options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
|---|---|---|---|---|---|
a ) 276 , b ) 289 , c ) 480 , d ) 400 , e ) 278 | c | multiply(divide(4000, add(4000, add(multiply(3000, 2), multiply(2000, 2)))), 4000) | a , b and c invests rs . 4000 , rs . 3000 and rs . 2000 in a business . after one year b removed his money ; a and c continued the business for one more year . if the net profit after 2 years be rs . 2400 , then b ' s share in the profit is ? | "4 * 24 : 3 * 12 : 2 * 24 8 : 3 : 4 3 / 15 * 2400 = 480 answer : c" | a = 3000 * 2
b = 2000 * 2
c = a + b
d = 4000 + c
e = 4000 / d
f = e * 4000
|
a ) 10 hr , b ) 14 hr , c ) 12 hr , d ) 9 hr , e ) 15 hr | b | inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 3), 1), 3)))) | a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water in ? | "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 leak will empty the tank in 14 hrs answer is b" | a = 1 / 2
b = 2 * 3
c = b + 1
d = c / 3
e = 1/(d)
f = a - e
g = 1/(f)
|
a ) rs . 32 , b ) rs . 28 , c ) rs . 36 , d ) rs . 25 , e ) none of these | e | multiply(multiply(16, const_4), divide(352, add(16, 4))) | the cost of 16 pens and 8 pencils is rs . 352 and the cost of 4 pens and 4 pencils is rs . 96 . find the cost of each pen ? | "let the cost of each pen and pencil be ' p ' and ' q ' respectively . 16 p + 8 q = 352 - - - ( 1 ) 4 p + 4 q = 96 8 p + 8 q = 192 - - - ( 2 ) ( 1 ) - ( 2 ) = > 8 p = 160 = > p = 20 answer : e" | a = 16 * 4
b = 16 + 4
c = 352 / b
d = a * c
|
a ) 80 , b ) 100 , c ) 150 , d ) 180 , e ) 220 | e | multiply(divide(const_60, 15), 55) | if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 55 minutes ? | "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 55 minutes the population increases by 55 x 4 = 220 people . answer . e ." | a = const_60 / 15
b = a * 55
|
a ) 1 / 32 , b ) 1 / 1296 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34 | b | multiply(multiply(multiply(divide(const_1, 6), divide(const_1, 6)), divide(const_1, 6)), divide(const_1, 6)) | five 6 faced dice are thrown together . the probability that all the three show the same number on them is ? | the three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways . hence the probability is 6 / 7776 = 1 / 1296 answer : b | a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
|
a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 11 . | e | add(multiply(21, divide(const_1, 1)), const_1) | in the junior basketball league there are 21 teams , 1 / 3 of them are bad and Β½ are rich . what ca n ' t be the number of teams that are rich and bad ? | "total teams = 21 bad teams = ( 1 / 3 ) * 21 = 7 rich teams = 10 so maximum value that the both rich and bad can take will be 10 . so e = 11 can not be that value . ans e ." | a = 1 / 1
b = 21 * a
c = b + 1
|
a ) 500 , b ) 600 , c ) 750 , d ) 800 , e ) none of them | b | multiply(divide(const_1, add(add(const_4, 3), const_1)), 1200) | a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a . | "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a β s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 Β» ) = rs . 150 . answer is b" | a = 4 + 3
b = a + 1
c = 1 / b
d = c * 1200
|
a ) 56 days , b ) 420 days , c ) 46 days , d ) 560 days , e ) 96 days | a | add(inverse(multiply(60, const_2)), inverse(multiply(35, const_3))) | a can do a half of certain work in 60 days and b one third of the same in 35 days . they together will do the whole work in . | "a = 120 days b = 105 days 1 / 120 + 1 / 105 = 45 / 2520 = 1 / 56 = > 56 days answer : a" | a = 60 * 2
b = 1/(a)
c = 35 * 3
d = 1/(c)
e = b + d
|
a ) 6 , b ) 4 , c ) 0 , d ) 8 , e ) 7 | b | subtract(add(15, power(add(const_1, const_4), 2)), multiply(12, 3)) | if p is a prime number greater than 3 , find the remainder when p ^ 2 + 15 is divided by 12 . | "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 15 = 36 n ^ 2 + 12 n + 1 + 15 = 36 n ^ 2 + 12 n + 12 + 4 if p = 6 n - 1 , then p ^ 2 + 15 = 36 n ^ 2 - 12 n + 1 + 15 = 36 n ^ 2 - 12 n + 12 + 4 when divided by 12 , it must leave a remainder of 4 . the answer is b ." | a = 1 + 4
b = a ** 2
c = 15 + b
d = 12 * 3
e = c - d
|
a ) 8 % , b ) 14 % , c ) 26 % , d ) 15 % , e ) 17 % | c | subtract(subtract(add(40, const_100), divide(multiply(add(40, const_100), 10), const_100)), const_100) | a merchant marks his goods up by 40 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ? | "let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 10 % on 126 . profit = 126 - 100 26 % answer c" | a = 40 + 100
b = 40 + 100
c = b * 10
d = c / 100
e = a - d
f = e - 100
|
a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9 | c | add(multiply(floor(power(100, inverse(3))), const_10), add(floor(power(100, inverse(3))), const_1)) | if a and b are positive numbers , and a ^ 3 + b ^ 3 = 100 , then the greatest possible value of a is between : | "if a = 4.5 and b is a bit more than 2 , then a ^ 3 + b ^ 3 can equal 100 . if a > 5 , then a ^ 3 + b ^ 3 > 100 . the answer is c ." | a = 1/(3)
b = 100 ** a
c = math.floor(b)
d = c * 10
e = 1/(3)
f = 100 ** e
g = math.floor(f)
h = g + 1
i = d + h
|
a ) 9 , b ) 31 , c ) 56 , d ) 72 , e ) 90 | c | subtract(subtract(multiply(18, 15), multiply(5, 14)), multiply(9, 16)) | the average age of 18 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ? | age of the 15 th student = 18 * 15 - ( 14 * 5 + 16 * 9 ) = 270 - 214 = 56 years answer is c | a = 18 * 15
b = 5 * 14
c = a - b
d = 9 * 16
e = c - d
|
a ) $ 16,200 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500 | a | multiply(1800, power(const_3, divide(28, divide(112, 8)))) | money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 1800 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ? | "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1800 triples to $ 5400 , in 28 years , it will again triple to $ 5400 * 3 = $ 16,200 answer a" | a = 112 / 8
