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a ) 899999 , b ) 899991 , c ) 899891 , d ) 899981 , e ) 899000
b
subtract(multiply(9, const_1000), 9)
the difference between the local value and the face value of 9 in the numeral 62975148 is
"explanation : ( local value of 9 ) - ( face value of 9 ) = ( 900000 - 9 ) = 899991 b )"
a = 9 * 1000 b = a - 9
a ) 220 km , b ) 224 km , c ) 230 km , d ) 234 km , e ) 255 km
b
multiply(const_2, divide(multiply(multiply(21, 24), 10), add(21, 24)))
a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
"( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 x / 21 + x / 24 = 20 15 x = 168 x 20 x = [ 168 x 20 / 15 ] = 224 km answer is b"
a = 21 * 24 b = a * 10 c = 21 + 24 d = b / c e = 2 * d
a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 9 : 10 , e ) 1 : 4
d
divide(divide(multiply(3, 3), multiply(4, 2)), divide(multiply(3, 4), multiply(2, 5)))
the compound ratio of 3 : 4 , 3 : 2 and 4 : 5 ?
"3 / 4 * 3 / 2 * 4 / 5 = 9 / 10 = 9 : 10 answer : d"
a = 3 * 3 b = 4 * 2 c = a / b d = 3 * 4 e = 2 * 5 f = d / e g = c / f
a ) rs . 432 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
b
multiply(divide(360, subtract(2460, 360)), 2460)
the true discount on a bill of rs . 2460 is rs . 360 . what is the banker ' s discount ?
"explanation : f = rs . 2460 td = rs . 360 pw = f - td = 2460 - 360 = rs . 2100 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2100 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2460 for unexpired time = 360 / 2100 Γ— 2460 = 0.17 Γ— 2460 = rs . 422 answer : option b"
a = 2460 - 360 b = 360 / a c = b * 2460
a ) 12 , b ) 29 , c ) 27 , d ) 16 , e ) 99
d
divide(subtract(111, multiply(const_3, 5)), multiply(const_3, const_2))
a number is doubled and 5 is added . if the resultant is trebled , it becomes 111 . what is that number ?
"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 111 6 x + 15 = 111 6 x = 96 x = 16 answer : d"
a = 3 * 5 b = 111 - a c = 3 * 2 d = b / c
a ) rs . 500 , b ) rs . 1400 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
b
multiply(multiply(subtract(4, 3), 700), 3)
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 700 more than d , what is b ' s share ?
"let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 700 x = 700 . b ' s share = rs . 2 x = rs . ( 2 x 700 ) = rs . 1400 . answer = b"
a = 4 - 3 b = a * 700 c = b * 3
a ) rs . 947.55 , b ) rs . 957.55 , c ) rs . 857.55 , d ) rs . 657.55 , e ) rs . 357.55
b
subtract(add(add(divide(multiply(divide(800, multiply(divide(9, const_100), 5)), 9), const_100), divide(800, multiply(divide(9, const_100), 5))), divide(multiply(add(divide(multiply(divide(800, multiply(divide(9, const_100), 5)), 9), const_100), divide(800, multiply(divide(9, const_100), 5))), 9), const_100)), divide(800, multiply(divide(9, const_100), 5)))
if the simple interest on a sum of money for 5 years at 9 % per annum is rs . 800 , what is the compound interest on the same sum at the rate and for the same time ?
"sum = ( 800 * 100 ) / ( 5 * 9 ) = rs . 1 , 777.78 c . i . on rs . rs . 1 , 777.78 for 5 years at 9 % = rs . 2 , 735.33 . = rs . 2 , 735.33 - 1 , 777.78 = rs . 957.55 answer : b"
a = 9 / 100 b = a * 5 c = 800 / b d = c * 9 e = d / 100 f = 9 / 100 g = f * 5 h = 800 / g i = e + h j = 9 / 100 k = j * 5 l = 800 / k m = l * 9 n = m / 100 o = 9 / 100 p = o * 5 q = 800 / p r = n + q s = r * 9 t = s / 100 u = i + t v = 9 / 100 w = v * 5 x = 800 / w y = u - x
a ) rs . 2.20 , b ) rs . 3.20 , c ) rs . 4.20 , d ) rs . 5.20 , e ) rs . 3.25
b
subtract(subtract(multiply(multiply(2000, add(const_1, divide(4, const_100))), add(const_1, divide(4, const_100))), 2000), multiply(2, multiply(2000, divide(4, const_100))))
find the difference between c . i and s . i on a sum of money rs . 2000 for 2 years . at 4 % p . a
p 9 r / 100 ) ^ 2 = 2000 ( 4 / 100 ) ^ 2 = rs . 3.20 answer : b
a = 4 / 100 b = 1 + a c = 2000 * b d = 4 / 100 e = 1 + d f = c * e g = f - 2000 h = 4 / 100 i = 2000 * h j = 2 * i k = g - j
a ) 25 , b ) 30 , c ) 35 , d ) 24 , e ) 96
a
divide(100, multiply(divide(divide(10, 10), 5), 20))
if 5 machines can produce 20 units in 10 hours , how long would it take 10 machines to produce 100 units ?
"5 machines would produce 100 units in 50 hours . increasing the amount of machines by 2 would mean dividing 50 hours by 2 . 50 / 2 = 25 answer : a"
a = 10 / 10 b = a / 5 c = b * 20 d = 100 / c
a ) $ 1100 , b ) $ 520 , c ) $ 1040 , d ) $ 1170 , e ) $ 630
c
multiply(2340, divide(inverse(8), add(inverse(12), add(inverse(6), inverse(8)))))
a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be a ' s share of the earnings ?
"explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 2340 / 9 = 1040 correct choice is ( c )"
a = 1/(8) b = 1/(12) c = 1/(6) d = 1/(8) e = c + d f = b + e g = a / f h = 2340 * g
a ) s . 666 , b ) s . 1140 , c ) s . 999 , d ) s . 1085 , e ) s . 1020
a
multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 1.00), 3)
the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.00 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
"a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.0 = 666 answer : a"
a = math.sqrt(3136) b = a * 4 c = 2 * 1 d = b - c e = d * 1 f = e * 3
a ) 25 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
a
multiply(60, divide(multiply(5, 5), 60))
the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 5 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
"number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 5 = 25 km imo , correct answer is ` ` a . ' '"
a = 5 * 5 b = a / 60 c = 60 * b
a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 10 / 3
e
divide(10, 3)
a positive number x is multiplied by 10 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
"sq rt ( 10 x / 3 ) = x = > 10 x / 3 = x ^ 2 = > x = 10 / 3 ans - e"
a = 10 / 3
a ) 900 , b ) 800 , c ) 600 , d ) 300 , e ) none
d
divide(30, 90)
if 90 % of a = 30 % of b and b = c % of a , then the value of c is ?
"answer ∡ 90 a / 100 = 30 b / 100 = ( 30 / 100 ) x ac / 100 ∴ c = 100 x ( 100 / 30 ) x ( 90 / 100 ) = 300 correct option : d"
a = 30 / 90
a ) 4 , b ) 7 , c ) 12 , d ) 14 , e ) 28
d
divide(28, const_2)
in a group of dogs and people , the number of legs was 28 more than twice the number of heads . how many dogs were there ? [ assume none of the people or dogs is missing a leg . ]
if there were only people , there would be exactly twice the number of legs as heads . each dog contributes two extra legs over and above this number . so 28 extra legs means 14 dogs . correct answer d
a = 28 / 2
a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %
b
multiply(const_100, divide(subtract(subtract(const_100, 50), subtract(60, multiply(60, divide(70, const_100)))), subtract(const_100, 60)))
in a company , 50 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
"the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 50 % of all employees are women , so non - union women are 50 % - 18 % = 32 % 40 % of all employees are non - union . the percent of non - union employees who are women is 32 % / 40 % = 80 % the answer is b ."
a = 100 - 50 b = 70 / 100 c = 60 * b d = 60 - c e = a - d f = 100 - 60 g = e / f h = 100 * g
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
d
divide(log(multiply(9, 9)), log(const_10))
9 log 9 ( 4 ) = ?
"exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 4 ) = 4 correct answer d"
a = 9 * 9 b = math.log(a) c = math.log(10) d = b / c
a ) 96 , b ) 106 , c ) 128 , d ) 137 , e ) 122
d
subtract(multiply(add(20, const_1), add(5, 32)), multiply(20, 32))
the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?
"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 5 = 37 runs total runs = new avg x new no . of innings = 37 * 21 = 777 runs made in the 11 th inning = 777 - 640 = 137 answer : d"
a = 20 + 1 b = 5 + 32 c = a * b d = 20 * 32 e = c - d
a ) 654 , b ) 655 , c ) 656 , d ) 588 , e ) 658
d
multiply(divide(subtract(const_100, 30), const_100), 840.00)
yearly subscription to professional magazines cost a company $ 840.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?
"total cost 840 840 * 30 / 100 = 252 so the cut in amount is 252 the less amount to be spend is 840 - 252 = 588 answer : d"
a = 100 - 30 b = a / 100 c = b * 840
a ) 5 : 8 , b ) 5 : 10 , c ) 5 : 13 , d ) 5 : 7 , e ) 5 : 16
d
divide(subtract(sqrt(4900), 20), multiply(sqrt(4900), const_2))
the area of a square is 4900 sq cm . find the ratio of the breadth and the length of a rectangle whose length is same the side of the square and breadth is 20 cm less than the side of the square ?
"let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4900 a = ( 4900 ) ^ 1 / 2 = 70 l = a and b = a - 20 b : l = a - 20 : a = 50 : 70 = 5 : 7 answer : d"
a = math.sqrt(4900) b = a - 20 c = math.sqrt(4900) d = c * 2 e = b / d
a ) 1521 , b ) 3000 , c ) 1667 , d ) 1254 , e ) 1112
b
multiply(divide(multiply(10, const_1000), const_60), 18)
a man walking at a rate of 10 km / hr crosses a bridge in 18 minutes . the length of the bridge is ?
"speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 18 * 60 = 3000 m answer is b"
a = 10 * 1000 b = a / const_60 c = b * 18
['a ) 84', 'b ) 86', 'c ) 82', 'd ) 80', 'e ) none of them']
a
add(14, divide(divide(440, const_pi), const_2))
the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle .
let inner radius be r metres . then , 2 ( 22 / 7 ) r = 440 = r = ( 440 x ( 7 / 44 ) ) = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer is a
a = 440 / math.pi b = a / 2 c = 14 + b
['a ) none', 'b ) two', 'c ) three', 'd ) five', 'e ) seven']
c
subtract(const_4, const_1)
r is the set of positive even integers less than 20 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
squares < 20 { 1,4 , 9,16 } s = { 1,4 , 9,16 } r = { 2 , . . . . . 18 } hence c .
a = 4 - 1
a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28
e
multiply(4, 7)
elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 7 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
"solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 7 we get : 21 b + 28 f = 7 x therefore , we got 21 ounces of butter and 7 x amount of quantity when we use 28 ounces of floor . ans : e"
a = 4 * 7
a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) 150
b
multiply(12, 45)
the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 45 , find the other ?
"other number = 12 * 600 / 45 = 160 answer is b"
a = 12 * 45
a ) 40 , b ) 36 , c ) 32 , d ) 28 , e ) 24
b
add(add(multiply(divide(multiply(1, 8), subtract(multiply(3, 2), multiply(1, 4))), 4), 8), multiply(divide(multiply(1, 8), subtract(multiply(3, 2), multiply(1, 4))), 3))
in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
"let c be the capacity of the can . ( 4 / 7 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 12 c - 96 + 168 = 14 c 2 c = 72 c = 36 the answer is b ."
a = 1 * 8 b = 3 * 2 c = 1 * 4 d = b - c e = a / d f = e * 4 g = f + 8 h = 1 * 8 i = 3 * 2 j = 1 * 4 k = i - j l = h / k m = l * 3 n = g + m
a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
b
divide(divide(multiply(272, 6), 12), const_4)
according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice ?
