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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__6rGl38SB15tdkLDp

If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 2 is subtracted and divided by 13? Choose the correct choice. A) 4 B) 7 C) 8 D) 5 E) 3

Explanation: Let the number be x. Then, (x - 5)/7 = 7 =&gt; x - 5 = 49 x = 54 .: (x - 2)/13 = (54 - 2)/13= <gadget id="calculator">(54 - 2)/13</gadget> <output>4</output> 4 4nswer: Option 4 <result>A</result>

A

If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 2 is subtracted and divided by 13?

aqua_rat__HFyykJCjAzYYYa6Y

An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank. Choose the correct choice from the following choices: A) 8600 litres B) 200 litres C) 12800 litres D) 6400 litres E) 13200 litres

Let the rate of outlet pipe be x liters/hour; Rate of inlet pipe is 8 litres/min, or 8*60= <gadget id="calculator"> 8*60</gadget> <output>480</output> 480 liters/hour; Net outflow rate when both pipes operate would be x-480 liters/hour. Capacity of the tank= x*5 hours = (x-480)*(5+3) hours 5x=(x-480)*8 --&gt; x=1280 --&gt; capacity = 5x = 6400 liters. Answer: 6400 litres <result>D</result>

D

An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank.

aqua_rat__b1OezqqHl9roacxp

If the simple interest on a sum of money for 3 years at 7% per annum is Rs. 570, what is the compound interest on the same sum at the rate and for the same time? Pick one: A) Rs. 610.83 B) Rs. 810.83 C) Rs. 617 D) Rs. 618 E) Rs. 610.83

Sum = (570 * 100) / (7 * 3) = Rs. 2,714.29 Amount = [2,714.29 * (1 + 7/100)3] = Rs. 3,325.12 C.I. = (3,325.12 - 2,714.29) = Rs. 610.83. ANSWRs. 610.83R:Rs. 610.83 <result>E</result>

E

If the simple interest on a sum of money for 3 years at 7% per annum is Rs. 570, what is the compound interest on the same sum at the rate and for the same time?

aqua_rat__pa8QB3qrmBvLRmxM

While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 4 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files? Choices: A) 2 B) 2.4 C) 2.7 D) 3 E) 3.5

Both computers together process files at a rate of 240/12 + 240/4 = 20+60= <gadget id="calculator">20+60</gadget> <output>80</output> 80 files per hour. The time required to process 240 files is 240/80= <gadget id="calculator"> 240/80</gadget> <output>3</output> 3 hours The answer is 3. <result>D</result>

D

While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 4 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?

aqua_rat__I9rq3cyJ3OxhCWnP

A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? Choose the most appropriate option: A) 150m B) 188m C) 267m D) 268m E) 287m

Length of the train be ‘X’ X + 150/15 = X + 250/20 4X + 600 = 3X + 750 X = 150m 150mnswer: 150m <result>A</result>

A

A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?

aqua_rat__dmQW10CZ893ImYWA

A group of 10 representatives is to be selected out of 15 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors? Choose the most appropriate option A) 15C₅ * 10 B) 15C₇ * 10 C) 15C10 * ¹⁰C₅ D) 12 * ¹⁰C₅ E) None of these

Here, five seniors out of 15 seniors can be selected in 15C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 1515C10 * ¹⁰C₅₅ * ¹⁰15C10 * ¹⁰C₅₅ =1515C10 * ¹⁰C₅10 * ¹⁰15C10 * ¹⁰C₅₅ since 1515C10 * ¹⁰C₅₅ = 1515C10 * ¹⁰C₅10 ANSWER:15C10 * ¹⁰C₅ <result>C</result>

C

A group of 10 representatives is to be selected out of 15 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?

aqua_rat__EJ0K7KM5eU0bUgzp

Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 10% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit? Pick one A) 127% B) 120% C) 121% D) 135% E) 140%

Since Michelle earns 10% interest compounded semiannually, then she earns 5% interest every 6 months. Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 5%*5=25%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 25%, only answer choice A fits. 127%nswer: 127% 5 *5= <gadget id="calculator"> 5 *5</gadget> <output>25</output> 25%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 25%, only answer choice A fits. 127%nswer: 127% <result>A</result>

A

Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 10% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?

aqua_rat__RqV97tzQTQfBRS7E

4.036 divided by 0.04 gives Choose the correct choice from the following: A) 1.009 B) 100.09 C) 10.9 D) None of these E) cannot be determined

