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 |
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a ) 5 a , b ) 10 a , c ) 15 a , d ) 18 a , e ) 25 a | a | floor(divide(75, add(2, const_1))) | during a certain two - week period , 75 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 2 / 3 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ? | "movies : 75 % comedies . 25 % remaining genre . now in this 25 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 2 x / 3 . total 5 x / 3 . 5 x / 3 = 25 ; x = 15 action movies : 15 % drama movies : 10 % we can say that out of 100 z , : comedies : 75 z action : 15 z drama : 10 z now action movies were a this means : a = 15 z . z = a / 15 comedies : 75 z = 75 * ( a / 15 ) 5 a a is the answer ." | a = 2 + 1
b = 75 / a
c = math.floor(b)
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a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000 | b | divide(subtract(divide(multiply(60000, 20), const_100), 7000), divide(10, const_100)) | rs 60000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ? | "let first parrt is x and second part is y then x + y = 60000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 60000 + y so y = 10000 then x = 50000 - 10000 = 40000 first part = 40000 answer : b" | a = 60000 * 20
b = a / 100
c = b - 7000
d = 10 / 100
e = c / d
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a ) 0.2 % , b ) 0.4 % , c ) 0.6 % , d ) 0.8 % , e ) 1 % | d | subtract(subtract(5, 4), divide(multiply(5, 4), const_100)) | in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the area calculated from these measurements . | "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 ) * x * ( 96 / 100 ) * y = ( 504 / 500 ) ( xy ) error in measurement = ( 504 / 500 ) xy - xy = ( 4 / 500 ) xy error % = [ ( 4 / 500 ) xy * ( 1 / xy ) * 100 ] % = ( 4 / 5 ) % = 0.8 % . answer d 0.8 %" | a = 5 - 4
b = 5 * 4
c = b / 100
d = a - c
|
a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1 | d | divide(const_2, 3) | a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability g that the first ball picked up is odd numbered ? | "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability g is 2 / 3 . d" | a = 2 / 3
|
a ) 22 , b ) 60 , c ) 4 , d ) 8 , e ) 10 | c | divide(multiply(multiply(4, 4), 2), const_2) | a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 2 rows or 4 rows or 4 rows , then no tree will be left . find the least number of trees required | "explanation : the least number of trees that are required = lcm ( 2 , 4,4 ) = 4 . answer : c" | a = 4 * 4
b = a * 2
c = b / 2
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a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68 | c | multiply(multiply(inverse(subtract(1, divide(1, 4))), add(divide(9, const_2), 15)), const_2) | bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 15 left in his pocket . what was the value of n ? | started to test answer c if he had 52 , then he spent 13 at hardware store now he was left with 39 $ he spent 9 dollars on cleaning , thus he remained with 30 $ he then spent 1 / 2 of 30 , or 15 , and was left with 15 . hence , the only option that can be right is c . | a = 1 / 4
b = 1 - a
c = 1/(b)
d = 9 / 2
e = d + 15
f = c * e
g = f * 2
|
a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 6 | d | subtract(9, reminder(329864, 9)) | a company has $ 329864 in its account . what is the least amount of money ( in whole number of dollars ) that it must add to the account if the money is paid evenly among 9 of its vendors ? | to find the least amount that must be added to the account to split the money evenly among 9 of its vendors , the total divisible by 9 simply add the individual digits of the total = 3 + 2 + 9 + 8 + 6 + 4 = 32 if you add 4 , the number is divisible by 9 ( 32 + 4 ) correct option : d | a = 9 - reminder
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a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec | d | divide(112, add(10, 4)) | an escalator moves towards the top level at the rate of 10 ft . sec and its length is 112 feet . if a person walks on the moving escalator at the rate of 4 feet per second towards the top level , how much time does he take to cover the entire length . | "time taken to cover the entire length = tot . dist / resultant speed = 112 / ( 10 + 4 ) = 8 sec answer : d" | a = 10 + 4
b = 112 / a
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a ) 2 / 3 , b ) 1 / 2 , c ) 5 / 3 , d ) 8 / 3 , e ) 7 / 3 | d | divide(2, multiply(2, 4)) | if - 2 / ( a - 6 ) = 4 / ( a + 4 ) , then a = ? | "multiply all terms of the given equation by ( a - 6 ) ( a + 4 ) , simplify and solve ( a - 6 ) ( a + 4 ) [ - 2 / ( a - 6 ) ] = ( a - 6 ) ( a + 4 ) [ 4 / ( a + 4 ) ] - 2 ( a + 4 ) = 4 ( a - 6 ) a = 8 / 3 correct answer d" | a = 2 * 4
b = 2 / a
|
a ) 11 , b ) 12 , c ) 14 , d ) 17 , e ) 18 | d | divide(34, const_2) | in a group of ducks and cows , the total number of legs are 34 more than twice the no . of heads . find the total no . of buffaloes . | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 34 = > 2 x = 34 = > x = 17 d" | a = 34 / 2
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a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | divide(add(multiply(factorial(7), factorial(6)), multiply(factorial(7), factorial(4))), 7) | what is the units digit of ( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 ? | "( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 = 6 ! ( 7 ! + 4 ! ) / 2 = 240 ( 1680 + 24 ) / 2 = 204480 units digit of the above product will be equal to 0 answer a" | a = math.factorial(7)
b = math.factorial(6)
c = a * b
d = math.factorial(7)
e = math.factorial(4)
f = d * e
g = c + f
h = g / 7
|
a ) 0 , b ) 36 , c ) 13 , d ) 20 , e ) 25 | b | divide(multiply(12, 63), 21) | in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 63 as quotient . what is the correct quotient ? | "12 * 63 = 756 756 % 21 = 36 answer : b" | a = 12 * 63
b = a / 21
|
a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16 | a | multiply(const_4, power(27, divide(const_1, const_3))) | a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many v cubes are painted on only 2 faces ? | "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . v = 4 + 4 + 4 = 12 . answer a" | a = 1 / 3
b = 27 ** a