"its b . total juice rquired = 272 * 6 = 1632 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1632 / 48 = 34 . answer b"
a = 272 * 6 b = a / 12 c = b / 4
a ) rs . 10,000 , b ) rs . 10,800 , c ) rs . 14,400 , d ) rs . 16,000 , e ) none of these
a
subtract(const_100, 90)
to produce an annual income of rs . 1200 from a 12 % stock at 90 , the amount of stock needed is :
solution for an income of rs . 12 , stock needed = rs . 100 . for an income of rs . 1200 , stock needed = rs . 100 / 12 x 1200 = 10000 answer a
a = 100 - 90
a ) 7 , b ) 9 , c ) 14 , d ) 17 , e ) 21
d
add(add(multiply(10, const_2), divide(10, 2)), add(const_3, const_3))
if the least common addition of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
"( x + y ) = 10 and both x an y are prime . the only values of x and y can be 7 and 3 ( x = 7 and y = 3 ) 2 x + y = 2 * 7 + 3 = 17 correct option : d"
a = 10 * 2 b = 10 / 2 c = a + b d = 3 + 3 e = c + d
a ) 308 , b ) 320 , c ) 332 , d ) 344 , e ) 356
d
subtract(multiply(multiply(45, const_0_2778), 40), 156)
what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 40 seconds ?
"speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 156 = 344 meters the answer is d ."
a = 45 * const_0_2778 b = a * 40 c = b - 156
a ) 2 / 11 , b ) 4 / 15 , c ) 6 / 17 , d ) 8 / 21 , e ) 10 / 25
d
divide(choose(6, 3), choose(10, 6))
a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
"the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d ."
a = math.comb(6, 3) b = math.comb(10, 6) c = a / b
a ) 120 , b ) 240 , c ) 360 , d ) 1200 , e ) 480
e
multiply(120, multiply(divide(20, 10), divide(30, 15)))
if 10 men can reap 120 acres of land in 15 days , how many acres of land can 20 men reap in 30 days ?
"10 men 120 acres 15 days 20 men ? 30 days 120 * 20 / 10 * 30 / 15 120 * 2 * 2 120 * 4 = 480 answer : e"
a = 20 / 10 b = 30 / 15 c = a * b d = 120 * c
a ) 960 , b ) 975 , c ) 1,200 , d ) 920 , e ) none of these
b
multiply(divide(add(852, 448), const_2), add(const_1, divide(50, const_100)))
the profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
"let the profit or loss be x and 852 – x = 448 + x or , x = 404 ⁄ 2 = 202 \ cost price of the article = 852 – x = 448 + x = 650 \ sp of the article = 650 Γ— 150 ⁄ 100 = 975 answer b"
a = 852 + 448 b = a / 2 c = 50 / 100 d = 1 + c e = b * d
a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 1 , e ) 1 : 3
d
divide(subtract(6, 2), subtract(10, 6))
cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
"( 10 / 100 ) a + ( 2 / 100 ) b = ( 6 / 100 ) ( a + b ) 4 a = 4 b = > a / b = 1 / 1 answer is d ."
a = 6 - 2 b = 10 - 6 c = a / b
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
b
divide(add(subtract(multiply(2, subtract(7, 2)), multiply(3, 2)), 31), add(3, 2))
zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 7 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 7 questions did zachary answer correctly ?
"i got two equations : 3 x - 2 y = 25 x + y = 7 3 x - 2 ( 7 - x ) = 25 3 x - 14 + 2 x = 25 5 x = 39 x = 7.8 or between 7 and 8 . ( ans b )"
a = 7 - 2 b = 2 * a c = 3 * 2 d = b - c e = d + 31 f = 3 + 2 g = e / f
a ) 366 , b ) 236 , c ) 367 , d ) 365 , e ) 386
e
add(1, lcm(35, 11))
find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case .
"explanation : the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 35 , 11 ) + 1 = 386 . answer : e"
a = math.lcm(35, 11) b = 1 + a
a ) 89 kmph , b ) 82.5 kmph , c ) 75 kmph , d ) 65 kmph , e ) 77 kmph
b
divide(add(90, 75), const_2)
the speed of a car is 90 km in the first hour and 75 km in the second hour . what is the average speed of the car ?
"s = ( 90 + 75 ) / 2 = 82.5 kmph b"
a = 90 + 75 b = a / 2
a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 34 hr , e ) 36 hr
d
inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 8), 1), 8))))
a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 8 hours to fill the tank . the leak can drain all the water of the tank in ?
"work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 8 ) = 1 / 34 leak will empty the tank in 34 hrs . answer : d"
a = 1 / 2 b = 2 * 8 c = b + 1 d = c / 8 e = 1/(d) f = a - e g = 1/(f)
a ) 50 sec , b ) 66 sec , c ) 48 sec , d ) 55 sec , e ) 45 sec
a
divide(divide(3125, divide(multiply(add(40, 35), const_1000), const_3600)), const_3)
two buses each 3125 m long are running in opposite directions on parallel roads . their speeds are 40 km / hr and 35 km / hr respectively . find the time taken by the slower bus to pass the driver of the faster one ?
relative speed = 40 + 35 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 3125 + 3125 = 6250 m . required time = 6250 * 6 / 125 = 50 sec . answer : a
a = 40 + 35 b = a * 1000 c = b / 3600 d = 3125 / c e = d / 3
a ) 299 m , b ) 777 m , c ) 200 m , d ) 167 m , e ) 150 m
e
subtract(divide(500, const_2), 100)
if the perimeter of a rectangular garden is 500 m , its length when its breadth is 100 m is ?