b = 28 / a
c = 3 ** b
d = 1800 * c
|
a ) s . 240 , b ) s . 140 , c ) s . 340 , d ) s . 50 , e ) s . 90 | b | subtract(divide(divide(700, add(divide(1, 2), divide(1, 3))), 2), divide(divide(700, add(divide(1, 2), divide(1, 3))), 3)) | a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ? | "a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 420 - 280 = 140 answer : b" | a = 1 / 2
b = 1 / 3
c = a + b
d = 700 / c
e = d / 2
f = 1 / 2
g = 1 / 3
h = f + g
i = 700 / h
j = i / 3
k = e - j
|
a ) 28.5 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these | c | subtract(divide(multiply(add(const_100, 23.5), const_100), subtract(const_100, 5)), const_100) | a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount had been offered ? | "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 Γ ( 100 + 23.5 ) / ( 100 β 5 ) = 100 Γ 247 / 190 = 130 hence , required % profit = 130 β 100 = 30 % answer c" | a = 100 + 23
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
|
a ) 2 : 7 , b ) 2 : 6 , c ) 17 : 6 , d ) 2 : 3 , e ) 7 : 8 | d | divide(10000, 15000) | p and q started a business investing rs 10000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively . | "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 10000 : 15000 = 10 : 15 = 2 : 3 option d" | a = 10000 / 15000
|
a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.11111 | e | multiply(divide(0.99999, 0.11112), const_100) | 0.99999 + 0.11112 = ? | "0.99999 + 0.11112 = 0.99999 + 0.11111 + 0.00001 = ( 0.99999 + 0.00001 ) + 0.11111 = 1 + 0.11111 = 1.11111 e" | a = 0 / 99999
b = a * 100
|
a ) 11.2 β 2 , b ) 13 β 2 , c ) 23 β 2 , d ) 12 β 4 , e ) 13 β 9 | a | sqrt(multiply(add(power(divide(40, const_4), const_2), power(divide(20, const_4), const_2)), const_2)) | the perimeter of one square is 40 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ? | "4 a = 40 4 a = 20 a = 10 a = 5 a 2 = 100 a 2 = 25 combined area = a 2 = 125 = > a = 11.2 d = 11.2 β 2 answer : a" | a = 40 / 4
b = a ** 2
c = 20 / 4
d = c ** 2
e = b + d
f = e * 2
g = math.sqrt(f)
|
a ) s . 650 , b ) s . 690 , c ) s . 680 , d ) s . 700 , e ) s . 720 | c | subtract(815, divide(multiply(subtract(860, 815), 3), 4)) | a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 860 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 860 - 815 ) = rs . 45 . s . i . for 3 years = rs . ( 45 x 3 ) = rs . 135 . principal = rs . ( 815 - 135 ) = rs . 680 . answer : option c" | a = 860 - 815
b = a * 3
c = b / 4
d = 815 - c
|
a ) s . 650 , b ) s . 638 , c ) s . 698 , d ) s . 700 , e ) s . 760 | b | subtract(815, divide(multiply(subtract(874, 815), 3), 4)) | a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 874 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 874 - 815 ) = rs . 59 . s . i . for 3 years = rs . ( 59 x 3 ) = rs . 177 . principal = rs . ( 815 - 177 ) = rs . 638 . answer : option b" | a = 874 - 815
b = a * 3
c = b / 4
d = 815 - c
|
a ) 7 / 98 , b ) 1 / 48 , c ) 1 / 98 , d ) 1 / 96 , e ) 3 / 42 | e | inverse(multiply(2, 7)) | the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 3 / 8 is given by ? | 2 / 3 * 6 / 7 * 1 / 3 * 3 / 8 = 36 / 504 = 3 / 42 answer : e | a = 2 * 7
b = 1/(a)
|
a ) 3.5 , 8.5 , b ) 7 , 5 , c ) 7.5 , 4.5 , d ) 8 , 4 , e ) 8 , 5 | c | floor(subtract(12, divide(subtract(multiply(12, 15), multiply(12, 12)), subtract(20, 12)))) | find the quantities of two types of rice to be mixed , first variety is of rs . 12 per kg and second variety is of rs . 20 per kg . to get 12 kg of rice mixture worth rs . 15 per kg ? ( in kg ) | from allegation & mixture ratio = c - m / m - d = 20 - 15 / 15 - 12 = 5 / 3 . from the option c r = 7.5 / 4.5 = 5 / 3 answer : c | a = 12 * 15
b = 12 * 12
c = a - b
d = 20 - 12
e = c / d
f = 12 - e
g = math.floor(f)
|
a ) 5 , b ) 1 , c ) 3 , d ) 6 , e ) 7 | d | add(choose(3, 2), choose(3, 2)) | there are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . | "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 3 and for second = 2 so total methods = 3 * 2 = 6 answer : d" | a = math.comb(3, 2)
b = math.comb(3, 2)
c = a + b
|
a ) 50 km , b ) 45 km , c ) 33 km , d ) 60 km , e ) 54 km | d | multiply(add(divide(add(multiply(2, 10), 20), subtract(20, 10)), 2), 10) | a boy is traveling from his house to school at 10 km / hr and reached school 2 hours late . next day he traveled 20 km / hr and reached 1 hour early . then find the distance between house and school ? | let distance be x s 1 = 10 km / hr s 2 = 20 km / hr t 1 = x / 10 hr t 2 = x / 20 hr difference in time = 2 + 1 = 3 hr ( x / 10 ) - ( x / 20 ) = 3 x = 60 km answer is d | a = 2 * 10
b = a + 20
c = 20 - 10
d = b / c
e = d + 2
f = e * 10
|
a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 415 , e ) none of these | d | divide(subtract(multiply(30, 350), multiply(15, 285)), 15) | the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 285 , then the mean profit for the last 15 days would be | "average would be : 350 = ( 285 + x ) / 2 on solving , x = 415 . answer : d" | a = 30 * 350
b = 15 * 285
c = a - b
d = c / 15
|
a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | c | add(divide(subtract(7.20, multiply(0.80, const_2)), 0.50), const_2) | a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.20 , what total number of apples and bananas did the customer purchase ? | "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.20 until we get a multiple of $ 0.50 . $ 7.20 , $ 6.40 , $ 5.60 , $ 4.80 , $ 4.00 = 8 * $ 0.50 the customer purchased 8 bananas and 4 apples . the answer is c ." | a = 0 * 80
b = 7 - 20
c = b / 0
d = c + 2
|
