Split (1)

test · 2.98k rows

Problem stringlengths 5 628	Rationale stringlengths 1 2.74k	options stringlengths 39 113	correct stringclasses 5 values	annotated_formula stringlengths 6 848	linear_formula stringlengths 7 357	category stringclasses 6 values
find the value of 72519 x 9999 = y ?	"72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"	a ) 23,200 , b ) 257 , c ) 58.65 ft , d ) 16 , e ) 725117481	e	multiply(subtract(9999, const_4), 72519)	subtract(n1,const_4)\|multiply(#0,n0)\|	general
a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 49 / 64 . how many marbles are in the bag ?	"ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probab...	a ) 12 , b ) 89 % , c ) 96 , d ) 10 , e ) 16	c	divide(12, subtract(const_1, sqrt(divide(49, 64))))	divide(n2,n3)\|sqrt(#0)\|subtract(const_1,#1)\|divide(n0,#2)\|	other
average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ?	option ' c '	a ) 60 liters , b ) 2 , 3,4 , c ) 43 , d ) 30 , e ) 625	c	subtract(multiply(15, 43), add(multiply(7, 41), multiply(7, 45)))	multiply(n0,n1)\|multiply(n2,n3)\|multiply(n2,n5)\|add(#1,#2)\|subtract(#0,#3)	general
the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 432 . find the principal ?	p = 432 ( 100 / 5 ) ^ 2 = > p = 10800 answer : e	a ) $ 25 , b ) 350 , c ) $ 37.8 , d ) 2500 , e ) 10800	e	divide(432, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1)))	divide(n1,const_100)\|add(#0,const_1)\|multiply(n0,#0)\|add(#2,const_1)\|power(#1,n0)\|subtract(#4,#3)\|divide(n2,#5)	gain
a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is π r during the first 30 seconds , π r / 2 during next one minute , π r / 4 during next 2 minutes , π r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for t...	explanation : there is more than 1 way to approach the solution ; however , i will detail the easiest way to go about it here . we want to find the ratio of time taken for nth round : time taken for ( n - 1 ) th round it will be same as finding the ratio of time taken for 2 nd round : time taken for 1 st round . 1 roun...	a ) 18 , b ) 16 , c ) - 4 , d ) 26 ° , e ) $ 300,000	b	power(2, 4)	power(n1,n2)	physics
. a car covers a distance of 1028 km in 4 hours . find its speed ?	"1028 / 4 = 257 kmph answer : d"	a ) 16 hrs , b ) 6 , c ) 150 , d ) 2.5 , e ) 257	e	divide(1028, 4)	divide(n0,n1)\|	physics
the cost price of a radio is rs . 2550 and it was sold for rs . 2130 , find the loss % ?	"2550 - - - - 400 100 - - - - ? = > 15 % answer : c"	a ) 15 , b ) 10750 , c ) 4 cm', ' , d ) 1 , e ) 9000	a	multiply(divide(subtract(2550, 2130), 2550), const_100)	subtract(n0,n1)\|divide(#0,n0)\|multiply(#1,const_100)\|	gain
if x * y = xy – 2 ( x + y ) for all integers x and y , then 4 * ( – 3 ) =	"4 * ( - 3 ) = 4 * ( - 3 ) - 2 ( 4 + ( - 3 ) ) = - 12 - 2 = - 14 option ( a )"	a ) 8 .', ' , b ) 20.9 , c ) – 14 , d ) 990 , e ) 37	c	add(negate(multiply(add(negate(3), 4), 2)), multiply(negate(3), 4))	negate(n2)\|add(n1,#0)\|multiply(n1,#0)\|multiply(#1,n0)\|negate(#3)\|add(#2,#4)\|	general
the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t...	"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"	a ) 10,800 , b ) 844.03 m , c ) t = 32 , d ) 420 gallons', ' , e ) 23 / 29	c	multiply(8, 4)	multiply(n0,n3)\|	geometry
an enterprising businessman earns an income of re 5 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 10 th day of business , he earns an income of :	2 nd day he earns = 3 ( 2 – 5 ) 3 rd day he earns = 3 ( 3 – 5 ) on 20 th day he earns 3 ( 20 - 5 ) = 45 rupees answer : d	a ) 9 years , b ) 4 % , c ) 500 , d ) 9620 , e ) 45	e	subtract(multiply(5, 10), 5)	multiply(n0,n1)\|subtract(#0,n0)	physics