"2 ( l + 100 ) = 500 = > l = 150 m answer : e"
a = 500 / 2 b = a - 100
a ) 13.7 kmph , b ) 13.3 kmph , c ) 13.8 kmph , d ) 13.9 kmph , e ) 12.3 kmph
b
divide(add(15, 12), const_2)
a man goes from a to b at a speed of 15 kmph and comes back to a at a speed of 12 kmph . find his average speed for the entire journey ?
distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 15 ) + ( d / 12 ] = ( 2 d ) / [ 9 d / 60 ) = > 13.3 kmph . answer : b
a = 15 + 12 b = a / 2
a ) 293 , b ) 294 , c ) 295 , d ) 296 , e ) 298
b
divide(subtract(729, multiply(multiply(const_4, const_2), const_3)), const_2)
a cube is divided into 729 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that the cube is coloured with green colour on one set of adjacent faces , red on the other set of adjacent faces , blue on the third set . so , how many cubelets are there which are painted with exactly one colour ?
"total cubes created are 729 so a plane of big cube has 9 * 9 cubes out of that ( n - 2 ) * ( n - 2 ) = 7 * 7 = 49 are painted only one side and a cube has six sides = 6 * 49 = 294 answer : b"
a = 4 * 2 b = a * 3 c = 729 - b d = c / 2
a ) 40 , b ) 60 , c ) 80 , d ) 120 , e ) 140
a
multiply(divide(160, 4), const_3)
in a mixed college 160 students are there in one class . out of this 160 students 3 / 4 students are girls . how many boys are there ?
"total number of students : 160 total girls : 160 * 3 / 4 = 120 total boys : 160 - 120 = 40 answer is a"
a = 160 / 4 b = a * 3
a ) 21 , b ) 15 , c ) 14 , d ) 10 , e ) 6
a
multiply(subtract(10, const_4), const_3)
the product z of two prime numbers is between 10 and 30 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24 , then what is z ?
"the smallest possible product is 21 which is 3 * 7 . all other products are too big . the answer is a ."
a = 10 - 4 b = a * 3
a ) 13 , b ) 16 , c ) 17 , d ) 18 , e ) 19
a
divide(44, const_10)
how many integers from 0 to 44 , inclusive , have a remainder of 1 when divided by 3 ?
"explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 43 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 43 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 42 or , n - 1 = 12 or , n = 13 a"
a = 44 / 10
a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
c
divide(150, const_2)
he total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c"
a = 150 / 2
a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 24 hr , e ) 30 hr
e
inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 7), 1), 7))))
a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 7 hours to fill the tank . the leak can drain all the water of the tank in ?
"work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 7 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : e"
a = 1 / 2 b = 2 * 7 c = b + 1 d = c / 7 e = 1/(d) f = a - e g = 1/(f)
a ) 33 , b ) 37 , c ) 41 , d ) 45 , e ) 49
d
add(add(lcm(7, multiply(divide(7, 2), 3)), 3), lcm(7, multiply(divide(7, 2), 3)))
a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
"5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 3 = 24 . the minimum number of horses and ponies is 45 . the answer is d ."
a = 7 / 2 b = a * 3 c = math.lcm(7, b) d = c + 3 e = 7 / 2 f = e * 3 g = math.lcm(7, f) h = d + g
a ) 88 , b ) 90 , c ) 92 , d ) 96 , e ) 98
a
multiply(choose(13, 2), choose(10, 1))
there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ?
"n ( s ) = sample space = 23 c 3 = 1771 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 13 or 1 girl from 10 = 13 c 2 + 10 c 1 = 88 ans - a"
a = math.comb(13, 2) b = math.comb(10, 1) c = a * b
a ) 75 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
a
subtract(multiply(75, const_3), add(70, 80))
a student gets 70 % in one subject , 80 % in the other . to get an overall of 75 % how much should get in third subject .
"a student gets 70 % in one subject , 80 % in the other . average of 2 subjects is 75 % , if they have equal weightage . to get an overall of 75 % , he should get 75 % in third subject to maintain same % age . . if they have equal weightage . answer : a"
a = 75 * 3 b = 70 + 80 c = a - b
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
a
divide(subtract(85, multiply(5, 2)), add(10, 5))
carina has 85 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
"lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 85 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 75 / 15 . = 5 a"
a = 5 * 2 b = 85 - a c = 10 + 5 d = b / c
a ) 10 litres , b ) 12 litres , c ) 14 litres , d ) 18 litres , e ) none of these
c
divide(20, add(1, divide(1, 2)))
how much water must be added to 56 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
"c . p . of 1 litre of milk = ( 20 Γ— 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 56 litres of milk = ( 1 ⁄ 4 Γ— 56 ) litres = 14 litres . answer c"
a = 1 / 2 b = 1 + a c = 20 / b
a ) 1500 , b ) 2500 , c ) 2507 , d ) 3200 , e ) 11500
b
divide(2000, subtract(const_1, divide(multiply(4, 5), const_100)))
if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2000 less than the principal . what was the principal ?
"p - 2000 = ( p * 5 * 4 ) / 100 p = 2500 answer : b"
a = 4 * 5 b = a / 100 c = 1 - b d = 2000 / c
a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240
d
add(add(add(add(add(add(add(10, 10), add(10, const_2)), add(10, const_1)), 10), 10), const_2), const_1)
if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ?