c = 4 * b
|
a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 18 | e | divide(multiply(divide(multiply(15, 20), subtract(30, 20)), 30), add(20, divide(multiply(15, 20), subtract(30, 20)))) | a tank can supply water to a village for 30 days . if a leak at the bottom of the tank drains out 15 liters per day , the supply lasts for 20 days only . for how many days will the supply last if the leak drains out 20 liters per day ? | "losing 15 liters per day results in a loss of 300 liters in 20 days . so , those 300 liters were for 10 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 30 = 900 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 900 / 50 = 18 days . the answer is e ." | a = 15 * 20
b = 30 - 20
c = a / b
d = c * 30
e = 15 * 20
f = 30 - 20
g = e / f
h = 20 + g
i = d / h
|
a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 5,000 | e | divide(const_180, const_1000) | the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 12348 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ? | "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 12348 pi r = 21 so area = 4 . pi . r ^ 2 = 1764 . pi = 1764 x 3.14 = 5000 ( approx ) e" | a = const_180 / 1000
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a ) 23 , b ) 25 , c ) 28 , d ) 60 , e ) 240 | c | divide(multiply(add(multiply(2, const_100), 40), add(multiply(4, const_100), 20)), power(divide(add(multiply(2, const_100), 40), power(const_2, const_4)), const_2)) | a room of 2 m 40 cm long and 4 m 20 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor . | "explanation : area of the room = 240 * 420 sq cm size of largest square tile = h . c . f of 240 cm and 420 cm = 60 cm area of 1 tile = 60 * 60 sq cm no . of tiles required = ( 240 * 420 ) / ( 60 * 60 ) = 28 answer : c ) 28" | a = 2 * 100
b = a + 40
c = 4 * 100
d = c + 20
e = b * d
f = 2 * 100
g = f + 40
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
|
a ) 12 , b ) 20 , c ) 21 , d ) 23 , e ) 22 | e | divide(subtract(multiply(const_2, multiply(const_2, const_12)), const_4), const_2) | how many times in a day , the hands of a clock are shows opposite directions ? | "sol . in 12 hours , the hands coincide or are in opposite direction 11 times . â ˆ ´ in 24 hours , the hands coincide or are in opposite direction 22 times a day . ( between 5 and 7 they point in opposite directions at 6 o ' clock only ) answer e" | a = 2 * 12
b = 2 * a
c = b - 4
d = c / 2
|
a ) 4 / 0 , b ) 4 / 1 , c ) 4 / 5 , d ) 4 / 2 , e ) 4 / 3 | c | divide(const_4, subtract(9, const_4)) | the difference between a positive proper fraction and its reciprocal is 9 / 20 . then the fraction is : | "explanation : let the required fraction be x . then , ( 1 / x ) - x = 9 / 20 1 - x ^ ( 2 ) / x = 9 / 20 = > 20 - 20 * x ^ ( 2 ) = 9 * x . 20 * x ^ ( 2 ) + 9 * x - 20 = 0 . = > ( 4 * x + 5 ) ( 5 * x - 4 ) = 0 . = > x = 4 / 5 . answer : c ) 4 / 5" | a = 9 - 4
b = 4 / a
|
a ) 1500 , b ) 2000 , c ) 2500 , d ) 2800 , e ) 3000 | e | multiply(multiply(subtract(5, 4), 1000), const_3.0) | a sum of money is to be distributed among a , b , c , d in the proportion of 6 : 3 : 5 : 4 . if c gets rs . 1000 more than d , what is b ' s share ? | "let the shares of a , b , c and d be rs . 5 x , rs . 3 x , rs . 5 x and rs . 4 x respectively . then , 5 x - 4 x = 1000 x = 1000 . b ' s share = rs . 3 x = rs . ( 3 x 1000 ) = rs . 3000 . answer : e" | a = 5 - 4
b = a * 1000
c = b * 3
|
a ) 50 , b ) 100 , c ) 70 , d ) 500 , e ) 980 | c | divide(686, 9.8) | a sports equipment store sold ping pong rackets for a total of $ 686 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ? | average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 686 x = 70 pairs were sold . answer : c | a = 686 / 9
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a ) 5 / 7 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 24 / 7 | e | inverse(add(divide(subtract(divide(add(inverse(add(add(const_4, const_1), const_4)), multiply(inverse(add(const_4, const_1)), const_2)), const_2), inverse(add(const_4, const_1))), divide(const_3, const_2)), inverse(add(const_4, const_1)))) | one woman and one man can build a wall together in four hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them eight hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ? | "solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 4 - - > ( 1 ) , w + 2 g = 1 / 4 - - > ( 2 ) and m + g = 1 / 8 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 24 , m = 1 / 12 and w = 1 / 6 . so , n = 1 / ( 7 / 24 ) = 24 / 7 option , e" | a = 4 + 1
b = a + 4
c = 1/(b)
d = 4 + 1
e = 1/(d)
f = e * 2
g = c + f
h = g / 2
i = 4 + 1
j = 1/(i)
k = h - j
l = 3 / 2
m = k / l
n = 4 + 1
o = 1/(n)
p = m + o
q = 1/(p)
|
a ) 80 , b ) 25 , c ) 75 , d ) 63 , e ) 90 | c | subtract(multiply(const_100, add(const_10, multiply(const_3, const_2))), 1300) | what is the least number to be subtracted from 1300 to make it a perfect square ? | "the numbers less than 1300 and are squares of certain number is 1225 . the least number that should be subtracted from 1300 to make it perfect square = 1300 - 1225 = 75 . answer : c" | a = 3 * 2
b = 10 + a
c = 100 * b
d = c - 1300
|
a ) kg , b ) 70 kg , c ) 80 kg , d ) 90 kg , e ) 93 kg | e | add(multiply(8, 3.5), 65) | the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . e )" | a = 8 * 3
b = a + 65
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a ) 5 : 24 , b ) 5 : 19 , c ) 5 : 13 , d ) 5 : 22 , e ) 5 : 18 | a | divide(subtract(sqrt(6400), 30), multiply(sqrt(6400), const_2)) | the area of a square is 6400 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 30 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 = 6400 a = ( 6400 ) ^ 1 / 2 = 80 l = 3 a and b = a - 30 b : l = a - 30 : 2 a = 50 : 240 = 5 : 24 answer : a" | a = math.sqrt(6400)
b = a - 30
c = math.sqrt(6400)
d = c * 2
e = b / d
|
a ) 1 / 25 , b ) 1 / 6 , c ) 3 / 5 , d ) 5 , e ) 6 | c | divide(divide(15, 5), 5) | if xy > 0 , 1 / x + 1 / y = 15 , and 1 / xy = 5 , then ( x + y ) / 5 = ? | ( 1 / x + 1 / y ) = 15 canbe solved as { ( x + y ) / xy } = 5 . substituting for 1 / xy = 5 , we get x + y = 15 / 5 = = > ( x + y ) / 5 = 15 / ( 5 * 5 ) = 3 / 5 . c | a = 15 / 5
b = a / 5