a ) 6.25 , b ) 8.42 , c ) 8.3 , d ) 8.1 , e ) 6.21 | b | divide(subtract(282, multiply(7, 4.2)), 30) | in the first 7 overs of a cricket game , the run rate was only 4.2 . what should be the rate in the remaining 30 overs to reach the target of 282 runs ? | "required run rate = [ 282 - ( 4.2 * 7 ) ] / 30 = 252.60 / 40 = 8.42 answer : b" | a = 7 * 4
b = 282 - a
c = b / 30
|
a ) 51.6 , b ) 51.5 , c ) 51.7 , d ) 51.1 , e ) 51.0 | b | divide(subtract(add(add(30, 35), 42), const_2), const_2) | an empty tank be filled with an inlet pipe β a β in 42 minutes . after 12 minutes an outlet pipe β b β is opened which can empty the tank in 30 minutes . after 6 minutes another inlet pipe β c β opened into the same tank , which can fill the tank in 35 minutes and the tank is filled . find the time taken to fill the ta... | assume total tank capacity = 210 liters now capacity of pipe a = 210 / 42 = 5 liters capacity of b = 210 / 30 = - 7 liters capacity of c = 210 / 35 = 6 min assume tank gets filled in x min after the third pipe got opened . so x Γ 5 + 6 Γ ( β 2 ) + 4 x = 210 x Γ 5 + 6 Γ ( β 2 ) + 4 x = 210 β 48 + 4 x = 210 β 4 x = 162 β... | a = 30 + 35
b = a + 42
c = b - 2
d = c / 2
|
a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | d | subtract(50, subtract(add(25, 23), 21)) | in a group of 50 people , 25 have visited iceland and 23 have visited norway . if 21 people have visited both iceland and norway , how many people have visited neither country ? | "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 50 = 25 + 23 - 21 + ( # in neither group ) = 23 the prompt gives you all of t... | a = 25 + 23
b = a - 21
c = 50 - b
|
a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3 | d | subtract(divide(4, divide(3, 5)), 4) | a container holds 4 quarts of alcohol and 4 quarts of water . how many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume ? | let the number of quarts that should be added to get the required ratio = x so total quarts of water = ( x + 4 ) but the original number of quarts of alcohol remains the same , so we have : 4 / ( x + 4 ) = 3 / 5 cross - multiply : now we have 20 = 3 x + 12 = > 3 x = 20 - 12 = > x = 8 / 3 answer - d | a = 3 / 5
b = 4 / a
c = b - 4
|
a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 26 | b | subtract(37, add(add(8, const_2), 8)) | set a of 8 positive integers may have the same element and have 37 . and set b of 8 positive integers must have different elements and have 37 . when m and n are the greatest possible differences between 37 and other elements β sums in set a and set b , respectively , m - n = ? | this is maximum - minimum . hence , 37 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 30 and 37 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 9 . so , 30 - 9 = 21 . the correct answer is b . | a = 8 + 2
b = a + 8
c = 37 - b
|
a ) 2 , b ) 4 , c ) 7 , d ) 14 , e ) 56 | b | lcm(6, 8) | if 6 and 8 are factors of 60 n , what is the minimum value of n ? | "60 n / 6 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 3 * 2 * 2 * 2 = 5 * n / 4 must be an integer for this to be true n must multiple of 4 , thus min of n = 4 hence b" | a = math.lcm(6, 8)
|
a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3 | b | subtract(15, add(multiply(const_4, 2), multiply(const_4, 1.5))) | an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how m... | "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = q , leaving 1 m of empty space . thus , i believe the answer is b ) 1" | a = 4 * 2
b = 4 * 1
c = a + b
d = 15 - c
|
a ) 20 , b ) 25 , c ) 30 , d ) 32 , e ) 42 | a | multiply(8, const_2) | if the average of 8 x and 8 y is greater than 120 , and x is twice y , what is the least integer value of x ? | "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 ... | a = 8 * 2
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a ) 179 , b ) 202 , c ) 210 , d ) 223 , e ) 229 | b | divide(add(150, subtract(multiply(61, 46), multiply(58, subtract(46, const_2)))), const_2) | the batting average of a particular batsman is 61 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score . | "explanation : total runs scored by the batsman = 61 * 46 = 2806 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2806 β 2552 = 254 runs . let the highest score be x , hence the lowest score = x β 150 x + ( x - 150 ) = 254 2 x = 404 x = 202 runs answer ... | a = 61 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 150 + d
f = e / 2
|
a ) 377 , b ) 126 , c ) 111 , d ) 727 , e ) 121 | c | sqrt(add(power(sqrt(subtract(37, multiply(const_2, 4107))), const_2), multiply(const_4, 4107))) | the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is ? | "let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c" | a = 2 * 4107
b = 37 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 4107
f = d + e
g = math.sqrt(f)
|
a ) 6 / Ο , b ) 9 / Ο , c ) 6 , d ) 9 , e ) 12 | d | add(divide(multiply(multiply(4, const_pi), divide(3, const_pi)), 2), multiply(const_pi, divide(3, const_pi))) | the surface area of a sphere is 4 Ο r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area t of that hemisphere ? | "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total sur... | a = 4 * math.pi
b = 3 / math.pi
c = a * b
d = c / 2
e = 3 / math.pi
f = math.pi * e
g = d + f
|
a ) 26 , b ) 32 , c ) 35 , d ) 30 , e ) 45 | a | divide(add(408, 216), multiply(multiply(multiply(const_2, const_2), const_2), const_3)) | there are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed . | "explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a" | a = 408 + 216
b = 2 * 2
c = b * 2
d = c * 3
e = a / d
|
['a ) 18', 'b ) 22', 'c ) 21', 'd ) 20', 'e ) 19'] | b | multiply(const_2, sqrt(divide(250, const_2))) | the number 250 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ? | sum of the squares of 3 different positive integers = 250 15 ^ 2 + 3 ^ 2 + 4 ^ 2 = 250 now , sum of these 3 different integers = 15 + 3 + 4 = 22 ans - b | a = 250 / 2