"if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 21 c 2 = 21 * 20 / 2 = 210 . therefore , the answer is d"
a = 10 + 10 b = 10 + 2 c = a + b d = 10 + 1 e = c + d f = e + 10 g = f + 10 h = g + 2 i = h + 1
a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
e
add(multiply(add(multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, 2)), power(const_100, 2))), add(multiply(divide(2, const_100), power(const_100, 2)), power(const_100, 2))), divide(4, const_100)), multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, 2)), power(const_100, 2))))
jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
"if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 926 . answer : e ."
a = 3 / 100 b = 2 / 100 c = 100 ** 2 d = b * c e = 100 ** 2 f = d + e g = a * f h = 2 / 100 i = 100 ** 2 j = h * i k = 100 ** 2 l = j + k m = g + l n = 4 / 100 o = m * n p = 3 / 100 q = 2 / 100 r = 100 ** 2 s = q * r t = 100 ** 2 u = s + t v = p * u w = o + v
a ) 30 , b ) 54 , c ) 72 , d ) 84 , e ) 27
a
divide(multiply(110, const_3), add(const_10, const_1))
the sum of the numbers is 110 . if the first number be twice the second and third number be one - third of the first , then the second number is :
"let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 110 11 x / 3 = 110 x = 30 answer : a"
a = 110 * 3 b = 10 + 1 c = a / b
a ) 21.84 , b ) 50.96 , c ) 53.84 , d ) 24.84 , e ) 50.26
b
divide(multiply(139.00, add(divide(const_1, 10), const_1)), 3)
total dinning bill of 3 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
"dinner bill of 3 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 3 = $ 50.96 answer : b"
a = 1 / 10 b = a + 1 c = 139 * 0 d = c / 3
a ) 1 : 8 , b ) 1 : 6 , c ) 25 : 9 , d ) 1 : 3 , e ) 1 : 2
c
divide(circle_area(5), circle_area(3))
the ratio of the radius of two circles is 5 : 3 , and then the ratio of their areas is ?
"r 1 : r 2 = 5 : 3 Ο€ r 12 : Ο€ r 22 r 12 : r 22 = 25 : 9 answer : c"
a = circle_area / (
a ) 18 , b ) 15 , c ) 13 , d ) 14 , e ) 12
d
subtract(multiply(log(divide(power(4, 4), const_2)), const_2), 4)
the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 512,000 locusts ?
"- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 + 12 hours : 256,000 + 14 hours : 512,000 answer : d"
a = 4 ** 4 b = a / 2 c = math.log(b) d = c * 2 e = d - 4
a ) 1 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 6 %
d
multiply(divide(subtract(add(20, const_100), add(14, const_100)), add(20, const_100)), const_100)
if the price of gasoline increases by 20 % and a driver intends to spend only 14 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.14 ( p * x ) y = ( 1.14 / 1.2 ) x = 0.95 x which is a reduction of 5 % . the answer is d .
a = 20 + 100 b = 14 + 100 c = a - b d = 20 + 100 e = c / d f = e * 100
a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225
b
divide(subtract(343, multiply(multiply(const_4, const_2), const_3)), const_2)
a cube is divided into 343 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
"each side of the cube has 7 x 7 = 49 cubelets . only the interior cubelets are painted one colour . on each side , 5 x 5 = 25 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 25 = 150 the answer is b ."
a = 4 * 2 b = a * 3 c = 343 - b d = c / 2
a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
c
add(divide(subtract(multiply(20, 7), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), const_1))), 7), add(add(add(add(const_1, const_2), const_1), const_1), const_1))
the average of 7 consecutive numbers is 20 . the largest of these numbers is :
"explanation : let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c"
a = 20 * 7 b = 1 + 2 c = b + 1 d = c + 1 e = d + 1 f = e + 1 g = 1 + f h = g + 1 i = h + 1 j = 1 + 2 k = j + 1 l = k + 1 m = l + 1 n = m + 1 o = 1 + n p = o + 1 q = p + 1 r = q + 1 s = i + r t = a - s u = t / 7 v = 1 + 2 w = v + 1 x = w + 1 y = x + 1 z = u + y
a ) - 4 , b ) - 2 , c ) 2 , d ) 1 and - 5 , e ) can not be determined .
d
divide(power(5, const_2), 4)
a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is 5 , what is the value of x ?
"a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = 5 i . e x ^ 2 + 4 x - 5 = 0 is the quadratic equation which needs to be solved . ( x - 1 ) ( x + 5 ) = 0 hence x = 1 . c = - 5 imo d"
a = 5 ** 2 b = a / 4
a ) 2 cm , b ) 4 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
a
multiply(divide(divide(divide(divide(multiply(divide(volume_cylinder(divide(8, const_2), 1), const_pi), const_3), const_4), 12), const_4), const_4), const_2)
12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 1 cm height . what is the diameter of each sphere ?
"volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 1 cm ^ 3 r = 1 cm d = 2 cm the answer is a ."
a = 8 / 2 b = volume_cylinder / ( c = b * math.pi d = c / 3 e = d / 4 f = e / 12 g = f / 4 h = g * 4
a ) 690.48 , b ) 690.49 , c ) 690.5 , d ) 690.51 , e ) 690.52
a
min(690.47, 690.47)
9 neighbors are to split the cost of topsoil . the cost of the 5 truck loads of dirt was $ 690.47 . what is the least amount of money ( in whole number of dollars ) that they must add to bill if they wants to split this money evenly among his 9 neighbors ?
if the bill was $ 690.47 dollars , how much money should be removed with 1 cent as the smallest unit ? this is equivalent to finding the first number that is divisible by 9 that occurs after 690.47 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 6 + 9 + 0 + 4 + 7 = 26 . if you add 1 , the number is divisible by 9 ( 26 + 1 ) . 27 is divisible by 9 . hence , we need to add 1 cent from this number for it to be divisible by 9 . correct option : a
a = min(690)
a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
e
add(11, sqrt(subtract(divide(multiply(6, 4), 3), 4)))
evaluate : 11 + sqrt ( - 4 + 6 Γ— 4 Γ· 3 )
"according to order of operations , inner brackets first where 6 Γ— 4 Γ· 3 is first calculated since it has a multiplication and a division . 6 Γ— 4 Γ· 3 = 24 Γ· 3 = 8 hence 11 + sqrt ( - 4 + 6 Γ— 4 Γ· 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer e ) 13"
a = 6 * 4 b = a / 3 c = b - 4 d = math.sqrt(c) e = 11 + d
a ) 309 / 26 , b ) 309 / 28 , c ) 309 / 22 , d ) 319 / 26 , e ) 339 / 26
a
divide(multiply(52, 12), divide(64, const_2))
16 people can write 52 book in 12 days working 8 hour a day . then in how many day 206 can be written by 64 people ?