Solution 4.036 / 0.04 = 403.6 / 4= <gadget id="calculator">403.6 / 4</gadget> <output>100.9</output> 100.9 1.009nswer 1.009 <result>A</result>

A

4.036 divided by 0.04 gives

aqua_rat__2j7JrGaXx6szyidB

What will come in place of the x in the following Number series? 18, 22, 30, 46 ,X, 142 Choose the correct choice from the following answers: A) 35 B) 56 C) 78 D) 87 E) 98

(78) The pattern is +4, +8, +16, +32, +64 So the missing term is = 78 <result>C</result>

C

What will come in place of the x in the following Number series? 18, 22, 30, 46 ,X, 142

aqua_rat__zsnMNHzcEgWLRmwb

One thief entered a cave where he found a pile of diamonds. At first he thought of taking all. But listening to his conscience he thought of taking only half of them. But while returning he picked up two more from the pile. After that Second thief entered the cave and bagged half of remaining diamonds and picked up two more while returning. Later third thief entered and did the same. Even the fourth thief did the same. When the fifth thief entered he found only one diamond in the cave. How many diamonds are there in the cave at first. Choose the correct answer: A) 86 B) 94 C) 80 D) 96 E) 55

Explanation : When 5th thief entered-1 diamond When 4th thief entered -(1+2)*2=6 diamonds When 3rd thief entered -(6+2)*2=16 diamonds When 2nd thief entered -(16+2)*2=36 diamonds When 1st thief entered -(36+2)*2=76 diamonds Hence(D) is the correct answer. Answer : 96 <result>D</result>

D

One thief entered a cave where he found a pile of diamonds. At first he thought of taking all. But listening to his conscience he thought of taking only half of them. But while returning he picked up two more from the pile. After that Second thief entered the cave and bagged half of remaining diamonds and picked up two more while returning. Later third thief entered and did the same. Even the fourth thief did the same. When the fifth thief entered he found only one diamond in the cave. How many diamonds are there in the cave at first.

aqua_rat__RaX8JLFnjXEgLlAe

A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is? Select: A) 90 m B) 120 m C) 150 m D) 190 m E) 210 m

Let the length of the train e x meter, and let the speed of train be y km/h, then \inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1) and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2) From eq (1) and (2), we get \inline (y+3)\times 36 = ( y+6)\times 30 y = 12 km/h \inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36 x= 150 m 150 m <result>C</result>

C

A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?

aqua_rat__9fxY0qJHTNQ3jfDI

In a 500 m race, the ratio of the speeds of two contestants A and B is 2 : 4. A has a start of 300 m. Then, A wins by: Choose the correct choice from the following options: A) 60 m B) 20m C) 43m D) 20m E) 100 m

To reach the winning post A will have to cover a distance of (500 - 300)m, i.e., 200 m. While A covers 2 m, B covers 4 m. While A covers 200 m, B covers 4 x 200/2 m = 400 m. Thus, when A reaches the winning post, B covers 400 m and therefore remains 100 m behind. A wins by 100 m. Answer: 100 m <result>E</result>

E

In a 500 m race, the ratio of the speeds of two contestants A and B is 2 : 4. A has a start of 300 m. Then, A wins by:

aqua_rat__2JFeeZA5gvuGKhfs

The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age? Choose the correct answer: A) 20 B) 21 C) 22 D) 25 E) 18

Let the present age of the son =x Then, present age of the father =(60−x) Six years ago father's age was 5 times the age of the son ⇒(60−x)−6=5(x−6)⇒84=6x⇒x=846=14 Son's age after 6 years =x+6=14+6= <gadget id="calculator">14+6</gadget> <output>20</output> 20 20nswer is 20. <result>A</result>

A

The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age?

aqua_rat__j3XLuVPlSSUtUKbX

A person incures loss for by selling a watch for rs1140.at what price should the watch be sold to earn a 5% profit ? Choose the correct choice from the following options. A) Rs.1160 B) Rs.1260 C) Rs.1200 D) Rs.1250 E) Rs.1280

let the new sp be Rs x.then (100-loss%) : (1st sp)=(100+gain%) (2nd sp) ={(100-5)/1400}={(100+5)/x}=&gt; x={(105*1140)/95} =Rs.1260. Answer is Rs.1260. <result>B</result>

B

A person incures loss for by selling a watch for rs1140.at what price should the watch be sold to earn a 5% profit ?

aqua_rat__PGiRX307duChjTA6

In a apartment, 20% of the people speak English, 60% speak Hindi and 60% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi? Pick. A) 1/5 B) 2/3 C) 2/5 D) 2/7 E) 2/9