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a ) 220 km , b ) 224 km , c ) 230 km , d ) 200 km , e ) 234 km | d | multiply(const_2, divide(multiply(multiply(21, 26), 10), add(21, 26))) | 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 26 km / hr . find the total journey in km . | "0.5 x / 10 + 0.5 x / 10 = 20 - - > x / 10 + x / 10 = 40 - - > 2 x = 10 x 40 - - > x = ( 10 x 40 ) / 2 = 200 km . answer : d ." | a = 21 * 26
b = a * 10
c = 21 + 26
d = b / c
e = 2 * d
|
a ) $ 14.40 , b ) $ 14.00 , c ) $ 10.00 , d ) $ 9.60 , e ) $ 5.00 | c | subtract(11.00, multiply(divide(10, const_100), 11.00)) | a bookseller sells his books at a 10 % markup in price . if he sells a book for $ 11.00 , how much did he pay for it ? | "let the cost price of book = x selling price of book = 11 $ markup % = 10 ( 110 / 100 ) x = 11 = > x = 10 answer c" | a = 10 / 100
b = a * 11
c = 11 - 0
|
a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9 | d | add(divide(60, const_10), 1) | there are 60 doors marked with numbers 1 to 60 . there are 60 individuals marked 1 to 60 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , and 60 . if every individual in the group gets one turn , then how many doors are open at the end ? | if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 , 49 for a total of 7 doors . the answer is d . | a = 60 / 10
b = a + 1
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a ) 7 sec , b ) 8 sec , c ) 10 sec , d ) 12 sec , e ) 14 sec | d | multiply(divide(divide(220, const_1000), subtract(59, 7)), const_3600) | a train 220 m long is running with a speed of 59 kmph . in what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going ? | "speed of the train relative to man = ( 59 + 7 ) kmph = 66 * 5 / 18 m / sec = 55 / 3 m / sec . time taken by the train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 * 3 / 55 ) sec = 12 sec answer : d ." | a = 220 / 1000
b = 59 - 7
c = a / b
d = c * 3600
|
a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 17.19 , e ) e ) 24 | d | max(multiply(subtract(add(55, 9), const_1), subtract(divide(9, 20), divide(9, 55))), const_4) | due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 20 = 9 * 3 / 1 = 27 time difference = 17.19 ans : d" | a = 55 + 9
b = a - 1
c = 9 / 20
d = 9 / 55
e = c - d
f = b * e
g = max(f)
|
a ) 3 , b ) 6 , c ) 5 , d ) 9 , e ) 1 | c | divide(add(add(1, 2), 7), 2) | the area of a triangle will be when a = 1 m , b = 2 m , c = 7 m , a , b , c being lengths of respective sides ? | s = ( 1 + 2 + 7 ) / 2 = 5 answer : c | a = 1 + 2
b = a + 7
c = b / 2
|
a ) 65 kmph , b ) 70 kmph , c ) 75 kmph , d ) 80 kmph , e ) 85 kmph | b | subtract(divide(divide(125, 6), const_0_2778), 5) | a train 125 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ? | "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 125 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2250 x = 70 kmph answer is b" | a = 125 / 6
b = a / const_0_2778
c = b - 5
|
a ) 0 , b ) 8 , c ) 4 , d ) 6 , e ) 3 | b | add(add(const_4, const_3), const_2) | what is the units digit of the expression 14 ^ 7 − 15 ^ 4 ? | i think answer on this one should be b too . since we know that 14 ^ 7 > 15 ^ 4 , as will said one should always check if the number is positive . | a = 4 + 3
b = a + 2
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a ) 8 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | multiply(divide(divide(subtract(1050, 750), 750), 5), const_100) | at what rate percent on simple interest will rs . 750 amount to rs . 1050 in 5 years ? | "300 = ( 750 * 5 * r ) / 100 r = 8 % . answer : a" | a = 1050 - 750
b = a / 750
c = b / 5
d = c * 100
|
a ) 25 hours , b ) 30 hours , c ) 20 hours , d ) 26 hours , e ) 32 hours | c | subtract(multiply(divide(120, add(add(4, 3), 5)), 5), multiply(divide(120, add(add(4, 3), 5)), 4)) | the amount of time that three people worked on a special project was in the ratio of 4 to 3 to 5 . if the project took 120 hours , how many more hours did the hardest working person work than the person who worked the least ? | "let the persons be a , b , c . hours worked : a = 4 * 120 / 12 = 40 hours b = 3 * 120 / 12 = 30 hours c = 5 * 120 / 12 = 50 hours c is the hardest worker and b worked for the least number of hours . so the difference is 50 - 30 = 20 hours . answer : c" | a = 4 + 3
b = a + 5
c = 120 / b
d = c * 5
e = 4 + 3
f = e + 5
g = 120 / f
h = g * 4
i = d - h
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a ) 1276 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1320 | e | multiply(add(add(30, divide(1200, 30)), sqrt(add(power(30, 2), power(divide(1200, 30), 2)))), 11) | a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 11 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ? | "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 11 = 1320 answer : option e" | a = 1200 / 30
b = 30 + a
c = 30 ** 2
d = 1200 / 30
e = d ** 2
f = c + e
g = math.sqrt(f)
h = b + g
i = h * 11
|
a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 11 , d ) 1 / 2 , e ) 1 / 5 | c | divide(multiply(8, 5), add(multiply(8, 5), multiply(5, 3))) | a call center has two teams . each member of team a was able to process 3 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ? | "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 3 calls , so total calls for team a = 15 fraction for team b = 40 / ( 40 + 15 ) = 8 / 11 = answer = c" | a = 8 * 5
b = 8 * 5
c = 5 * 3
d = b + c
e = a / d
|
a ) $ 10079.44 , b ) r = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11 | b | multiply(10000, power(add(const_1, divide(divide(3.96, const_100), const_2)), const_4)) | jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much r does she have in her account after two years ? | "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer" | a = 3 / 96
b = a / 2
c = 1 + b
d = c ** 4
e = 10000 * d
|
a ) $ 5.625 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.25 , e ) $ 6.80 | d | subtract(multiply(71.4, divide(add(const_100, 25), const_100)), divide(71.4, divide(subtract(const_100, 15), const_100))) | cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 71.4 after it went on sale for 15 % off , what is the difference between the original price and the final price ? | "0.85 * { original price } = $ 71.4 - - > { original price } = $ 84 . { final price } = $ 71.4 * 1.25 = $ 89.25 . the difference = $ 89.25 - $ 84 = $ 5.25 answer : d ." | a = 100 + 25
b = a / 100