"work per day epr hour per person = 52 / ( 12 * 8 * 16 ) / / eq - 1 people = 64 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 206 / ( p * 8 * 64 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 309 / 26 answer : a"
a = 52 * 12 b = 64 / 2 c = a / b
a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 33.16
c
divide(add(211.00, divide(multiply(15, 211.00), const_100)), 7)
total dinning bill for 7 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
"211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 7 = 34.66 answer : c"
a = 15 * 211 b = a / 100 c = 211 + 0 d = c / 7
a ) 8.1 , b ) 8.3 , c ) 8.6 , d ) 9.6 , e ) 9.0
d
divide(add(8, 812), const_2)
a cyclist bikes x distance at 8 miles per hour and returns over the same path at 812 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
"distance = d 1 = x miles speed = s 1 = 8 miles per hour time = t 1 = distance / speed = x / 8 2 . going from b to a distance = d 2 = x miles speed = s 2 = 12 miles per hour time = t 2 = distance / speed = x / 12 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 12 + x / 8 = x ( 1 / 12 + 1 / 8 ) = = 5 x / 24 speed = 2 x / ( 5 x / 24 ) = 48 / 5 = 9.6 answer : d"
a = 8 + 812 b = a / 2
a ) 7 / 12 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 40 / 69
e
divide(subtract(345, add(subtract(54, divide(multiply(12.5, 104), multiply(const_1, const_100))), 104)), 345)
in a survey of 345 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
"- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 291 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 345 we have to find not part time and not uninsured . in other words not part time and insured = x / 345 = ( 291 - 104 + 13 ) / 345 = 40 / 69 answer is e ."
a = 12 * 5 b = 1 * 100 c = a / b d = 54 - c e = d + 104 f = 345 - e g = f / 345
a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
d
divide(divide(300, 5), 3)
two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team w . if team a ' s average speed was 5 mph greater than team w ' s , what was team w ' s average mph ?
"this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team w ' s speed was s . then team w ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team w . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team w is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
a = 300 / 5 b = a / 3
a ) βˆ’ 48 , b ) βˆ’ 2 , c ) 2 , d ) 9 , e ) 5
e
subtract(subtract(subtract(subtract(add(add(5, 6), subtract(5, 6)), const_1), const_1), const_1), const_1)
if a ( a - 5 ) = 6 and b ( b - 5 ) = 6 where a β‰  b , then a + b =
"i . e . if a = - 1 then b = 6 or if a = 6 then b = - 1 but in each case a + b = - 1 + 6 = 5 answer : option e"
a = 5 + 6 b = 5 - 6 c = a + b d = c - 1 e = d - 1 f = e - 1 g = f - 1
a ) 2 , b ) 7 , c ) 6 , d ) 9 , e ) 10
c
divide(factorial(subtract(add(const_4, 6), const_1)), multiply(factorial(6), factorial(subtract(const_4, const_1))))
how many positive integers less than 100 have a remainder of 6 when divided by 13 ?
"we have to include 6 also . as 13 * 0 + 6 = 6 if somebody says to divide 6 by 13 , we will be telling we have 0 quotient and remainder as 6 . answer is c"
a = 4 + 6 b = a - 1 c = math.factorial(b) d = math.factorial(6) e = 4 - 1 f = math.factorial(e) g = d * f h = c / g
a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
b
divide(subtract(add(multiply(2, 5), 1), add(multiply(3, 3), 5)), subtract(multiply(2, 3), multiply(3, const_1)))
given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 1 = f ( 3 x – 6 )
"explanations we have the function f ( x ) = 3 x – 5 , and we want to some sophisticated algebra with it . let ’ s look at the two sides of the prompt equation separately . the left side says : 2 * [ f ( x ) ] – 1 β€” - this is saying : take f ( x ) , which is equal to its equation , and multiply that by 2 and then subtract 1 . 2 * [ f ( x ) ] – 1 = 2 * ( 3 x – 5 ) – 1 = 6 x – 10 – 1 = 6 x – 11 the right side says f ( 3 x – 6 ) β€” this means , take the algebraic expression ( 3 x – 6 ) and plug it into the function , as discussed above in the section β€œ how a mathematician things about a function . ” this algebraic expression , ( 3 x – 6 ) , must take the place of x on both sides of the function equation . f ( 3 x – 6 ) = 3 * [ 3 x – 6 ] – 5 = 9 x – 18 – 5 = 9 x – 23 now , set those two equal and solve for x : 9 x – 23 = 6 x – 11 9 x = 6 x – 11 + 23 9 x = 6 x + 12 9 x – 6 x = 12 3 x = 12 x = 4 answer = b"
a = 2 * 5 b = a + 1 c = 3 * 3 d = c + 5 e = b - d f = 2 * 3 g = 3 * 1 h = f - g i = e / h
a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
a
add(divide(add(const_1, const_4), divide(divide(divide(60, const_2), const_2), const_3)), const_2)
in n is a positive integer less than 200 , and 18 n / 60 is an integer , then n has how many different positive prime factors ?