a student chose a number , multiplied it by 3 , then subtracted 138 from the result and got 102 . what was the number he chose ?	"solution : let xx be the number he chose , then 3 ⋅ x − 138 = 102 3 x = 240 x = 80 answer a"	a ) 120 , b ) 1173.98 , c ) 475 , d ) 80 , e ) 9000	d	divide(add(102, 138), 3)	add(n1,n2)\|divide(#0,n0)\|	general
two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively find the time taken by the slower train to pass the driver of the faster one .	solution relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec total distance covered = ( 500 + 500 ) m = 1000 m required time = ( 1000 x 6 / 125 ) sec = 48 sec answer c	a ) 48 sec , b ) 1 / 12 , c ) 50 , d ) 15 , e ) 25	a	multiply(divide(500, divide(multiply(const_1000, add(45, 30)), const_3600)), const_2)	add(n1,n2)\|multiply(#0,const_1000)\|divide(#1,const_3600)\|divide(n0,#2)\|multiply(#3,const_2)	physics
the population of a village is 14300 . it increases annually at the rate of 15 % p . a . what will be its population after 2 years ?	formula : ( after = 100 denominator ago = 100 numerator ) 14300 × 115 / 100 × 115 / 100 = 18911 a	a ) 18911 , b ) 257 , c ) $ 300 , d ) 24000 , e ) 22.8	a	multiply(14300, power(add(const_1, divide(15, const_100)), 2))	divide(n1,const_100)\|add(#0,const_1)\|power(#1,n2)\|multiply(n0,#2)	gain
what is the sum of all possible solutions to \| x - 3 \| ^ 2 + \| x - 3 \| = 20 ?	"first of all \| x - 3 \| ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + \| x - 3 \| = 20 . when x < 3 , x - 3 is negative , thus \| x - 3 \| = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 ,...	a ) 6 % , b ) 11 , c ) 0.01616 , d ) 6 , e ) 5.6	d	add(add(const_4, 3), subtract(3, const_4))	add(n0,const_4)\|subtract(n0,const_4)\|add(#0,#1)\|	general
if x / 5 + 9 / x = 14 / 5 , what are the values of 3 x - 7 ?	i got the same thing b is the answer 8 or 20	a ) 3 / 4 , b ) 40.46 , c ) 8 and 20 , d ) 81 , e ) 228.623	c	add(multiply(subtract(add(subtract(9, 5), sqrt(subtract(power(subtract(9, 5), 5), multiply(5, multiply(9, 5))))), 3), const_10), subtract(subtract(subtract(9, 5), sqrt(subtract(power(subtract(9, 5), 5), multiply(5, multiply(9, 5))))), 3))	multiply(n0,n1)\|subtract(n1,n0)\|multiply(n0,#0)\|power(#1,n3)\|subtract(#3,#2)\|sqrt(#4)\|add(#5,#1)\|subtract(#1,#5)\|subtract(#6,n4)\|subtract(#7,n4)\|multiply(#8,const_10)\|add(#10,#9)\|	general
two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 23 seconds , what is the ratio of their speeds ?	"speed = x and y resp length of first = 27 x length of second train = 17 y related speed = x + y time taken to cross each other = 23 s 27 x + 17 y / x + y = 23 27 x + 17 y = 23 ( x + y ) 4 x = 6 y x / y = 6 / 4 = 3 / 2 answer b"	a ) 36 , b ) 3 : 2 , c ) 28 m , d ) 51 , e ) 600	b	divide(subtract(27, 23), subtract(23, 17))	subtract(n0,n2)\|subtract(n2,n1)\|divide(#0,#1)\|	physics
a closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity . when the tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . when the tank is placed on its side on level ground , what is the height , in feet , of the surface of th...	36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d	a ) 1804 , b ) 1400 , c ) 3 feet', ' , d ) 9 , e ) x + 2 x + 2	c	sqrt(divide(divide(multiply(36, const_pi), 4), const_pi))	multiply(n0,const_pi)\|divide(#0,n1)\|divide(#1,const_pi)\|sqrt(#2)	geometry