P (E) = 20 / 100 = 1 / 5 , P (H) = 60 / 100 = 3 / 5 and P (E ∩ H) = 60 / 100 = 3 / 5 P (E or H) = P (E U H) = P (E) + P (H) - P (E ∩ H) = (1 / 5) + (3 / 5) - (3 / 5) = 4 / 10 = 1/5 1/5 <result>A</result>

A

In a apartment, 20% of the people speak English, 60% speak Hindi and 60% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?

aqua_rat__zPWnuNs61f0hQqBx

The difference between the length and breadth of a rectangle is 30 m. If its perimeter is 240 m, then its area is: Options A) 1520 m2 B) 2420 m2 C) 3375 m2 D) 2520 m2 E) None

EXPLANATION We have: (l – b) = 30 and 2(l + b) = 240 or (l + b) = 120. Solving the two equations, we get: l = 75 and b = 45. Area = (l x b) = (75x 45) m2 = 3375 m2. Answer 3375 m2 <result>C</result>

C

The difference between the length and breadth of a rectangle is 30 m. If its perimeter is 240 m, then its area is:

aqua_rat__ypadkugakILJrSh7

A straight line in the xy- plane has slope 4 . On this line the x-coordinate of the point is 50 and y-coordinate is 300 then what is the y intercept of the plane? Choose the correct choice from the following answers A) 150 B) 110 C) 100 D) 200 E) 50

Eq of line = Y = MX +C M= 4 X=50 Y=50*4 + C, Substitute Y by 300 as given in question. 300=200+100 , 100 =100 correct option is 100 <result>C</result>

C

A straight line in the xy- plane has slope 4 . On this line the x-coordinate of the point is 50 and y-coordinate is 300 then what is the y intercept of the plane?

aqua_rat__7KZoPLi4i7LnGsac

If a truck is travelling at a speed of 54 kmph, crosses a pole in 1 sec, then the length of train is? Choose the correct choice from the following options: A) 13 m B) 14 m C) 15 m D) 16 m E) 17 m

Explanation: D = 54 * 5/18 * 1= <gadget id="calculator">54 * 5/18 * 1</gadget> <output>15</output> 15 m Answer: Option 15 m <result>C</result>

C

If a truck is travelling at a speed of 54 kmph, crosses a pole in 1 sec, then the length of train is?

aqua_rat__KK091v78eeFxKcaY

What is the sum of all the prime factors of 220 and 330? Pick one: A) 15 B) 21 C) 35 D) 41 E) 64

Prime factorization of both the numbers is as follows 220 = 2 * 2 * 5 * 11 sum of the prime factors of 220 = 20 330 = 2 *3 * 5 * 11 sum of prime factors of 330 = 21 addition of both = 20 + 21= <gadget id="calculator">20 + 21</gadget> <output>41</output> 41 ANSWER 41 <result>D</result>

D

What is the sum of all the prime factors of 220 and 330?

aqua_rat__yn6mu8XuDSvlFtUf

Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite direction for 4 miles and then turn to left and run for another 3 miles. what is the distance between the the two twins when they stop ? Pick. A) 10 miles B) 11 miles C) 18 miles D) 16 miles E) 13 miles

10 miles 10 miles <result>A</result>

A

Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite direction for 4 miles and then turn to left and run for another 3 miles. what is the distance between the the two twins when they stop ?

aqua_rat__vgzz0qlGXm6nzhIp

If x and y are positive integers, then xy - y is Choose the correct choice from the following answers. A) Always odd B) Odd whenever y is odd C) Odd whenever x+y is even D) Even whenever y is odd E) It cannot be determined

x and y are positive integers, then xy - y.. Let's take even as 4 and odd as 5. IMO option A is correct answer.. If you consider your fourth scenario, that turns out to be even. Hence option Odd whenever y is odd should be correct. <result>B</result>

B

If x and y are positive integers, then xy - y is

aqua_rat__zjZrfWtFLQpC1rq1

If x, y, and z are all factors of 21, which of the following must be true? Choose the correct option: A) The product xyz > 21 B) Either x = y, y = z, or x = z C) x – y – z = even D) The product xyz is odd E) yz/x is an integer

All the factors of 21 are odd numbers. The product of odd numbers is odd. The answer is The product xyz is odd. <result>D</result>

D

If x, y, and z are all factors of 21, which of the following must be true?