b = math.sqrt(a)
c = 2 * b
|
a ) 7.33 % , b ) 9 % , c ) 9.67 % , d ) 11 % , e ) 11.5 % | a | multiply(const_100, divide(multiply(divide(16, const_100), 11), add(13, 11))) | 13 ltr of water is added with 11 ltr of a solution containing 16 % of alcohol in the water . the % of alcohol in the new mixture is ? | "we have an 11 litre solution containing 16 % of alcohol in the water . = > quantity of alcohol in the solution = 11 Γ£ β 16 / 100 now 13 litre of water is added to the solution . = > total quantity of the new solution = 11 + 13 = 24 percentage of alcohol in the new solution = 11 Γ£ β 16 / 100 24 Γ£ β 100 = 11 Γ£ β 1610024... | a = 16 / 100
b = a * 11
c = 13 + 11
d = b / c
e = 100 * d
|
a ) 0.5 , b ) 0.51 , c ) - 0.52 , d ) 0.31 , e ) - 0.49 | c | divide(subtract(12, 49), 71) | a straight line in the xy - plane has y - intercept of 49 . on this line the x - coordinate of the point is 71 and y - coordinate is 12 then what is the slope of the line ? | "eq of line = y = mx + c c = 49 x = 71 y = 12 substitute given : m = ( y - c ) / x = ( 12 - 49 ) / 71 = - 37 / 71 = - 0.52 correct option is c" | a = 12 - 49
b = a / 71
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a ) 36 , b ) 57 , c ) 44 , d ) 48 , e ) 52 | b | add(40, divide(subtract(1116, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100))) | a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1116 in total compen... | "for 40 hrs = 40 * 16 = 640 excess = 1116 - 640 = 476 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 476 / 28 = 17 total hrs = 40 + 17 = 57 answer b 57" | a = 16 * 40
b = 1116 - a
c = 100 + 75
d = 16 * c
e = d / 100
f = b / e
g = 40 + f
|
a ) 271 , b ) 250 , c ) 350 , d ) 277 , e ) 232 | b | subtract(multiply(20, multiply(126, const_0_2778)), 450) | a train 450 m long running at 126 kmph crosses a platform in 20 sec . what is the length of the platform ? | "length of the platform = 126 * 5 / 18 * 20 = 700 β 450 = 250 answer : b" | a = 126 * const_0_2778
b = 20 * a
c = b - 450
|
a ) 200 , b ) 210 , c ) 250 , d ) 190 , e ) 220 | c | add(200, multiply(200, divide(25, const_100))) | 200 is increased by 25 % . find the final number . | explanation final number = initial number + 25 % ( original number ) = 200 + 25 % ( 200 ) = 200 + 50 = 250 . answer c | a = 25 / 100
b = 200 * a
c = 200 + b
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a ) 1.9332 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none | a | multiply(divide(268, const_100), divide(74, const_100)) | given that 268 x 74 = 19332 , find the value of 2.68 x . 74 . | "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 Γ . 74 = 1.9332 answer a" | a = 268 / 100
b = 74 / 100
c = a * b
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a ) 21 % , b ) 22.5 % , c ) 25 % , d ) 30 % , e ) 40 % | d | multiply(divide(subtract(add(add(100, 30), 100), multiply(2, 100)), 100), 100) | a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 30 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he ... | "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.3 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 30 % income the savings increased by 100 % . or s = . 3 i or s = 3... | a = 100 + 30
b = a + 100
c = 2 * 100
d = b - c
e = d / 100
f = e * 100
|
a ) 8 , b ) 14 , c ) 15 , d ) 17 , e ) 30 | d | add(multiply(8, const_2), const_1) | the average age of applicants for a new job is 31 , with a standard deviation of 8 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ? | "within one standard deviation of the average age means 31 + / - 7 23 - - 31 - - 39 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 total = 17 d" | a = 8 * 2
b = a + 1
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a ) 12 , b ) 18 , c ) 24 , d ) 30 , e ) 36 | e | multiply(12, multiply(12, divide(4, multiply(4, 4)))) | 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 12 weavers in 12 days ? | "1 weaver can weave 1 mat in 4 days . 12 weavers can weave 12 mats in 4 days . 12 weavers can weave 36 mats in 12 days . the answer is e ." | a = 4 * 4
b = 4 / a
c = 12 * b
d = 12 * c
|
a ) 420 , b ) 520 , c ) 620 , d ) 620 , e ) none of these | b | add(200, multiply(divide(200, 5), 8)) | in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 200 girls , the total number of students in the college is | explanation : let the boy are 8 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 8 x + 5 x = 13 x = 13 ( 40 ) = 520 answer : b | a = 200 / 5
b = a * 8
c = 200 + b
|
a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2 | b | divide(add(multiply(divide(add(multiply(divide(3, add(3, 2)), subtract(20, 10)), 10), 20), subtract(20, 10)), 10), multiply(divide(multiply(divide(2, add(3, 2)), subtract(20, 10)), 20), subtract(20, 10))) | a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio q of milk and water in the resultant mixture ? | he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of m... | a = 3 + 2
b = 3 / a
c = 20 - 10
d = b * c
e = d + 10
f = e / 20
g = 20 - 10
h = f * g
i = h + 10
j = 3 + 2
k = 2 / j
l = 20 - 10
m = k * l
n = m / 20
o = 20 - 10
p = n * o
q = i / p
|
a ) 6 hr , b ) 2 hr , c ) 4 hr , d ) 1 hr , e ) none of these | b | divide(8, subtract(subtract(divide(96, 8), 4), 4)) | a boatman can row 96 km downstream in 8 hr . if the speed of the current is 4 km / hr , then find in what time will be able to cover 8 km upstream ? | "explanation : speed downstream = 96 β 8 = 12 kmph speed of current = 4 km / hr speed of the boatman in still water = 12 - 4 = 8 kmph speed upstream = 8 - 4 = 4 kmph time taken to cover 8 km upstream = 8 β 4 = 2 hours . answer : option b" | a = 96 / 8
b = a - 4
c = b - 4
d = 8 / c
|