"( a ) . 18 n / 60 must be an integer . = > 3 n / 10 must be an integer . hence n must be a multiple of 2 * 5 . = > n has 2 different prime integers ."
a = 1 + 4 b = 60 / 2 c = b / 2 d = c / 3 e = a / d f = e + 2
a ) 12 , b ) 96 , c ) 24 , d ) 48 , e ) 98
b
lcm(multiply(3, 8), multiply(4, 8))
the ratio of numbers is 3 : 4 and their h . c . f is 8 . their l . c . m is :
let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 8 . so , the numbers are 24 and 32 . l . c . m of 24 and 32 = 96 . answer : b
a = 3 * 8 b = 4 * 8 c = math.lcm(a, b)
a ) 81000 , b ) 81007 , c ) 74671.875 , d ) 81066 , e ) 81022
c
add(add(59000, multiply(divide(1, 8), 59000)), multiply(divide(1, 8), add(59000, multiply(divide(1, 8), 59000))))
every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 59000 ?
"59000 * 9 / 8 * 9 / 8 = 74671.875 answer : c"
a = 1 / 8 b = a * 59000 c = 59000 + b d = 1 / 8 e = 1 / 8 f = e * 59000 g = 59000 + f h = d * g i = c + h
a ) 650 , b ) 882 , c ) 772 , d ) 652 , e ) 271
a
add(500, multiply(500, divide(30, const_100)))
a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 30 % ?
"cost price = rs . 500 profit = 30 % of 500 = rs . 150 selling price = cost price + profit = 500 + 150 = 650 answer : a"
a = 30 / 100 b = 500 * a c = 500 + b
a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 18
c
subtract(power(divide(add(20, 8), const_2), const_2), power(subtract(20, divide(add(20, 8), const_2)), const_2))
if the sum and difference of two numbers are 20 and 8 respectively , then the difference of their square is :
"let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 8 = 160 . answer : c"
a = 20 + 8 b = a / 2 c = b ** 2 d = 20 + 8 e = d / 2 f = 20 - e g = f ** 2 h = c - g
a ) 200 km , b ) 250 km , c ) 224 km , d ) 255 km , e ) 260 km
c
add(multiply(divide(10, const_2), 24), multiply(divide(10, const_2), 21))
raja complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
consider x - - > ( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 = = > x / 21 + x / 24 = 20 15 x = 168 * 20 = = > 224 km answer c
a = 10 / 2 b = a * 24 c = 10 / 2 d = c * 21 e = b + d
a ) 44 % , b ) 46 % , c ) 48 % , d ) 50 % , e ) 51 %
a
multiply(subtract(multiply(divide(add(const_100, 20), const_100), divide(add(const_100, 20), const_100)), const_1), const_100)
the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is :
"let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy a"
a = 100 + 20 b = a / 100 c = 100 + 20 d = c / 100 e = b * d f = e - 1 g = f * 100
a ) 1 km , b ) 500 mts , c ) 600 mts , d ) 2 km , e ) 250 mts
c
multiply(multiply(divide(divide(11, const_60), add(add(divide(const_1, 2), divide(const_1, 4)), divide(const_1, 6))), const_3), const_1000)
a person travels equal distances with speeds of 2 km / hr , 4 km / hr , 6 km / hr . and takes a total time of 11 minutes . find the total distance ?
"let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 4 ) + ( x / 6 ) = 11 / 60 x = 0.2 total distance = 3 * 0.2 = 0.6 km = 600 meters correct option is c"
a = 11 / const_60 b = 1 / 2 c = 1 / 4 d = b + c e = 1 / 6 f = d + e g = a / f h = g * 3 i = h * 1000
a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 81
e
divide(circle_area(1), circle_area(9))
the ratio of the radius of two circles is 1 : 9 , and then the ratio of their areas is ?
"r 1 : r 2 = 1 : 9 Ο€ r 12 : Ο€ r 22 r 12 : r 22 = 1 : 81 answer : e"
a = circle_area / (
a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12
e
add(6, divide(multiply(6, subtract(12000, 9000)), subtract(9000, 6000)))
the average salary of all the workers in a workshop is rs . 9000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
"let the total number of workers be x . then , 9000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 3000 x = 36000 = x = 12 . answer : e"
a = 12000 - 9000 b = 6 * a c = 9000 - 6000 d = b / c e = 6 + d
a ) 6 , b ) 7 , c ) 9 , d ) 4 , e ) 11
d
subtract(add(multiply(divide(60, const_100), const_10), const_1), 3)
the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 60 % ? i will see what is the quickest way to solve it then i will provide the explanation
the following approach might be the easiest one and less error prone . we need on - time departure rate to be higher than 6 / 10 , so it should be at least 7 / 11 , which means that 7 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 7 - 3 = 4 subsequent flights need to depart on - time . answer : d
a = 60 / 100 b = a * 10 c = b + 1 d = c - 3
a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 45
d
divide(subtract(subtract(300, 80), 60), const_4)
6 ) a marketing firm determined that , of 300 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
"220 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 220 = > 4 x = 160 = > x = 40 answer - d"
a = 300 - 80 b = a - 60 c = b / 4
a ) 7 / 15 , b ) 11 / 25 , c ) 17 / 35 , d ) 23 / 45 , e ) 27 / 55
d
divide(const_4, add(multiply(const_4, 8), const_1))
tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 8 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
"tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 15 / 24 ) = 8 / 15 hours peter worked for 23 / 15 hours so he painted 23 / 15 * 1 / 3 = 23 / 45 of the room . the answer is d ."
a = 4 * 8 b = a + 1 c = 4 / b
['a ) 3', 'b ) 4', 'c ) 5', 'd ) 6', 'e ) 7']
d
divide(add(const_4, const_2), const_1)
a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube ?
if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d .