c = 71 * 4
d = 100 - 15
e = d / 100
f = 71 / 4
g = c - f
|
a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | b | subtract(add(const_4, const_4), const_1) | if ( n + 2 ) ! / n ! = 110 , n = ? | "( n + 2 ) ! / n ! = 110 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 110 from here , we might just test the answer choices . since ( 11 ) ( 10 ) = 110 , we can see that n = 9 b" | a = 4 + 4
b = a - 1
|
a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36 | d | divide(35, 1) | ( 1 / 5 ) ^ e * ( 1 / 4 ) ^ 18 = 1 / ( 2 ( 10 ) ^ 35 ) . what is e ? | we need to arrive at a common base . - - > ( 5 ) ^ ( - e ) * 2 ^ ( - 36 ) = 2 ^ ( - 36 ) * 5 ^ ( - 35 ) 5 ^ ( - e ) = 5 ^ ( - 35 ) - e = - 35 e = 35 = d | a = 35 / 1
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a ) 197 , b ) 210 , c ) 189 , d ) 278 , e ) 268 | b | divide(multiply(360, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | i bought two books ; for rs . 360 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | "x * ( 85 / 100 ) = ( 360 - x ) 119 / 100 x = 210 answer : b" | a = 100 + 19
b = 360 * a
c = 100 - 15
d = 100 + 19
e = c + d
f = b / e
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a ) 6 only , b ) 12 only , c ) 6 and 12 both , d ) by 18 only , e ) 15 only | c | add(multiply(6, const_100), multiply(2, 6)) | if n is a natural number , then ( 6 n 2 + 6 n ) is always divisible by : | "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer c ) 6 and 12 both ." | a = 6 * 100
b = 2 * 6
c = a + b
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a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4 | e | subtract(subtract(13, 3), subtract(10, 4)) | | 13 - 3 | - | 4 - 10 | = ? | "| 13 - 3 | - | 4 - 10 | = | 10 | - | - 6 | = 10 - 6 = 4 correct answer e" | a = 13 - 3
b = 10 - 4
c = a - b
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a ) 450 min , b ) 360 min , c ) 240 min , d ) 306 min , e ) 500 min | a | divide(90, 1) | a fill pipe can fill 1 / 6 of cistern in 90 minutes in how many minutes , it can fill 5 / 6 of the cistern ? | "1 / 6 of the cistern can fill in 90 min 5 / 6 of the cistern can fill in = 90 * 6 * 5 / 6 = 450 min answer is a" | a = 90 / 1
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a ) 12.1 % , b ) 12.36 % , c ) 12.94 % , d ) 13.65 % , e ) 14.56 % | b | multiply(const_100, subtract(multiply(add(const_1, divide(6, const_100)), add(const_1, divide(6, const_100))), const_1)) | increasing the original price of an article by 6 percent and then increasing the new price by 6 percent is equivalent to increasing the original price by | 1.06 * 1.06 * x = 1.1236 * x the answer is b . | a = 6 / 100
b = 1 + a
c = 6 / 100
d = 1 + c
e = b * d
f = e - 1
g = 100 * f
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a ) $ 2291.7 , b ) $ 1546.8 , c ) $ 2546.5 , d ) $ 1879.3 , e ) $ 3125.3 | a | divide(add(add(add(add(add(1000, 2500), 3100), 3650), 1500), 2000), 6) | the monthly salaries of 6 employees in a company are $ 1000 , $ 2500 , $ 3100 , $ 3650 , $ 1500 , $ 2000 . what is the mean of the salaries of 6 employees . | mean of the salaries = ( $ 1000 + $ 2500 + $ 3100 + $ 3650 + $ 1500 + $ 2000 ) / 6 = 13750 / 6 = $ 2291.7 answer is a | a = 1000 + 2500
b = a + 3100
c = b + 3650
d = c + 1500
e = d + 2000
f = e / 6
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a ) 1 : 3 , b ) 36 : 25 , c ) 3 : 2 , d ) 4 : 5 , e ) 20 : 45 | b | divide(multiply(multiply(multiply(multiply(8, const_3), multiply(10, const_2)), const_100), 8), multiply(10000, 10)) | ravi and sunil are partners in a business . ravi invests rs . 18,000 for 8 months and sunil invested rs . 10000 for 10 months then after one year ratio of their profits will be | "= ( 18000 * 8 ) : ( 10000 * 10 ) = 144000 : 100000 = 36 : 25 answer : b" | a = 8 * 3
b = 10 * 2
c = a * b
d = c * 100
e = d * 8
f = 10000 * 10
g = e / f
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a ) 1 , b ) 1 / 2 , c ) 2 , d ) - 1 / 2 , e ) - 1 | c | divide(3, subtract(5, const_1)) | if | x | = 5 x - 3 , then x = ? | "answer : a approach : substituted option a i . e x = 1 . inequality satisfied . c" | a = 5 - 1
b = 3 / a
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a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 43 : 134 | e | divide(subtract(sqrt(4489), 24), multiply(sqrt(4489), const_2)) | the area of a square is 4489 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 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 = 4489 a = 67 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 43 : 134 answer : e" | a = math.sqrt(4489)
b = a - 24
c = math.sqrt(4489)
d = c * 2
e = b / d
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a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 36 | e | subtract(divide(12, divide(2, 3)), 12) | a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 12 brown mice in the experiment , how many mice in total are in the experiment ? | "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 12 = > m = 36 answer e" | a = 2 / 3
b = 12 / a
c = b - 12
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['a ) 4', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 2'] | e | floor(divide(surface_rectangular_prism(3, 2, 0.5), multiply(const_2, const_3))) | a rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high . if the surface area of the rectangle is the same as a cube , what do the sides / walls of the cube measure ? round to the nearest whole number . | first calculate the surface area of the rectangle by multiplying the length and width of the rectangle together , then multiply by 2 to get both sides of the rectangle . this calculates to 12 inches . find the surface area of the sides of the rectangular cube . multiply the height by the length of the rectangle . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 3 inches . then multiply the width of the rectangle by the height . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 2 inches . add the totals together to get the rectangular cube surface area of 17 inches . since a square cube has 6 sides , divide the surface area by 6 . this calculates to 2.833 inches as the surface area of each side of the cube . the square root of 2.833 is 1.683 . rounding to the nearest whole number that makes each side of the cube measuring 2 inches . the correct answer is ( e ) . | a = surface_rectangular_prism / (