a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 26 | e | subtract(subtract(multiply(16, 15), multiply(5, 14)), multiply(9, 16)) | the average age of 16 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ? | "age of the 15 th student = 16 * 15 - ( 14 * 5 + 16 * 9 ) = 240 - 214 = 26 years answer is e" | a = 16 * 15
b = 5 * 14
c = a - b
d = 9 * 16
e = c - d
|
a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45 | c | divide(50, add(divide(25, 60), divide(subtract(50, 25), 30))) | a driver goes on a trip of 50 kilometers , the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ? | "the time for the first part of the trip was 25 / 60 = 5 / 12 hours . the time for the second part of the trip was 25 / 30 = 5 / 6 hours . the total time for the trip was 5 / 12 + 5 / 6 = 15 / 12 = 5 / 4 hours . the average speed for the trip was 50 / ( 5 / 4 ) = 40 kph the answer is c ." | a = 25 / 60
b = 50 - 25
c = b / 30
d = a + c
e = 50 / d
|
a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15 | b | divide(multiply(const_12, log(2)), log(2)) | if 2 ^ ( 2 w ) = 8 ^ ( w β 2 ) , what is the value of w ? | "2 ^ ( 2 w ) = 8 ^ ( w β 2 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w β 2 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 6 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 6 w = 6 the answer is b ." | a = math.log(2)
b = 12 * a
c = math.log(2)
d = b / c
|
a ) 227.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these | a | subtract(895.7, divide(573.07, 95.007)) | 895.7 β 573.07 β 95.007 = ? | "solution given expression = 895.7 - ( 573.07 + 95.007 ) = 895.7 - 668.077 = 227.623 . answer a" | a = 573 / 7
b = 895 - 7
|
a ) $ 1.40 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20 | a | divide(subtract(9.65, 6.85), const_2) | a train ride from two p to town q costs $ 6.85 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.65 . what is the cost of a bus ride from town p to town q ? | "let x be the cost of a bus ride . x + ( x + 685 ) = 965 2 x = 280 x = $ 1.40 the answer is a ." | a = 9 - 65
b = a / 2
|
a ) 18 , b ) 91 , c ) 11 , d ) 17.4 , e ) 12 | d | subtract(divide(multiply(60, 50), const_100), divide(multiply(42, 30), const_100)) | how much 60 % of 50 is greater than 42 % of 30 ? | "( 60 / 100 ) * 50 β ( 42 / 100 ) * 30 30 - 12.6 = 17.4 answer : d" | a = 60 * 50
b = a / 100
c = 42 * 30
d = c / 100
e = b - d
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | divide(subtract(const_1000, const_100), subtract(250, subtract(250, 150))) | matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ? | let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x... | a = 1000 - 100
b = 250 - 150
c = 250 - b
d = a / c
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | c | multiply(divide(divide(divide(3, power(divide(3, const_10), const_0_33)), power(divide(3, const_10), const_0_33)), divide(divide(3, power(divide(3, const_10), const_0_33)), power(divide(3, const_10), const_0_33))), const_100) | what is the smallest positive integer x for which x 3 + 5 xx 3 + 5 x has a value more than 80 ? | "4 ^ 3 + 5 * 4 = 64 + 20 = 84 that ' s pretty close to 80 already so i can cancel d and e since they ' ll be more than 80 . b just needs to be checked just in case so . . . 3 ^ 3 + 5 * 3 = 27 + 15 = not close to 80 . therefore , 4 ( c ) is the smallest positive integer x for which x ^ 3 + 5 x has a value more than 80 .... | a = 3 / 10
b = a ** const_0_33
c = 3 / b
d = 3 / 10
e = d ** const_0_33
f = c / e
g = 3 / 10
h = g ** const_0_33
i = 3 / h
j = 3 / 10
k = j ** const_0_33
l = i / k
m = f / l
n = m * 100
|
a ) 12 , b ) 72 , c ) 48 , d ) 99 , e ) 11 | b | subtract(divide(multiply(1.75, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(1.25, const_1000), divide(multiply(90, const_1000), const_3600))) | two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.75 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ? | "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.75 + 1.25 = 3 km = 3000 m . required time = 3000 * 3 / 125 = 72 sec . answer : b" | a = 1 * 75
b = 60 * 1000
c = b / 3600
d = a / c
e = 1 * 25
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
|
a ) 4 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9 | a | multiply(divide(20, const_100), 20) | uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 13 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ? | answer is a . x / x + 36 = 1 / 5 x = 9 13 - 9 = 4 | a = 20 / 100
b = a * 20
|
['a ) 23.12', 'b ) 24.12', 'c ) 25.12', 'd ) 26.12', 'e ) 27.12'] | c | multiply(add(divide(2, const_2), 3), multiply(const_2, const_pi)) | a cylinder is inserted in a sphere d / h = 2 / 3 . find the surface area of the cylinder ? | take r = 1 , h = 3 = 2 * 3.14 * r * r + 2 * 3.14 * r * h = 2 * 3.14 * r ( r + h ) = 2 * 3.14 * 1 ( 1 + 3 ) = 2 * 3.14 ( 4 ) = 25.12 answer : c | a = 2 / 2
b = a + 3
c = 2 * math.pi
d = b * c
|
['a ) 90,000', 'b ) 95,000', 'c ) 93,000', 'd ) 92,000', 'e ) 91,000'] | a | add(add(multiply(150, 150), multiply(150, 225)), multiply(225, 150)) | the measurements obtained for the interior dimensions of a rectangular box are 150 cm by 150 cm by 225 cm . if each of the three measurements has an error of at most 1 centimeter , which of the following is the closes maximum possible difference , in cubic centimeters , between the actual capacity of the box and the ca... | the options are well spread so we can approximate . changing the length by 1 cm results in change of the volume by 1 * 150 * 225 = 33,750 cubic centimeters ; changing the width by 1 cm results in change of the volume by 150 * 1 * 225 = 33,750 cubic centimeters ; changing the height by 1 cm results in change of the volu... | a = 150 * 150
b = 150 * 225
c = a + b
d = 225 * 150
e = c + d
|