the ratio of two speeds of two trains is 3 to 4 . if each of the trains slows its speed 5 km / hr , what will be the ratio of these two train speeds ?	3 / 4 = 3 x / 4 x we need to find out ( 3 x + 5 ) / ( 4 x + 5 ) off course we can not solve this to arrive at any rational number hence e .	a ) 2599980 , b ) 11 / 48,000 , c ) it can not be determined from the information given , d ) 500 , e ) 8	c	divide(3, 4)	divide(n0,n1)	other
shopkeeper rise price by 33 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?	"let d initial price be 100 33 % rise now price = 133 / 100 * 100 = 133 10 % discount then price = 133 * 90 / 100 = 119.7 15 % discount then price = 119.7 * 85 / 100 = 101.745 so gain = 101.745 - 100 = 1.745 gain % = gain * 100 / cp = = > 1.745 * 100 / 100 = 1.745 % answer : a"	a ) $ 8 , b ) 2200 , c ) 24 , d ) 30 , e ) 1.745 %	e	subtract(multiply(multiply(add(const_100, 33), divide(subtract(const_100, 10), const_100)), divide(subtract(const_100, 15), const_100)), const_100)	add(n0,const_100)\|subtract(const_100,n2)\|subtract(const_100,n1)\|divide(#1,const_100)\|divide(#2,const_100)\|multiply(#0,#4)\|multiply(#3,#5)\|subtract(#6,const_100)\|	gain
in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13 . if the shop carries 352 dogs and bunnies total in stock , how many dogs are there ?	"let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 13 x total dogs and bunnies = 16 x . and we are given that 16 x = 352 . hence x = 22 . dogs = 3 x = 3 * 22 = 66 ( option b )"	a ) 1260 , b ) 11 , c ) 4 : 5 , d ) 66 , e ) rs . 3800	d	multiply(divide(352, add(3, 13)), 3)	add(n0,n2)\|divide(n3,#0)\|multiply(n0,#1)\|	other
a box contain the number of balls which is as much times greater than 15 as much times lesser than 240 . the no . of ball is ?	"answer let the number be x . x / 15 = 240 / x x ^ 2 = 240 * 15 = 3600 x = √ 3600 = 60 correct option : c"	a ) $ 875 , b ) 60 , c ) 1600 , d ) 48 , e ) 2500	b	divide(add(240, 15), const_2)	add(n0,n1)\|divide(#0,const_2)\|	general
when the price of an article was reduced by 25 % its sale increased by 80 % . what was the net effect on the sale ?	"if n items are sold for $ p each , revenue is $ np . if we reduce the price by 25 % , the new price is 0.75 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.75 p ) ( 1.8 n ) = 1.35 np , which is 1.35 times the old revenue , so is 35 % greater . answer : a"	a ) 3 , b ) 16 , c ) 1.33 , d ) 35 : 44 , e ) 35 % increase	e	subtract(divide(multiply(add(80, const_100), subtract(const_100, 25)), const_100), const_100)	add(n1,const_100)\|subtract(const_100,n0)\|multiply(#0,#1)\|divide(#2,const_100)\|subtract(#3,const_100)\|	gain
5 years ago , the average age of a and b was 15 years . average age of a , b and c today is 20 years . how old will c be after 14 years ?	explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b	a ) 16.2 % , b ) 158.256 m , c ) 3 : 4 , d ) 34 , e ) 33 %	d	add(subtract(multiply(20, const_3), add(add(multiply(15, const_2), 5), 5)), 14)	multiply(n2,const_3)\|multiply(n1,const_2)\|add(n0,#1)\|add(n0,#2)\|subtract(#0,#3)\|add(n3,#4)	general
one fourth of a solution that was 10 % sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?	"say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : a ."	a ) 3 , b ) 351 , c ) 34 % , d ) 10.5 , e ) 1 / 25	c	multiply(divide(subtract(multiply(const_100, divide(16, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(10, const_100))), multiply(divide(const_1, const_4), const_100)), const_100)	divide(n1,const_100)\|divide(n0,const_100)\|divide(const_1,const_4)\|multiply(#0,const_100)\|multiply(#2,const_100)\|subtract(const_100,#4)\|multiply(#1,#5)\|subtract(#3,#6)\|divide(#7,#4)\|multiply(#8,const_100)\|	gain