a = 4 + 2 b = a / 1
a ) 4 / 25 , b ) 8 / 23 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 5
e
divide(divide(multiply(40, 40), const_100), add(divide(multiply(40, 40), const_100), divide(multiply(40, subtract(const_100, 40)), const_100)))
at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 40 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
"let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 40 % of 60 = 24 total new books = 24 + 16 = 40 fraction = 16 / 40 = 2 / 5 ans : e"
a = 40 * 40 b = a / 100 c = 40 * 40 d = c / 100 e = 100 - 40 f = 40 * e g = f / 100 h = d + g i = b / h
a ) $ 11.73 , b ) $ 12.66 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
b
multiply(multiply(divide(209.00, add(const_100, 15)), const_100), divide(const_1, 15))
the price of lunch for 15 people was $ 209.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
"take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 209 is for 115 then we have to calculate for 100 for 115 209 for 100 x so by cross multiplication we get 115 x = 100 * 209 = > x = 100 * 209 / 110 by simplifying we get x as 190 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 190 / 15 = 12.66 so our answer is b )"
a = 100 + 15 b = 209 / 0 c = b * 100 d = 1 / 15 e = c * d
a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 11.35 , e ) 43.75
e
divide(subtract(multiply(50, 44), add(45, 55)), subtract(50, const_2))
the average of 50 numbers id 44 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
"explanation : total of 50 numbers = ( 50 Γ— 44 ) = 2200 total of 48 numbers = ( 2200 - ( 45 + 55 ) ] = 2100 required average = 2100 / 48 = 43.75 answer : e"
a = 50 * 44 b = 45 + 55 c = a - b d = 50 - 2 e = c / d
a ) 25 % , b ) 32.5 % , c ) 14 % , d ) 37.5 % , e ) 40 %
c
multiply(divide(12, 14), const_100)
mike earns $ 14 per hour and phil earns $ 12 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
"what % less of 14 is 12 let it be x % less , then = 14 ( 1 - x / 100 ) = 12 1 - x / 100 = 12 / 14 x = 100 / 7 x = 14 % ans c"
a = 12 / 14 b = a * 100
a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7
d
subtract(divide(8, const_2), multiply(45, 45))
what is the remainder when 45 * 49 is divided by 8 ?
"we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 45 * 49 ) / 8 } } = remainder of ( 45 / 8 ) * remainder of ( 49 / 8 ) = 5 * 1 = 7 answer : d"
a = 8 / 2 b = 45 * 45 c = a - b
a ) 3 / 10 , b ) 1 / 70 , c ) 3 / 14 , d ) 1 / 10 , e ) 11 / 14
a
divide(power(6, const_2), multiply(multiply(6, subtract(6, const_1)), subtract(subtract(6, const_1), const_1)))
6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ?
the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose a and b and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : a
a = 6 ** 2 b = 6 - 1 c = 6 * b d = 6 - 1 e = d - 1 f = c * e g = a / f
a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
e
multiply(divide(divide(subtract(50, 68), subtract(68, 80)), add(divide(subtract(50, 68), subtract(68, 80)), const_1)), const_100)
solution x is 80 % chemical a and 20 % chemical b by volume . solution y is 50 % chemical a and 50 % chemical b by volume . if a mixture of x and y is 68 % chemical a , what percent of the mixture is solution x ?
"the volume of the mixture be x + y . 0.8 x + 0.5 y = 0.68 ( x + y ) 0.12 x = 0.18 y x = 3 y / 2 x / ( x + y ) = ( 3 y / 2 ) / ( 5 y / 2 ) = 3 / 5 = 40 % . the answer is e ."
a = 50 - 68 b = 68 - 80 c = a / b d = 50 - 68 e = 68 - 80 f = d / e g = f + 1 h = c / g i = h * 100
a ) 22 , b ) 50 , c ) 55 , d ) 52 , e ) 12
c
multiply(11, 5)
what number has a 5 : 1 ratio to the number 11 ?
"5 : 1 = x : 10 x = 55 answer : c"
a = 11 * 5
a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 20 % , e ) 10 %
d
multiply(divide(subtract(multiply(add(const_1, divide(50, const_100)), divide(50, const_100)), divide(50, const_100)), add(subtract(multiply(add(const_1, divide(50, const_100)), divide(50, const_100)), divide(50, const_100)), const_1)), const_100)
in a class , if 50 % of the boys were girls , then there would be 50 % more girls than boys . what percentage of the overall class is girls ?
detailed solution for questions of this type , it is best to go from the final step . in the final state , the number of girls should be 1.5 * the number of boys . when 50 % of the boys are taken as girls , let the number of boys = x number of girls = 1.5 x total number of students = 2.5 x original number of boys = 2 x ( 50 % of boys = x ) original number of girls = 0.5 x girls form 20 % of the overall class . correct answer d .
a = 50 / 100 b = 1 + a c = 50 / 100 d = b * c e = 50 / 100 f = d - e g = 50 / 100 h = 1 + g i = 50 / 100 j = h * i k = 50 / 100 l = j - k m = l + 1 n = f / m o = n * 100
a ) 10 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
a
divide(subtract(30, 10), const_2)
a man can row downstream at the rate of 30 kmph and upstream at 10 kmph . find the man ’ s rate in still water and rate of current ?
"rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 30 + 10 ) = 20 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 30 - 10 ) = 1 / 2 ( 20 ) = 10 kmph answer is a ."
a = 30 - 10 b = a / 2
a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
a
multiply(divide(subtract(multiply(multiply(const_12, multiply(const_4, const_4)), const_1000), multiply(multiply(const_12, const_1000), const_10)), multiply(multiply(const_12, const_1000), const_10)), const_100)
the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 192,000 . what was the percent increase in the cost of the home ?
increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
a = 4 * 4 b = 12 * a c = b * 1000 d = 12 * 1000 e = d * 10 f = c - e g = 12 * 1000 h = g * 10 i = f / h j = i * 100
a ) 11.11 % , b ) 25 % , c ) 22 % , d ) 29 % , e ) 45 %
a
subtract(multiply(divide(const_100, 900), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)
a dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg , what is his percent ?
"900 - - - 100 100 - - - ? = > 11.11 % answer : a"
a = 100 / 900 b = 3 + 2 c = b * 2 d = 100 * c e = a * d f = e - 100