aqua_rat__09XG6k13Ttx9wAP2

Ratio of the ages of Mahesh and Nilesh is 5 : x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x? Choose the correct option. A) 72.9 B) 62.2 C) 14.2 D) 13.7 E) 14.5

Let the present ages of Mahesh, Nilesh and Ramesh be m, n and r respectively. m/n = 5/x ------ (1) m = r - 18 ------ (2) r + 9 = 47 ------ (3) m - n = r ----- (4) (3) =&gt; r = 47 - 9= <gadget id="calculator">47 - 9</gadget> <output>38</output> 38 years (2)=&gt; m = 38 -18= <gadget id="calculator">38 -18</gadget> <output>20</output> 20 years (1)=&gt; 20/n = 5/x =&gt; n = 4x (4) =&gt; 4x - 20 = 38 =&gt; 4x = 58 =&gt; x = 14.5 Answer:14.5 <result>E</result>

E

Ratio of the ages of Mahesh and Nilesh is 5 : x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?

aqua_rat__BLI2O4ucgXezUVRF

Which one of the following can't be the square of natural number ? Choices: A) 128881 B) 128242 C) 131044 D) 130321 E) 130322

Square of a natural number cannot end with 2 . Hence 128242 cannot be the square of natural number Answer is 128242 <result>B</result>

B

Which one of the following can't be the square of natural number ?

aqua_rat__axvRts3b08m5bpz2

Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1) What is the largest prime number (written in binary) that is a factor of both 10110000 and 101100000 ? Choose the correct choice from the following answers: A) 10 B) 11 C) 101 D) 1011 E) 10001

Binary Divison can provide a quick answer if you are comfortable with it. as option E is the biggest binary number we try with it first : 100010000/ 1011 =10000 1000100000/ 1011 =100000 so answer is option is 1011 <result>D</result>

D

Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1) What is the largest prime number (written in binary) that is a factor of both 10110000 and 101100000 ?

aqua_rat__gQ9DRLoDy0lWEM69

If x = - |x| , then which one of the following statements could be true? I. x <1 II. x < 0 III. x > 0 Choose the most appropriate option: A) None B) I only C) II only D) I and II E) II and III

Answer copied from NOVA guide Statement I could be false because 1/2 = −(1/2) = −1/2 . Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number]. Now, if one side of an equation is always negative, then the other side must always be negative, otherwise the opposite sides of the equation would not be equal. Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly: Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction. Hence, x cannot be positive. The answer is II only). <result>C</result>

C

If x = - |x| , then which one of the following statements could be true? I. x <1 II. x < 0 III. x > 0

aqua_rat__131SBwMREpizCZxc

Of the 14,210 employees of the anvil factory, 3/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen? Choose the correct option: A) 14.3% B) 16.67% C) 33% D) 28.6% E) 49.67%

The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers. If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice. What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 14.3%. Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation. The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in? The correct answer is 2nd place. Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you. 14.3% <result>A</result>

A

Of the 14,210 employees of the anvil factory, 3/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?

aqua_rat__9xqT51c5O1WMqFGm

If a and b are positive numbers, and a^3 + b^3 = 140, then the greatest possible value of a is between: Select A) 0 and 2 B) 2 and 3 C) 3 and 4 D) 4 and 5 E) 5 and 8

If a = 5.1 and b is a bit less than 2, then a^3 + b^3 can equal 140. If a &gt; 8, then a^3 + b^3 &gt; 140. The answer is 5 and 8. <result>E</result>

E

If a and b are positive numbers, and a^3 + b^3 = 140, then the greatest possible value of a is between:

aqua_rat__3PKshSX2tVcJmcVo

Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 3? Select A) A)1 B) B)2 C) C)4 D) D)3 E) E)16

Points to remember - 1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change. 2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number. Hence the answer to the above question is 3 <result>D</result>

D

Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 3?

aqua_rat__frb7Del9zgJG3Cx0

Two trains of length 100 meters and 200 meters are 630 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. After how many seconds will the trains meet? Choose the correct choice from the following answers A) 12 B) 14 C) 16 D) 18 E) 20

The speeds are 90000/3600= <gadget id="calculator">90000/3600</gadget> <output>25</output> 25 m/s and 72000/3600= <gadget id="calculator">72000/3600</gadget> <output>20</output> 20 m/s The relative speed is 45 m/s. time= 630 / 45= <gadget id="calculator">630 / 45</gadget> <output>14</output> 14 seconds The answer is 14. <result>B</result>