b = 2 * 3
c = math.floor(a, b)
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a ) $ 2,250 , b ) $ 2,500 , c ) $ 1,600 , d ) $ 1,250 , e ) $ 1,500 | c | floor(divide(subtract(subtract(multiply(500, 7.00), multiply(5.00, 100)), multiply(subtract(500, 100), 3.50)), const_1000)) | company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 7.00 each , what was company c ’ s gross profit ? | "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 7 = $ 3500 profit : 3500 - 1900 = $ 1600 option c is correct" | a = 500 * 7
b = 5 * 0
c = a - b
d = 500 - 100
e = d * 3
f = c - e
g = f / 1000
h = math.floor(g)
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a ) 79.55 $ , b ) 80.63 $ , c ) 81.63 $ , d ) 80.27 $ , e ) 83.15 $ | d | divide(100, add(divide(add(7, 15), const_100), const_1)) | a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 100 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ? | "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 100 x = 81.27 hence , the correct option is d" | a = 7 + 15
b = a / 100
c = b + 1
d = 100 / c
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a ) 1977 , b ) 1893 , c ) 1979 , d ) 1900 , e ) 1300 | e | subtract(divide(subtract(multiply(2000, 54), multiply(2000, 21)), 20), 2000) | a garrison of 2000 men has provisions for 54 days . at the end of 21 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ? | "2000 - - - - 54 2000 - - - - 33 x - - - - - 20 x * 20 = 2000 * 33 x = 3300 2000 - - - - - - - 1300 answer : e" | a = 2000 * 54
b = 2000 * 21
c = a - b
d = c / 20
e = d - 2000
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a ) 240 , b ) 260 , c ) 220 , d ) 300 , e ) 360 | c | add(200, multiply(200, divide(10, const_100))) | a person buys an article at $ 200 . at what price should he sell the article so as to make a profit of 10 % ? | "c 220 cost price = $ 200 profit = 10 % of 200 = $ 20 selling price = cost price + profit = 200 + 20 = 220" | a = 10 / 100
b = 200 * a
c = 200 + b
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a ) 6 : 1 , b ) 1 : 6 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 1 | a | divide(multiply(subtract(20, const_1), 1), multiply(4, 1)) | 200 liters of a mixture contains milk and water in the ratio 4 : 1 . if 20 liters of this mixture be replaced by 20 liters of milk , the ratio of milk to water in the new mixture would be ? | "quantity of milk in 200 liters if mix = 200 * 4 / 5 = 160 liters quantity of milk in 210 liters of new mix = 160 + 20 = 180 liters quantity of water in it = 210 - 180 = 30 liters ratio of milk and water in new mix = 180 : 30 = 6 : 1 answer is a" | a = 20 - 1
b = a * 1
c = 4 * 1
d = b / c
|
a ) 550 m , b ) 500 m , c ) 375 m , d ) 420 m , e ) 440 m | a | multiply(multiply(66, const_0_2778), 30) | if the speed of a man is 66 km per hour , then what is the distance traveled by him in 30 seconds ? | "the distance traveled in 30 sec = 66 * ( 5 / 18 ) * 30 = 550 m answer : a" | a = 66 * const_0_2778
b = a * 30
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a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12 | c | divide(6, subtract(6.12, floor(6.12))) | when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ? | "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c" | a = math.floor(6, 12)
b = 6 - 12
c = 6 / b
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a ) 40 sec , b ) 50 sec , c ) 60 sec , d ) 20 sec , e ) 25 sec | d | multiply(divide(multiply(2, const_60), add(12, 12)), subtract(16, 12)) | two identical trains aa and bb running in opposite direction at same speed tale 2 min to cross each other completely . the number of bogies of aa are increased from 12 to 16 . how much more time would they now require to cross each other ? | total initial bogies is 12 + 12 = 2412 + 12 = 24 additional bogies = 16 â ˆ ’ 12 = 4 24 bogies is 12 + 12 = 24 additional bogies = 16 - 12 = 4 24 bogies take 2 min 2 * 60 / 24 * 4 = 20 sec answer d | a = 2 * const_60
b = 12 + 12
c = a / b
d = 16 - 12
e = c * d
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a ) 22 , b ) 88 , c ) 90 , d ) 18 , e ) 24 | d | multiply(divide(5, const_1000), const_3600) | express 5 mps in kmph ? | "5 * 18 / 5 = 18 kmph answer : d" | a = 5 / 1000
b = a * 3600
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a ) rs . 23 , b ) rs . 37 , c ) rs . 45 , d ) rs . 67 , e ) rs . 77 | b | subtract(64, multiply(multiply(64, power(add(const_1, divide(1, 2)), const_3)), power(divide(1, 2), const_3))) | a person starting with rs . 64 and making 6 bets , wins 3 times and loses 3 times , the wins and loses occurring in random order . the chance for a win is equal to the chance for a loss . if each wager is for 1 / 2 the money remaining at the time of the bet , then the final result is ? | as the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5 , we will multiply initial amount by 1.5 thrice and by 0.5 thrice ( in any order ) . the overall resultant will remain same . so final amount with the person will be ( in all cases ) : = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = rs 2727 hence the final result is : 64 − 27 = 3764 − 27 = 37 : a loss of rs . 37 b | a = 1 / 2
b = 1 + a
c = b ** 3
d = 64 * c
e = 1 / 2
f = e ** 3
g = d * f
h = 64 - g
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a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs | c | divide(90, add(25, 5)) | a boat can travel with a speed of 25 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 90 km downstream . | "speed downstream = ( 25 + 5 ) km / hr = 30 km / hr . time taken to travel 90 km downstream = 90 / 30 hrs = 3 hrs . answer : c" | a = 25 + 5
b = 90 / a
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a ) 16.67 , b ) 30 , c ) 50 , d ) 60 , e ) 70 | d | divide(subtract(multiply(divide(40, const_100), 60), multiply(divide(20, const_100), 60)), subtract(divide(40, const_100), divide(20, const_100))) | how many ounces of a 60 % salt solution must be added to 60 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ? | "let x = ounces of 60 % salt solution to be added . 2 * 60 + . 6 x = . 4 ( 60 + x ) x = 60 answer d" | a = 40 / 100
b = a * 60
c = 20 / 100
d = c * 60
e = b - d
f = 40 / 100
g = 20 / 100
h = f - g
i = e / h