['a ) 1 : 1', 'b ) 1 : 2', 'c ) 2 : 3', 'd ) 2 : 1', 'e ) none of these'] | d | divide(rectangle_area(const_1, const_1), triangle_area(rectangle_area(const_1, const_1), rectangle_area(const_1, const_1))) | what will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ? | explanation : as far as questions of area or volume and surface area are concerned , it is all about formulas and very little logic . so its a sincere advice to get all formulas remembered before solving these questions . lets solve this , area of rectangle = l β b area of triangle = 1 / 2 l β b ratio = l β b : 1 / 2 l... | a = rectangle_area / (
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a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14 | c | add(divide(add(power(const_3.0, 4), sqrt(add(power(power(4, 4), const_2), power(subtract(316, power(4, 4)), const_2)))), multiply(power(4, const_2), const_2)), subtract(divide(add(power(4, 4), sqrt(add(power(power(4, 4), const_2), power(subtract(316, power(4, 4)), const_2)))), multiply(power(4, const_2), const_2)), 4)) | if one positive integer is greater than another positive integer by 4 , and the difference of their cubes is 316 , what is their sum ? | "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 7 ^ 3 = 343 the two numbers are 3 and 7 . the answer is c ." | a = 3 ** 0
b = 4 ** 4
c = b ** 2
d = 4 ** 4
e = 316 - d
f = e ** 2
g = c + f
h = math.sqrt(g)
i = a + h
j = 4 ** 2
k = j * 2
l = i / k
m = 4 ** 4
n = 4 ** 4
o = n ** 2
p = 4 ** 4
q = 316 - p
r = q ** 2
s = o + r
t = math.sqrt(s)
u = m + t
v = 4 ** 2
w = v * 2
x = u / w
y = x - 4
z = l + y
|
a ) 10 , b ) 12 , c ) 15 , d ) 17 , e ) 18 | a | divide(subtract(multiply(10, subtract(40, 4)), multiply(10, 32)), 4) | the average age of an adult class is 40 years . 10 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ? | "let original strength = y then , 40 y + 10 x 32 = ( y + 10 ) x 36 Γ’ β‘ β 40 y + 320 = 36 y + 360 Γ’ β‘ β 4 y = 40 Γ’ Λ Β΄ y = 10 a" | a = 40 - 4
b = 10 * a
c = 10 * 32
d = b - c
e = d / 4
|
a ) 1 , b ) 499 , c ) 500 , d ) 999 , e ) 10 | e | divide(1000, const_100) | a king has 1000 bottles of wine , a queen wants to kill the king and sends a servant to poison the wine . fortunately the king ' s guard ' s catch d servant after he has only poisoned one bottle and the guard do n ' t know which bottle is poisoned . furthermore it takes one month to have an effect , and there is an ann... | since you need 10 digits to represent 1000 numbers in binary , you will need 10 prisoners . now the logic is this : every bottle has a unique number from 1 to 1000 and a unique binary representation from 0000000001 to 1111101000 . now you have 10 prisoners . each bottle will be tasted by the prisoners depending on the ... | a = 1000 / 100
|
['a ) 120 cm', 'b ) 200 cm', 'c ) 88 cm', 'd ) 666 cm', 'e ) 776 cm'] | b | multiply(sqrt(divide(120, 30)), const_100) | 30 square stone slabs of equal size were needed to cover a floor area of 120 sq . m . find the length of each stone slab ? | area of each slab = 120 / 30 m 2 = 4 m 2 length of each slab β 4 = 2 m = 200 cm b | a = 120 / 30
b = math.sqrt(a)
c = b * 100
|
a ) 14 , b ) 28 , c ) 36 , d ) 84 , e ) 252 | c | add(12, const_1) | if x and y are positive integers and 18 x = 12 y what is the least possible value of xy ? | "18 x = 12 y = > x / y = 2 / 3 = > 3 x = 2 y 3 ( 3 ) = 2 ( 3 ) = > x * y = 9 but it is not given 3 ( 6 ) = 2 ( 6 ) = > x * y = 36 c" | a = 12 + 1
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a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6468 | e | multiply(circumface(multiply(sqrt(divide(13.86, const_pi)), const_100)), 4.90) | the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.90 per metre . | "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.90 ) = rs . 6468 . answer : e ) 6468" | a = 13 / 86
b = math.sqrt(a)
c = b * 100
d = circumface * (
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a ) 6 : 5 , b ) 7 : 5 , c ) 9 : 8 , d ) 8 : 9 , e ) 8 : 7 | c | divide(subtract(divide(9, add(7, 9)), divide(6, add(6, 6))), subtract(divide(6, add(6, 6)), divide(4, add(5, 4)))) | two containers of milk contain mixtures of water and milk in ratio 5 : 4 and 7 : 9 . in what ratio they should be mixed so that mixture is of 6 : 6 ratio ? | 6 / 6 - 5 / 4 = = > - 1 / 4 7 / 9 - 6 / 6 = = > - 2 / 9 now , - 1 / 4 = - 2 / 9 = = > 1 / 4 = 2 / 9 = = > 9 : 8 answer : c | a = 7 + 9
b = 9 / a
c = 6 + 6
d = 6 / c
e = b - d
f = 6 + 6
g = 6 / f
h = 5 + 4
i = 4 / h
j = g - i
k = e / j
|
a ) 25 , b ) 36 , c ) 23 , d ) 49 , e ) 27 | c | subtract(negate(11), multiply(subtract(5, 7), divide(subtract(5, 7), subtract(3, 5)))) | 3 , 5 , 7 , 11 , 13 , 17 , 19 , ____ | "the sequence is a series of prime numbers , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 . . . . answer : c ." | a = negate - (
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a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes | a | divide(360, add(36, divide(36, divide(const_3, const_2)))) | earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 360 envelopes | "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 360 envelopes they will take 360 / 60 mins . i . e . , 6 mins . answer : a" | a = 3 / 2
b = 36 / a
c = 36 + b
d = 360 / c
|
a ) 31 , b ) 35 , c ) 30 , d ) 40 , e ) 28 | a | subtract(multiply(multiply(4, 4), 4), divide(subtract(14, const_1), const_2)) | if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 4 x years from now ? | "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 4 x years from now , age will be 15 + 4 * 4 = 31 option a" | a = 4 * 4
b = a * 4
c = 14 - 1
d = c / 2
e = b - d
|
a ) 100 , b ) 120 , c ) 200 , d ) 242 , e ) 250 | d | add(220, divide(multiply(220, 10), const_100)) | the present population of a town is 220 . population increase rate is 10 % p . a . find the population of town after 1 years ? | "p = 220 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 220 * ( 1 + 10 / 100 ) = 220 * ( 11 / 10 ) = 242 answer is d" | a = 220 * 10