B

Two trains of length 100 meters and 200 meters are 630 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. After how many seconds will the trains meet?

aqua_rat__lSVFQXojf3Zlv9e4

Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for q dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs? Select the correct option: A) (x – s)q – sd B) xq – (xd – sd) C) xd – sq D) (x – s)d – xq E) (s – q)d – xq

Answer D: The amount of hotdogs she can sell is x-s. The price per pound is d, so the revenue is (x-s)d. The total costs are x time q, so the profit is (x-s)d-xq. <result>D</result>

D

Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for q dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs?

aqua_rat__tBScxvS4oEIfESrU

Allen walks at an average speed of 4km/h, to the park and then return to the home he walks at an average speed of 8km/h. Which of the following is the closest approximation of Allen's average speed, in kilometers per hour, for the trip? Choose one. A) 8 B) 32 C) 25 D) 16 E) 4

Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 4 km/hour and 8 km/hour, using a multiple of both 4 and 8 would make the math easiest. Let's set the Distance up the hill at 16 km. So, going park, we have.... D = (R)(T) 16 = (4)(T) 16/4= <gadget id="calculator">16/4</gadget> <output>4</output> 4= T 4 hours to go park Going home, we have.... 16 = (R)(T) 16 = (8)(T) 16/8= <gadget id="calculator">16/8</gadget> <output>2</output> 2= T 2 hours to go home Total 16istance = 32 km Total Time = 4+2= <gadget id="calculator">4+2</gadget> <output>6</output> 6 hours Average Speed= 32/2= <gadget id="calculator">32/2</gadget> <output>16</output> 16 km/hour 16 <result>D</result>

D

Allen walks at an average speed of 4km/h, to the park and then return to the home he walks at an average speed of 8km/h. Which of the following is the closest approximation of Allen's average speed, in kilometers per hour, for the trip?

aqua_rat__4ZzL6jhkBK7Hc8wO

Each child has 8 crayons and 15 apples. If there are 7 children, how many crayons are there in total? Choose one. A) 22 B) 56 C) 12 D) 36 E) 10

8*7= <gadget id="calculator">8*7</gadget> <output>56</output> 56.Answer is 56. <result>B</result>

B

Each child has 8 crayons and 15 apples. If there are 7 children, how many crayons are there in total?

aqua_rat__dsjAcsCXxCgxp2Nl

A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? Choose the correct choice from the following A) 87 Kmph B) 28 Kmph C) 72 Kmph D) 18 Kmph E) 29 Kmph

Length = Speed * time Speed = L/T S = 400/20= <gadget id="calculator">400/20</gadget> <output>20</output> 20 M/Sec Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 72 Kmph Answer:72 Kmph <result>C</result>

C

A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?

aqua_rat__gWfgpU6CEohY90YH

Two sets A and B consists only of positive integers such that mean of set A is 40 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is => Choose the correct choice. A) [A] 65 B) [B] 60 C) [C 70 D) [D] 55 E) [E] cannot be determined

For this question, we have zero information about the size of two sets, sets AB. These two sets may have the same size or may be wildly different. Thus, the answer is (E), the mathematical answer cannot be determined. This is a very weak math question. As someone who writes GMAT practice questions, I would give this a grade of anD-as a question. Answer [E] cannot be determined <result>E</result>

E

Two sets A and B consists only of positive integers such that mean of set A is 40 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>

aqua_rat__VItWkDS45VQKvNEC

A train 280 m long passed a pole in 28 sec. How long will it take to pass a platform 660 m long? Choose one: A) 52 B) 94 C) 71 D) 68 E) 88

Speed = 280/28= <gadget id="calculator">280/28</gadget> <output>10</output> 10 m/sec. Required time= (280 + 660)/10= <gadget id="calculator">(280 + 660)/10</gadget> <output>94</output> 94 sec. Answer: 94 <result>B</result>

B

A train 280 m long passed a pole in 28 sec. How long will it take to pass a platform 660 m long?

aqua_rat__yetKsQoa9dpmm0q6

A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 97 cookies, what is the minimum number of chocolate chip cookies he makes? Choices. A) 7 B) 14 C) 21 D) 35 E) 49

7C+6P=97 We need to maximize P to minimize C so that the eq is also satisfied Try substitution for CP to solve so that eqn is satisfied The least value of C for which equation gets satisfied is 5 i.e. 7*1+6*15=7+90= <gadget id="calculator">7+90</gadget> <output>97</output> 97 Hence 7 is the answer <result>A</result>

