130C1=12C130C1 =1230=1230 =25=25 Since, the ball is not replaced; hence the number of balls left in bag is 29. Hence, the probability the second ball is black: =18C129C1=18C129C1 =1829=1829 Required probability, =(25)Γ(1829)=(25)Γ(1829) =36/145 36/145
<result>B</result> | B | {
"A": "13/213",
"B": "36/145",
"C": "25/113",
"D": "27/137",
"E": "31/128"
} | A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black? |
aqua_rat__6cYsJPaPPdxLKwqj | A can finish a work in 36days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
Choices: A) 15days B) 12days C) 6days D) 7days E) 8days | B+C 1day work = 1/9 + 1/12 + 1=
<gadget id="calculator">+ 1</gadget>
<output>1</output>
1/9 + 1/12= 7/36 work done by B and C in 3days = 7/36 * 3 = 7/12 Remaining work = 1 - 7/12 = 5/12 1/36 work is done by 15days in 1day 5/12 work is done by 15days in 36*5/12=
<gadget id="calculator"> 36*5/12</gadget>
<output>15</output>
15days 15daysnswer is 15days
<result>A</result> | A | {
"A": "15days",
"B": "12days",
"C": "6days",
"D": "7days",
"E": "8days"
} | A can finish a work in 36days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in? |
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