b = a / 100
c = 220 + b
|
a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54 | d | divide(power(105, 3), multiply(multiply(21, 25), 45)) | if a = 105 and a ^ 3 = 21 Γ 25 Γ 45 Γ b , what is the value of b ? | "a = 105 = 3 * 5 * 7 a ^ 3 = 21 Γ 25 Γ 45 Γ b = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x b = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b b = 7 ^ 2 = 49 answer d" | a = 105 ** 3
b = 21 * 25
c = b * 45
d = a / c
|
a ) 3 / 4 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16 | a | add(add(add(add(divide(1, 2), divide(divide(1, 2), 2)), divide(divide(divide(1, 2), 2), 2)), divide(divide(divide(divide(1, 2), 2), 2), 2)), divide(divide(divide(divide(divide(1, 2), 2), 2), 2), 2)) | if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 2 strokes ? | "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 so removed = 1 - 1 / 4 = 3 / 4" | a = 1 / 2
b = 1 / 2
c = b / 2
d = a + c
e = 1 / 2
f = e / 2
g = f / 2
h = d + g
i = 1 / 2
j = i / 2
k = j / 2
l = k / 2
m = h + l
n = 1 / 2
o = n / 2
p = o / 2
q = p / 2
r = q / 2
s = m + r
|
a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500 | a | subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(6, 150))) | a man purchased 3 blankets @ rs . 100 each , 6 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? | "explanation : 10 * 150 = 1500 3 * 100 + 6 * 150 = 1200 1500 β 1200 = 300 a" | a = 10 * 150
b = 3 * 100
c = 6 * 150
d = b + c
e = a - d
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a ) 2200 , b ) 2520 , c ) 2600 , d ) 3354 , e ) none of these | b | add(divide(270, divide(multiply(divide(9, multiply(const_4, const_3)), 16), const_100)), 270) | the true discount on a bill due 9 months hence at 16 % per annum is rs . 270 . the amount of the bill is | "explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 270 . x Γ£ β 16 Γ£ β ( 9 / 12 ) Γ£ β ( 1 / 100 ) = 270 or x = 2250 . p . w . = rs . 2250 sum due = p . w . + t . d . = rs . ( 2250 270 ) = rs . 2520 answer : b" | a = 4 * 3
b = 9 / a
c = b * 16
d = c / 100
e = 270 / d
f = e + 270
|
a ) 0.05 , b ) 0.36 , c ) 0.2 , d ) 0.25 , e ) 0.6 | b | subtract(divide(subtract(25, 8), 25), divide(8, 25)) | for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 25 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the gr... | "index for females = ( 25 - 8 ) / 25 = 17 / 25 = 0.68 index for males = ( 25 - 17 / 25 = 8 / 25 = 0.32 index for females exceeds males by 0.68 - 0.32 = 0.36 answer : b" | a = 25 - 8
b = a / 25
c = 8 / 25
d = b - c
|
a ) 62 , b ) 171 , c ) 475 , d ) 513 , e ) 684 | c | divide(multiply(57, 3), divide(36, const_100)) | at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at ... | "total automobile instalment credit = 57 * 3 = 171 total consumer instalment credit = 171 β 100 / 36 = 475 ; answer = c . 475" | a = 57 * 3
b = 36 / 100
c = a / b
|
a ) 17 , b ) 28 , c ) 24 , d ) 11 , e ) 12 | c | divide(122, add(const_2, const_pi)) | the perimeter of a semi circle is 122 cm then the radius is ? | "36 / 7 r = 122 = > r = 24 answer : c" | a = 2 + math.pi
b = 122 / a
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a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6 | b | divide(add(multiply(factorial(493), factorial(915)), multiply(factorial(493), factorial(756))), 493) | what is the units digit of ( 493 ) ( 915 ) ( 381 ) ( 756 ) ( 28 ) | "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 1 . imo b ." | a = math.factorial(493)
b = math.factorial(915)
c = a * b
d = math.factorial(493)
e = math.factorial(756)
f = d * e
g = c + f
h = g / 493
|
a ) β 220 , b ) β 100 , c ) 120 , d ) 135 , e ) it can not be determined from the information given | c | subtract(multiply(90, const_2), multiply(150, const_2)) | if the average ( arithmetic mean ) of a and b is 150 , and the average of b and c is 90 , what is the value of a β c ? | "a + b = 300 b + c = 180 a - c = 120 . imo option c ." | a = 90 * 2
b = 150 * 2
c = a - b
|
a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95 | d | add(multiply(const_2, const_3), subtract(const_100, const_10)) | a number is said to be prime saturated if the product of all the different positive prime factors of e is less than the square root of e . what is the greatest two digit prime saturated integer ? | "e = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ." | a = 2 * 3
b = 100 - 10
c = a + b
|
a ) 39 , b ) 68 , c ) 54 , d ) 57 , e ) 60 | b | add(subtract(92, 25), const_1) | claire has a total of 92 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ? | "g + h = 92 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 92 - h or 3 ( 92 - h ) + 4 h = 300 h = 300 - 276 = 24 then g = 92 - 24 = 68 b" | a = 92 - 25
b = a + 1
|
a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20 | e | add(divide(60, add(0.75, 5)), divide(60, add(0.75, 5))) | a car ferry can hold up to 60 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 5 tons ? | "the weight of one car and one truck is 5.75 tons . 60 / 5.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is e ." | a = 0 + 75
b = 60 / a
c = 0 + 75
d = 60 / c
e = b + d
|
a ) 3 km , b ) 4 km , c ) 5 km , d ) 6 km , e ) 7 km | b | multiply(4, divide(add(add(multiply(4, 6), multiply(5, 6)), 6), const_60)) | if a man walks at the rate of 4 kmph , he misses a train by only 6 min . however , if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train . the distance covered by him to reach the station is | let the distance covered be d and time taken to reach the station in time t d / 4 = t + 6 / 60 - - - ( 1 ) d / 5 = t - 6 / 60 - - - ( 2 ) ( 1 ) - ( 2 ) gives d / 4 - d / 5 = ( 6 + 6 ) / 60 d / 20 = 12 / 60 d = 12 * 20 / 60 = 4 km answer : b | a = 4 * 6
b = 5 * 6
c = a + b