A

A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 97 cookies, what is the minimum number of chocolate chip cookies he makes?

aqua_rat__FB41NrgjuAM5bNdd

9 persons a, b, c, ... and i are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there? Choices: A) 24 B) 36 C) 48 D) 72 E) 144

firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly.. total 9 are there.. take a,b, and c as one,so total =7.. these 7 can be arranged in 7! ways.. a,b, and c can be arranged within themselves in 3! ways .. TOTAL = 7!*3!=30240 144 <result>E</result>

E

9 persons a, b, c, ... and i are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?

aqua_rat__2j8mfEmiPOZjtT43

Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,600 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees? Options: A) 38,000 B) 40,000 C) 42,600 D) 45,600 E) 48,500

Median is just the value in the middle when you arrange all values in the ascending order In this question, the 7th value would be the median (Since there are 13 employees) 38, 40, 40, 40, 42.5, 42.5,45.6 So, answer is 45,600. <result>D</result>

D

Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,600 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?

aqua_rat__mDBI5aCsh94IYRHc

The botanic garden is planting bulbs for the spring flower show. The head gardener is trying to decide how to place three Tulips bulbs, three Daffodil bulbs, and three Crocus bulbs along the front row. How many different arrangements can he make of these bulbs in the front row? Choose the correct answer: A) 27 B) 108 C) 216 D) 512 E) 1,680

total number of bulbs is 9, hence possible arrangements is 9! But all the 3 bulbs are 3 each, hence i.e.,9!/3!3!3!=1680 ways answer is 1,680. <result>E</result>

E

The botanic garden is planting bulbs for the spring flower show. The head gardener is trying to decide how to place three Tulips bulbs, three Daffodil bulbs, and three Crocus bulbs along the front row. How many different arrangements can he make of these bulbs in the front row?

aqua_rat__vXKp4GWknkW9IGNI

What sum of money put at C.I amounts in 2 years to Rs.8880 and in 3 years to Rs.9261? Choose one A) 8164 B) 8877 C) 2877 D) 2678 E) 1011

8880 ---- 381 100 ---- ? =&gt; 4.29% x *104.29/100 * 104.29/100 = 8880 x*1.0876=8880 x=8880/1.0876 =&gt; 8164.38 8164nswer: 8164 <result>A</result>

A

What sum of money put at C.I amounts in 2 years to Rs.8880 and in 3 years to Rs.9261?

aqua_rat__BnylWvyCCybOGLdh

Find the area of a parallelogram with base 24 cm and height 16 cm? Pick: A) 298 cm2 B) 384 cm2 C) 279 cm2 D) 297 cm2 E) 278 cm2

Area of a parallelogram = base * height = 24 * 16= <gadget id="calculator">24 * 16</gadget> <output>384</output> 384 cm2 Answer: 384 cm2 <result>B</result>

B

Find the area of a parallelogram with base 24 cm and height 16 cm?

aqua_rat__UUZg4piTnLQ9iBY0

A fresh water aquarium contains Molly fish and Guppy fish at a ratio of 15:16. If 35 additional Guppy fish were put in the aquarium, the ratio of Molly fish to Guppy fish would be 15:21. How many Molly fish does the aquarium contain? Select: A) 90 B) 105 C) 120 D) 135 E) 150

15x/21x = 15y/(16y+35) 15x=15y x=y 21x=16y+35 5y=35 y=7 M=7*15= <gadget id="calculator">7*15</gadget> <output>105</output> 105 ANSWER:105 <result>B</result>

B

A fresh water aquarium contains Molly fish and Guppy fish at a ratio of 15:16. If 35 additional Guppy fish were put in the aquarium, the ratio of Molly fish to Guppy fish would be 15:21. How many Molly fish does the aquarium contain?

aqua_rat__Ndes9O5NbIqu7lno

After M students took a test, the average score was 65%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 70%? Choose the correct choice from the following A) 2.5M + 35 B) M + 37.5 C) 0.65M + 70 D) 70 - 0.65M E) 35+0.65M

The total number of correct answers for M students is (0.65)*50*M=32.5*M For an average of 70%: (total correct answers) / (M+1) = 0.7*50= <gadget id="calculator">0.7*50</gadget> <output>35</output> 35 Let x be the number of correct answers for the next student. (x + 32.5M) / M+1= 35 x + 32.5M= 35M+35 x = 2.5M + 35 The answer is 2.5M + 35. <result>A</result>

A

After M students took a test, the average score was 65%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 70%?