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a ) 322 , b ) 340 , c ) 333 , d ) 327 , e ) 500 | d | add(add(multiply(400, divide(50, const_100)), multiply(divide(25, const_100), 100)), multiply(divide(85, const_100), 120)) | in a college , 50 % of total 400 arts students are locals . 25 % of students from 100 science students are locals and 85 % of total 120 commerce students are locals . what is the total percentage of locals from arts , science and commerce . | locals from arts = 50 % of 400 = 200 locals from science = 25 % of 100 = 25 locals from commerce = 85 % of 120 = 102 total locals = 200 + 25 + 102 = 327 d | a = 50 / 100
b = 400 * a
c = 25 / 100
d = c * 100
e = b + d
f = 85 / 100
g = f * 120
h = e + g
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a ) 10 , b ) 15 , c ) 16 , d ) 25 , e ) 30 | c | multiply(8, divide(12, 6)) | 12 : 6 seconds : : ? : 8 minutes | "12 * 8 = 6 * x x = 16 answer : c" | a = 12 / 6
b = 8 * a
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a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25 | e | add(multiply(divide(3, 5), divide(3, 5)), add(multiply(divide(3, 5), divide(const_2, 5)), multiply(divide(3, 5), divide(const_2, 5)))) | a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability y that you can still row the canoe ? | "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer y : 1 – 4 / 25 = 21 / 25 . answer choice e ." | a = 3 / 5
b = 3 / 5
c = a * b
d = 3 / 5
e = 2 / 5
f = d * e
g = 3 / 5
h = 2 / 5
i = g * h
j = f + i
k = c + j
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a ) 63 , b ) 93 , c ) 139 , d ) 147 , e ) 188 | b | add(multiply(divide(subtract(132, 15), const_3), const_2), 15) | if jake loses 15 pounds , he will weigh twice as much as his sister . together they now weigh 132 pounds . what is jake ’ s present weight , in pounds ? | "lets say j is the weight of jack and s is the wt of his sister . if he loses 15 pounds , he s twice as heavy as his sister . j - 15 = 2 * s also , together they weight 132 pounds j + s = 132 solvong the 2 equation , we get j = 93 pounds ! b" | a = 132 - 15
b = a / 3
c = b * 2
d = c + 15
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a ) 4.6 days , b ) 4.78 days , c ) 5.65 days , d ) 3.77 days , e ) 5.75 days | a | inverse(add(inverse(7), inverse(14))) | a and b complete a work in 7 days . a alone can do it in 14 days . if both together can do the work in how many days ? | "1 / 7 + 1 / 14 = 3 / 14 14 / 3 = 4.6 days answer : a" | a = 1/(7)
b = 1/(14)
c = a + b
d = 1/(c)
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a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 13 | e | inverse(add(multiply(4, subtract(4, const_1)), const_1)) | a car traveled the first quarter of a certain distance at 4 times the speed it traveled the remaining distance . what proportion of the total time traveled , was the time taken to travel the first quarter of the distance ? | these problems can be solved through algebra or sly number picking . being a big fan of solving problems with numbers , let ' s pick a total distance divisible by 4 ( say 40 ) so we can break it up into quarters , and a speed that can easily be one fourth , say 10 . each quarter is thus 10 kilometers ( or miles or feet or angstroms for all it matters ) , and the runner ' s speed is 10 km / h for the first quarter and 5 / 2 km / h for the remaining quarters . he ' ll take 1 hour to do the first quarter and then 4 hours for the second quarter , 4 hours for the third and 4 hours for the fourth . on total he will take 13 hours to complete this race , of which 1 hour was spent on the first quarter . so 1 / 13 . answer e . | a = 4 - 1
b = 4 * a
c = b + 1
d = 1/(c)
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a ) 140 , b ) 204 , c ) 180 , d ) 200 , e ) 250 | b | divide(multiply(divide(17, multiply(multiply(divide(const_1, const_4), divide(const_1, const_3)), divide(const_2, add(const_2, const_3)))), 40), const_100) | one fourth of one third of two fifth of a number is 17 . what will be 40 % of that number | "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 17 then x = 17 * 30 = 510 40 % of 510 = 204 answer : option b" | a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3
e = 2 / d
f = c * e
g = 17 / f
h = g * 40
i = h / 100
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a ) 0.0016 , b ) 0.04 , c ) 0.16 , d ) 0.25 , e ) 0.5 | b | power(divide(1, 5), 2) | what is the decimal equivalent of ( 1 / 5 ) ^ 2 ? | "( 1 / 5 ) ² = ( 1 / 5 ) ( 1 / 5 ) = 1 / 25 approach # 1 : use long division to divide 25 into 1 to get 1 / 25 = 0.04 b" | a = 1 / 5
b = a ** 2
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a ) 4 / 10 , b ) 4 / 9 , c ) 6 / 5 , d ) 9 / 2 , e ) 6 / 4 | b | divide(add(multiply(10, const_0_33), multiply(5, divide(const_2, const_3))), add(10, 5)) | at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 10 : 5 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ? | red : blue = 10 : 5 let red = 10 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 10 x = 10 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 10 x / 3 + 10 x / 3 ) / ( 10 x + 5 x ) = 20 / 45 = 4 / 9 answer : b | a = 10 * const_0_33
b = 2 / 3
c = 5 * b
d = a + c
e = 10 + 5
f = d / e
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a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26 | b | divide(subtract(multiply(5, 900), multiply(5, 700)), subtract(750, 700)) | the average salary / head of allthe workers in a workshop is rs . 750 , if the average salary / head of 5 technician is rs . 900 and the average salary / head of the rest is rs . 700 , the total no . of workers in the work - shop is ? | let the total number of workers be y . so sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y - 5 workers . 5 x 900 + 700 ( y - 5 ) = 750 y ⇒ 4500 + 700 y - 3500 = 750 y ⇒ 50 y = 1000 ∴ y = 20 so total number of workers = 20 b | a = 5 * 900
b = 5 * 700
c = a - b
d = 750 - 700
e = c / d
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a ) 37 , b ) 26 , c ) 30 , d ) 50 , e ) 11 | d | divide(add(add(18, 22), multiply(10, 6)), const_2) | the average age of 10 men increases by 6 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ? | "explanation : 18 + 22 + 10 * 6 = 100 / 2 = 50 answer : d" | a = 18 + 22