d = c + 6
e = d / const_60
f = 4 * e
|
a ) 20200 , b ) 20000 , c ) 40400 , d ) 40000 , e ) 44000 | a | multiply(add(divide(subtract(subtract(301, 99), const_2), const_2), 99), divide(add(subtract(301, 99), const_2), const_2)) | what is the sum of all even integers between 99 and 301 ? | "a = 100 , tn = 300 a + ( n - 1 ) d = 300 = > n = 101 sn = n / 2 ( a + l ) = 101 / 2 ( 100 + 300 ) sn = 20200 answer : a" | a = 301 - 99
b = a - 2
c = b / 2
d = c + 99
e = 301 - 99
f = e + 2
g = f / 2
h = d * g
|
a ) 18 , b ) 32 , c ) 27 , d ) 26 , e ) 19 | b | add(multiply(4, 4), multiply(4, 4)) | a person was asked to state his age in years . his reply was , ` ` take my age 4 years hence , multiply it by 4 and subtract 4 times my age 4 years ago and you will know how old i am . ' ' what was the age of the person ? | "explanation : let the present age of person be x years . then , 4 ( x + 4 ) - 4 ( x - 4 ) = x < = > ( 4 x + 16 ) - ( 4 x - 16 ) = x < = > x = 32 . . answer : b" | a = 4 * 4
b = 4 * 4
c = a + b
|
a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22 | c | subtract(divide(add(24, 12), const_2), divide(add(48, 24), const_2)) | the average ( arithmetic mean ) of the even integers from 24 to 48 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 12 to 24 inclusive ? | "so , according to a mean of a set of even numbers from 24 to 48 = ( 24 + 48 ) / 2 = 36 and mean of a set of even numbers from 12 to 24 = ( 12 + 24 ) / 2 = 18 difference = 36 - 18 = 18 answer : c ." | a = 24 + 12
b = a / 2
c = 48 + 24
d = c / 2
e = b - d
|
a ) 100 minute , b ) 110 minute , c ) 120 minute , d ) 130 minute , e ) 140 minute | b | multiply(divide(5, subtract(divide(440, const_10), const_4)), multiply(440, 2)) | 2 friends a and b running up hill and then to get down length of road - 440 yads a on his return journey met b going up at 20 yards from top if a has finished race 5 minute earlier than b then how much time a had taken to complete the race ? | total journey = 440 * 2 = 880 a meet b 20 yards from top in getting down it means he has covered 440 + 20 = 460 yards while b is 420 yards . so he is 40 yards ahead of b which is equals to 5 minute . so 40 yards in 5 min 880 yards will be in 5 * 880 / ( 40 ) = 110 minute answer : b | a = 440 / 10
b = a - 4
c = 5 / b
d = 440 * 2
e = c * d
|
a ) 1150 m , b ) 2250 m , c ) 1450 m , d ) 1350 m , e ) 1250 m | e | multiply(500, subtract(const_2, const_1)) | a train speeds past a pole in 25 seconds and a platform 500 m long in 35 seconds . its length is : | "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 x + 500 / 35 = x / 25 x = 1250 m . answer : option e" | a = 2 - 1
b = 500 * a
|
a ) 22 , b ) 27 , c ) 28 , d ) 26 , e ) 56 | e | subtract(add(add(multiply(40, 15), 16), 40), multiply(40, 15)) | the average age of 40 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher . | "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 40 ) = 56 years answer : e" | a = 40 * 15
b = a + 16
c = b + 40
d = 40 * 15
e = c - d
|
a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 2548 | e | multiply(divide(divide(factorial(14), factorial(subtract(14, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2)) | 14 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ? | "no . of ways of picking 2 biology books ( from 14 books ) = 14 c 2 = ( 14 * 13 ) / 2 = 91 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 91 * 28 = 2548 ( option e )" | a = math.factorial(14)
b = 14 - 2
c = math.factorial(b)
d = a / c
e = d / 2
f = math.factorial(8)
g = 8 - 2
h = math.factorial(g)
i = f / h
j = i / 2
k = e * j
|
a ) 9 , b ) 7 , c ) 8 , d ) 5 , e ) 3 | a | subtract(multiply(5, const_2), const_1) | the average of non - zero number and its square is 5 times the number . the number is : | let the number be x . then , ( x + x 2 ) / 2 = 5 x = > x 2 - 9 x = 0 = > x ( x - 9 ) = 0 = > x = 0 or x = 9 so , the number is 9 . answer : a | a = 5 * 2
b = a - 1
|
a ) 44 , b ) 54 , c ) 16 , d ) 27 , e ) 30 | a | subtract(50, multiply(multiply(12, 4), 2)) | evaluate : 50 - 12 Γ· 4 Γ 2 = | "according to order of operations , 12 Γ· 4 Γ 2 ( division and multiplication ) is done first from left to right 12 Γ· 4 Γ 2 = 3 Γ 2 = 6 hence 50 - 12 Γ· 4 Γ 2 = 50 - 6 = 44 correct answer a ) 44" | a = 12 * 4
b = a * 2
c = 50 - b
|
a ) 80 , b ) 150 , c ) 75 , d ) 90 , e ) none of these | b | divide(36, multiply(divide(40, const_100), divide(3, 5))) | if 40 % of 3 / 5 of a number is 36 , then the number is ? | "let the number be x . then 40 % of 3 / 5 of x = 36 40 / 100 * 3 / 5 * x = 36 x = ( 36 * 50 / 12 ) = 150 required number = 150 . correct option : b" | a = 40 / 100
b = 3 / 5
c = a * b
d = 36 / c
|
a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 22 | e | sqrt(subtract(subtract(power(24, const_2), multiply(23, const_2)), multiply(23, const_2))) | the sum and the product of two numbers are 24 and 23 respectively , the difference of the number is ? | explanation : x + y = 24 xy = 23 ( x - y ) 2 = ( x + y ) 2 - 4 xy ( x - y ) 2 = 576 - 92 = > ( x - y ) = 22 answer : e | a = 24 ** 2
b = 23 * 2
c = a - b
d = 23 * 2
e = c - d
f = math.sqrt(e)
|
a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75 | d | add(multiply(0.25, subtract(7, 1)), 0.25) | at a certain company , each employee has a salary grade s that is at least 1 and at most 7 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s β 1 ) . an employee with a salary grade of 7 receives how many more dollars per hour than an employee with a salary grade of 1... | "salary grade of 7 is p ( 7 ) = 9.50 + 0.25 ( 7 β 1 ) = 9.50 + 0.25 * 6 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 β 1 ) = 9.50 ; p ( 7 ) - p ( 1 ) = 9.50 + 0.25 * 6 - 9.50 = 1.5 . answer : d ." | a = 7 - 1
b = 0 * 25
c = b + 0
|
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