aqua_rat__tYA3vhGj8249k880

Jim bought edging to go around a circular garden with a radius of 4 feet. Later he decided to double the diameter of the garden. How many more feet of edging must he buy? Answers. A) 28.84' additional edging B) 48.84' additional edging C) 38.84' additional edging D) 18.84' additional edging E) 25.12' additional edging

circumference of small garden = 2 x 3.14 x 4 = 25.12' double of the circumference of small garden = 2 x 25.12' = 50.24' More feet to be buy = 50.24 - 25.12= <gadget id="calculator">50.24 - 25.12</gadget> <output>25.12</output> 25.12 Answer : 25.12' additional edging <result>E</result>

E

Jim bought edging to go around a circular garden with a radius of 4 feet. Later he decided to double the diameter of the garden. How many more feet of edging must he buy?

aqua_rat__AsTvrSJc32R9Ljof

There are 50 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played? Choose the correct choice: A) 1000 B) 3000 C) 1225 D) 6000 E) 9000

50 players are there. two players play one game with one another. so 5012252=50*49/2= <gadget id="calculator">50*49/2</gadget> <output>1_225</output> 1225 SO OPTION 1225 is correct <result>C</result>

C

There are 50 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?

aqua_rat__0DYKk83H0SxMtKhr

The diameter of a cylindrical tin is 14 cm and height is 2 cm. Find the volume of the cylinder? Options. A) 33 B) 45 C) 66 D) 77 E) 98

r = 7 h = 5 π * 7 * 7 * 5 = 98 π cc Answer:98 <result>E</result>

E

The diameter of a cylindrical tin is 14 cm and height is 2 cm. Find the volume of the cylinder?

aqua_rat__lwXbRS1S51FDaKpJ

What approximate value should come in place of the question mark (?) in the following equation? 16√524 + 1492 - 250.0521? Choose one. A) 1600 B) 1800 C) 1900 D) 2400 E) 1400

? ≈ 16 × 23 + 1490 – 250 ≈ 1600 1600nswer 1600 <result>A</result>

A

What approximate value should come in place of the question mark (?) in the following equation? 16√524 + 1492 - 250.0521?

aqua_rat__mSFO4a2PPfYNRhT1

A retail item is offered at a discount of b percent (where b > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of b, would result in the same final price? Select: A) b+5/1.05 B) b/1.05 +5 C) 1.05b-5 D) b-5/1.05 E) 1.05(p – 5)

Let x be the price of the item. Final price after discount and sales tax = x * (1 - b/100) * 1.05 Let c be the percent discount which would result in the same final price. Then, x * (1 - b/100) * 1.05 = x * (1 - c/100) =&gt; 1.05 - 1.05b/100 = 1 - c/100 =&gt; c/100 = 1.05b/100 - .05 =&gt; c = 1.05b - 5 Hence ,option 1.05b-5 is correct. <result>C</result>

C

A retail item is offered at a discount of b percent (where b > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of b, would result in the same final price?

aqua_rat__QhoTx0JLwhBo527m

A train 1600 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 60 sec. The speed of the train is? Choose one: A) 42 km/hr B) 44 km/hr C) 46 km/hr D) 48 km/hr E) 50 km/hr

Speed of the train relative to man = 1600/60 = 80/6 m/sec. = 80/6 * 18/5= <gadget id="calculator">80/6 * 18/5</gadget> <output>48</output> 48 km/hr Let the speed of the train be x km/hr. Then, relative speed= (x - 5) km/hr. x - 6 = 48 =&gt; x = 42 km/hr. 42 km/hrnswer: 42 km/hr <result>A</result>

A

A train 1600 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 60 sec. The speed of the train is?

aqua_rat__9C49a304OO8WDJIp

In a company of 16 employees, 8 employees earn $38,000, 4 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 16 employees is $44,000, what is the annual salary for each of the highest-paid employees? Choose the correct choice. A) $54,000 B) $55,000 C) $56,000 D) $57,000 E) $58,000

8*38,000+4*42,000+4x=16*44,000 4x=704,000-304,000-168,000 4x=232,000 x=58,000 The answer is $58,000. <result>E</result>

E

In a company of 16 employees, 8 employees earn $38,000, 4 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 16 employees is $44,000, what is the annual salary for each of the highest-paid employees?

aqua_rat__hbad8DrKHxE4X1CH

What is the area of a square field whose diagonal of length 20 m? Choose the correct choice from the following answers. A) 288 B) 289 C) 200 D) 112 E) 178

d2/2 = (20 * 20)/2= <gadget id="calculator">(20 * 20)/2</gadget> <output>200</output> 200 Answer: 200 <result>C</result>