b = 10 * 6
c = a + b
d = c / 2
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a ) 33888 , b ) 36000 , c ) 27778 , d ) 27772 , e ) 81122 | b | subtract(43000, multiply(const_60, const_100)) | a started a business with an investment of rs . 70000 and after 3 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 43000 , then the share of b is ? | ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 9 ) = 7 : 36 total profit = rs . 43000 share of b = 36 / 43 ( 43000 ) = rs . 36000 answer : b | a = const_60 * 100
b = 43000 - a
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a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225 | b | multiply(divide(5, subtract(divide(30, 10), const_1)), 30) | working together , printer a and printer b would finish the task in 10 minutes . printer a alone would finish the task in 30 minutes . how many pages does the task contain if printer b prints 5 pages a minute more than printer a ? | "10 * a + 10 * b = x pages in 10 mins printer a will print = 10 / 30 * x pages = 1 / 3 * x pages thus in 10 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 5 more pages per min that printer a . in 10 mins printer b will print 50 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 50 = > x = 150 pages answer : b" | a = 30 / 10
b = a - 1
c = 5 / b
d = c * 30
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a ) 300 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2000 | b | multiply(divide(1500, 5), 4) | the ratio of boys to girl in a school is 5 : 4 . if there are 1500 boys in the school , how many girls are there ? | think of the ratio as 5 parts : 4 parts . divide 1500 by 5 to find 1 ` ` part ' ' of the ratio . 1500 / 5 = 300 multiply this by 4 to get 4 ` ` parts ' ' of the ratio . 300 * 4 = 1200 there are 1200 girls in the school . the answer is b | a = 1500 / 5
b = a * 4
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a ) 15 mins , b ) 20 mins , c ) 25 mins , d ) 30 mins , e ) none of these | d | divide(multiply(multiply(40, const_3), const_2), add(const_4, const_4)) | a tank can be filled by two pipes a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tank from empty state if b is used for the first half time and then a and b fill it together for the other half | "explanation : let the total time be x mins . part filled in first half means in x / 2 = 1 / 40 part filled in second half means in x / 2 = 1 / 60 + 1 / 40 = 1 / 24 total = x / 2 ∗ 1 / 40 + x / 2 ∗ 1 / 24 = 1 = > x / 2 ( 1 / 40 + 1 / 24 ) = 1 = > x / 2 ∗ 1 / 15 = 1 = > x = 30 mins option d" | a = 40 * 3
b = a * 2
c = 4 + 4
d = b / c
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a ) 35.2 m 2 , b ) 44 m 2 , c ) 48 m 2 , d ) 36 m 2 , e ) none of these | a | multiply(4, multiply(multiply(multiply(2, divide(22, 7)), divide(1.4, 2)), 2)) | the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 4 revolutions ? ( use ï € = 22 â „ 7 ) | "required area covered in 5 revolutions = 4 ã — 2 ï € rh = 4 ã — 2 ã — 22 â „ 7 ã — 0.7 ã — 2 = 35.2 m 2 answer a" | a = 22 / 7
b = 2 * a
c = 1 / 4
d = b * c
e = d * 2
f = 4 * e
|
a ) 28 , b ) 12 , c ) 24 , d ) 16 , e ) 19 | c | divide(48, const_2) | in a group of ducks and cows , the total number of legs are 48 more than twice the no . of heads . find the total no . of buffaloes . | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 48 = > 2 x = 48 = > x = 24 c" | a = 48 / 2
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a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 2 / 3 , e ) 146 / 25 | d | sqrt(divide(multiply(64, const_3), multiply(216, const_2))) | two - third of a positive number and 64 / 216 of its reciprocal are equal . the number is : | "let the number be x . then , 2 / 3 x = 64 / 216 * 1 / x x 2 = 64 / 216 * 3 / 2 = 64 / 144 = 4 / 9 x = 2 / 3 answer : d" | a = 64 * 3
b = 216 * 2
c = a / b
d = math.sqrt(c)
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a ) 120 , b ) 60 , c ) 30 , d ) 24 , e ) 12 | b | divide(12, reminder(24.2, const_1)) | when positive integer m is divided by positive integer n , the remainder is 12 . if m / n = 24.2 , what is the value of n ? | n = decimal part of 24.2 * remainder i . e . ( 12 ) hence 0.2 * n = 12 n = 60 . b | a = 12 / reminder
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a ) 9 , b ) 28 , c ) 63 , d ) 84 , e ) 252 | a | add(21, const_1) | if x and y are positive integers and 12 x = 21 y what is the least possible value of xy ? | "12 x = 21 y = > x / y = 7 / 4 = > 4 x = 7 y 4 ( 3 ) = 7 ( 3 ) = > x * y = 9 a" | a = 21 + 1
|
a ) 100 m , b ) 180 m , c ) 159 m , d ) 250 m , e ) 152 m | a | subtract(multiply(500, divide(15, divide(15, const_3))), multiply(350, divide(20, divide(15, const_3)))) | a train crosses a platform of 350 m in 15 sec , same train crosses another platform of length 500 m in 20 sec . then find the length of the train ? | "length of the train be ‘ x ’ x + 350 / 15 = x + 500 / 20 4 x + 1400 = 3 x + 1500 x = 100 m answer : a" | a = 15 / 3
b = 15 / a
c = 500 * b
d = 15 / 3
e = 20 / d
f = 350 * e
g = c - f
|
a ) 0.1 , b ) 0.001 , c ) 0.01 , d ) 1.0 e - 06 , e ) none of these | d | multiply(divide(0.001, 0.001), const_100) | 0.001 ã — 0.001 = ? | "0.001 ã — 0.001 = ? or , ? = 0.000001 answer d" | a = 0 / 1
b = a * 100
|
a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7 | c | divide(add(20, 4), subtract(8, const_2)) | if doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product , the number is | solution let the number be x . = then , 2 x + 20 = 8 x – 4 = 6 x = 24 ‹ = › x = 4 . answer c | a = 20 + 4
b = 8 - 2
c = a / b
|
a ) 2.25 , b ) 3.25 , c ) 10.25 , d ) 5.25 , e ) 6.25 | c | subtract(power(3.5, 2), const_2) | x + ( 1 / x ) = 3.5 find x ^ 2 + ( 1 / x ^ 2 ) | squaring on both sides ( x + 1 / x ) ^ 2 = 3.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 12.25 - 2 x ^ 2 + 1 / x ^ 2 = 10.25 answer : c | a = 3 ** 5
b = a - 2
|
a ) 6084 , b ) 3788 , c ) 2077 , d ) 8262 , e ) 1812 | d | subtract(add(add(add(multiply(multiply(9, const_100), const_10), multiply(5, const_100)), multiply(2, const_10)), 1), add(add(add(const_1000, multiply(2, const_100)), multiply(5, const_10)), 9)) | what is the difference between the largest number and the least number written with the digits 9 , 2 , 1 , 5 ? | "explanation : 1259 9521 - - - - - - - - - - - - 8262 answer : d" | a = 9 * 100
b = a * 10
c = 5 * 100
d = b + c
e = 2 * 10
f = d + e
g = f + 1
h = 2 * 100
i = 1000 + h
j = 5 * 10
k = i + j
l = k + 9
m = g - l
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | c | multiply(divide(2, 2), multiply(const_4, 1)) | the ratio of flour to water to sugar in a recipe is 7 : 2 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ? | "the ratio of flour to water is 14 : 2 . the ratio of flour to sugar is 3.5 : 1 = 14 : 4 . the new ratio of flour to water to sugar is 14 : 2 : 4 if we need 2 cups of water , then we need 4 cups of sugar . the answer is c ." | a = 2 / 2
b = 4 * 1
c = a * b
|
a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m | b | subtract(multiply(multiply(45, const_0_2778), 30), 130) | a train , 130 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is | explanation : assume the length of the bridge = x meter total distance covered = 130 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 130 + x ) / 30 m / s = > 45 × ( 10 / 36 ) = ( 130 + x ) / 30 = > 45 × 10 × 30 / 36 = 130 + x = > 45 × 10 × 10 / 12 = 130 + x = > 15 × 10 × 10 / 4 = 130 + x = > 15 × 25 = 130 + x = 375 = > x = 375 - 130 = 245 answer : option b | a = 45 * const_0_2778
b = a * 30
c = b - 130
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | c | subtract(multiply(multiply(multiply(1258, 6754), 4512), 9783), subtract(multiply(multiply(multiply(1258, 6754), 4512), 9783), add(const_4, const_4))) | the unit digit in the product 1258 * 6754 * 4512 * 9783 is ? | "unit digit in the given product = unit digit in 8 * 4 * 2 * 3 = 2 answer is c" | a = 1258 * 6754
b = a * 4512
c = b * 9783
d = 1258 * 6754
e = d * 4512
f = e * 9783
g = 4 + 4
h = f - g
i = c - h
|
a ) 671.5 , b ) 600 , c ) 672.5 , d ) 673 , e ) 773.5 | b | divide(1, divide(add(multiply(const_3600, divide(1, 900)), 2), const_3600)) | a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ? | "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 900 kilometers per hour is 1 / 900 hours = 3,600 / 900 seconds = 4 seconds ; time to cover this distance at regular speed is 900 + 2 = 902 seconds = 902 / 3,600 hours = 1 / 600 hours ; so , we get that to cover 1 kilometer 1 / 600 hours is needed - - > regular speed 600 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : b ." | a = 1 / 900
b = 3600 * a
c = b + 2
d = c / 3600
e = 1 / d
|
a ) 50.9 , b ) 52.9 , c ) 51.9 , d ) 53.25 , e ) none of the above | c | divide(add(add(add(multiply(70, 50), multiply(35, 60)), multiply(45, 55)), multiply(42, 45)), add(add(add(70, 35), 45), 42)) | a school has 4 section of chemistry in class x having 70 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student . | "required average marks = 70 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 70 + 35 + 45 + 42 = 3500 + 2100 + 2475 + 1890 / 192 = 9965 â „ 192 = 51.90 answer c" | a = 70 * 50
b = 35 * 60
c = a + b
d = 45 * 55
e = c + d
f = 42 * 45
g = e + f
h = 70 + 35
i = h + 45
j = i + 42
k = g / j
|
a ) 2 , b ) 5 , c ) 12 , d ) 8 , e ) 4 | e | subtract(multiply(60, divide(40, const_100)), multiply(divide(4, 5), 25)) | how much is 40 % of 60 is greater than 4 / 5 of 25 ? | "( 40 / 100 ) * 60 â € “ ( 4 / 5 ) * 25 24 - 20 = 4 answer : e" | a = 40 / 100
b = 60 * a
c = 4 / 5
d = c * 25
e = b - d
|
a ) $ 6512.50 , b ) $ 7512.50 , c ) $ 5512.50 , d ) $ 4512.50 , e ) $ 5250.00 | c | add(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 5), const_100)), divide(multiply(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 5), const_100)), 5), const_100)) | today joelle opened an interest - bearing savings account and deposited $ 5,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ? | "interest for 1 st year = 5000 * 5 / 100 = 250 interest for 2 nd year = 5250 * 5 / 100 = 262.50 total = 5000 + 250 + 262.50 = 5512.50 answer : c" | a = 3 * 2
b = a * 100
c = b * 10
d = 3 * 2
e = d * 100
f = e * 10
g = f * 5
h = g / 100
i = c + h
j = 3 * 2
k = j * 100
l = k * 10
m = 3 * 2
n = m * 100
o = n * 10
p = o * 5
q = p / 100
r = l + q
s = r * 5
t = s / 100
u = i + t
|
a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150 | c | divide(multiply(26, 10), const_2) | if the sides of a triangle are 30 cm , 26 cm and 10 cm , what is its area ? | "the triangle with sides 30 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : option c" | a = 26 * 10
b = a / 2
|
a ) $ 15,202 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155 | a | multiply(divide(const_3, const_4), const_1000) | a store owner estimates that the average price of type a products will increase by 15 % next year and that the price of type b products will increase by 18 % next year . this year , the total amount paid for type a products was $ 4600 and the total price paid for type b products was $ 8400 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ? | "cost of type a products next year = 1.15 * 4600 = 5290 cost of type b products next year = 1.18 * 8400 = 9912 total 5290 + 9912 = 15202 answer : a" | a = 3 / 4
b = a * 1000
|
a ) 151 , b ) 331 , c ) 511 , d ) 43 , e ) 87 | d | multiply(18, divide(subtract(add(multiply(10, 2), 3), 7), subtract(18, 10))) | when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 10 and the remainder is 3 . what is the value of n ? | "n / p = 18 7 / p = 18 p + 7 n / ( p + 2 ) = 10 1 / ( p + 2 ) = 10 p + 20 + 3 solving these two equations we get p = 2 n = 43 answer is d" | a = 10 * 2
b = a + 3
c = b - 7
d = 18 - 10
e = c / d
f = 18 * e
|
a ) 16060 , b ) 14000 , c ) 18000 , d ) 12000 , e ) none of these | d | divide(11400, add(divide(multiply(14, subtract(subtract(9, const_3), const_2)), const_100), add(divide(multiply(6, const_2), const_100), divide(multiply(9, 3), const_100)))) | ashok borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years and at the rate of 14 % p . a . for the period beyond 5 years . if he pays a total interest of 11400 / - at the end of 9 years , how much money did he borrow ? | we have , si = p × r × t / 100 ∴ 11400 = p × 6 × 2 / 100 + p × 9 × 3 / 100 + p × 14 × 4 / 100 or , 12 p + 27 p + 56 p = 11400 × 100 or , 95 p = 11400 × 100 ∴ p = 12000 answer d | a = 9 - 3
b = a - 2
c = 14 * b
d = c / 100
e = 6 * 2
f = e / 100
g = 9 * 3
h = g / 100
i = f + h
j = d + i
k = 11400 / j
|
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