C

What is the area of a square field whose diagonal of length 20 m?

aqua_rat__c41sq7Z9C02oNn2H

How many times are the hands of a clock at right angle in a day? Select the correct option: A) 22 B) 24 C) 44 D) 48 E) None

EXPLANATION In 12 hours, they are at right angles 22 times. In 24 hours, they are at right angles 44 times. Answer 44 <result>C</result>

C

How many times are the hands of a clock at right angle in a day?

aqua_rat__59QqSopq43WYTGZm

Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is Choose the correct option. A) 5/6 B) 5/9 C) 5/5 D) 5/2 E) 5/1

No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways. Thus 6 * 5 * 4= <gadget id="calculator"> 6 * 5 * 4</gadget> <output>120</output> 120 favourable cases. The total cases are 6 * 6 * 6= <gadget id="calculator"> 6 * 6 * 6</gadget> <output>216</output> 216. The probability= 120/216 = 5/9.Answer: 5/9 <result>B</result>

B

Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is

aqua_rat__0987CdeKse28YVgp

If 0.5% of A =70 paise, then the value of A is ? Answers: A) Rs. 170 B) Rs. 140 C) Rs. 1.70 D) Rs. 4.25 E) None

Answer ∵ 0.5/100 of A = 70/100 ∴ A = Rs. (70 / 0.5) = Rs. 140 Correct Option: Rs. 140 <result>B</result>

B

If 0.5% of A =70 paise, then the value of A is ?

aqua_rat__1uNfc9CejWBKUoUP

Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/5, what is the value of X/Y ? Select the correct option: A) 3. B) 5 C) 1/2. D) 1/3. E) There isn't enough data to answer the question.

Answer is 5 : 5 X - Y = (X + Y)/2 Solving for X/Y = 5 <result>B</result>

B

Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/5, what is the value of X/Y ?

aqua_rat__k2ZoUQYFQFciecFN

The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 60 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? Choose the correct choice from the following: A) 42 B) 44 C) 46 D) 48 E) 40

The time it takes Cara to drive to City B is 120 / 30= <gadget id="calculator">120 / 30</gadget> <output>4</output> 4 hours. Dan needs to take less than 3 hours for the trip. Dan needs to exceed a constant speed of 120 / 3= <gadget id="calculator"> 120 / 3</gadget> <output>40</output> 40 miles per hour. The answer is 40. <result>E</result>

E

The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 60 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?

aqua_rat__zGILMFw3KEbI0zjU

Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. Choices. A) 348 B) 277 C) 960 D) 872 E) 121

60(x + 1) = 64x X = 15 60 * 16= <gadget id="calculator">60 * 16</gadget> <output>960</output> 960 km Answer: 960 <result>C</result>

C

Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.

aqua_rat__bbvHHzSS2A5hT1pm

An article is bought for Rs.675 and sold for Rs.900, find the gain percent? Pick. A) 33 1/8% B) 33 9/3% C) 33 1/3% D) 93 1/3% E) 33 2/3%

675 ---- 225 100 ---- ? =&gt; 33 1/3% Answer:33 1/3% <result>C</result>

C

An article is bought for Rs.675 and sold for Rs.900, find the gain percent?

aqua_rat__b6YhX6CW0Ef3fTf5

|x+3| – |4-x| = |9+x| How many solutions will this equation have? Choose the correct option A) 0 B) 1 C) 2 D) 3 E) 4

You have |x+3| - |4-x| = |8+x| First, look at the three values independently of their absolute value sign, in other words: |x+3| - |4-x| = |8+x| (x+3) - (4-x) = (8+x) Now, you're looking at x &lt; - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand. when x=-10 I.) (x+3) (-10+3) (-7) II.) (4-x) (4-[-10]) (double negative, so it becomes positive) (4+10) (14) III.) (8+x) (8+-10) (-2) In other words, when x &lt; -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change. Here is how I do it step by step. I.) |x+3| - |4-x| = |8+x| II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows: (x+3) x=-3 (-3+3)= <gadget id="calculator">(-3+3)</gadget> <output>0</output> 0 (4-x) x=4 (4-4)= <gadget id="calculator">(4-4)</gadget> <output>0</output> 0 (8+x) x=-8 (8+-8) = 1 1 <result>B</result>

B

|x+3| – |4-x| = |9+x| How many solutions will this equation have?