from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king or queen ?	"p ( black card ) = 1 / 2 p ( king or queen ) = 2 / 13 p ( black card then a king / queen ) = 1 / 2 * 2 / 13 = 1 / 13 the answer is b ."	a ) 1 / 13 , b ) 227.04 mtrs , c ) 87 % , d ) 7 , e ) 7.2 hr	a	multiply(divide(add(multiply(const_3, const_4), const_1), const_52), divide(const_2, const_52))	divide(const_2,const_52)\|multiply(const_3,const_4)\|add(#1,const_1)\|divide(#2,const_52)\|multiply(#3,#0)\|	probability
a man whose bowling average is 22.2 , takes 4 wickets for 36 runs and thereby decreases his average by 1.2 . the number of wickets , taken by him before his last match is :	"explanation : let the number of wickets taken before the last match is x . then , ( 22.2 x + 36 ) / ( x + 4 ) = 21 = > 22.2 x + 36 = 21 x + 84 = > 1.2 x = 48 = > x = 48 / 1.2 = 40 answer : d"	a ) $ 110 , b ) 24 , c ) 150 , d ) 7 , e ) 40	e	divide(subtract(multiply(floor(22.2), 4), 36), subtract(22.2, floor(22.2)))	floor(n0)\|multiply(n1,#0)\|subtract(n0,#0)\|subtract(#1,n2)\|divide(#3,#2)\|	general
a can give b 100 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?	"explanation : a runs 1000 meters while b runs 900 meters and c runs 880 meters . therefore , b runs 900 meters while c runs 880 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 880 ) / 900 = 977.778 meters thus , b can give c ( 1000 - 977.77 ) = 22.22 meters start answer : c"	a ) 2700 , b ) $ 370,000 , c ) 108 , d ) 22.22 meters , e ) 54	d	subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 120)), subtract(multiply(const_100, const_10), 100)))	multiply(const_10,const_100)\|subtract(#0,n1)\|subtract(#0,n0)\|multiply(#0,#1)\|divide(#3,#2)\|subtract(#0,#4)\|	physics
a train 450 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :	"relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 450 × 2 / 15 ) sec = 60 sec answer : e"	a ) 60 sec , b ) 300 , c ) 3.2 . , d ) 3024 , e ) rs . 20985	a	multiply(const_3600, divide(divide(450, const_1000), add(25, 2)))	add(n1,n2)\|divide(n0,const_1000)\|divide(#1,#0)\|multiply(#2,const_3600)\|	physics
a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?	you need to divide the width and length of the rectangular to equal pieces where l = w you can solve this using gcf 35 = 5 * 7 45 = 3 * 3 * 5 gcf = 5 p . s you can make squares with side of 5 answer : c	a ) 20 , b ) 2 , c ) $ 96 , d ) 5 inches', ' , e ) 62	d	divide(subtract(45, 35), const_2)	subtract(n1,n0)\|divide(#0,const_2)	geometry
find the greatest number which leaves the same remainder when it divides 25 , 50 and 120 .	"120 - 50 = 70 50 - 25 = 25 120 - 25 = 95 the h . c . f of 25 , 70 and 95 is 5 . answer : b"	a ) 25 , b ) 20 , c ) 21600 , d ) 5 , e ) 180 ares .	d	divide(subtract(50, 25), const_2)	subtract(n1,n0)\|divide(#0,const_2)\|	general
o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 11.6 ) + ...	"o ( 11.6 ) + e ( – 10.4 ) + o ( – 9.2 ) + e ( 9.5 ) = 13 + ( - 10 ) + ( - 11 ) + 8 = 0 the answer is c ."	a ) 200 % , b ) 220 , c ) 3 , d ) s . 180 , e ) 0	e	add(add(add(multiply(11.6, const_1), multiply(negate(10.4), const_1)), negate(9.2)), multiply(9.5, const_1))	multiply(n0,const_1)\|multiply(n3,const_1)\|negate(n1)\|negate(n2)\|multiply(#2,const_1)\|add(#0,#4)\|add(#5,#3)\|add(#6,#1)\|	general
what is the smallest positive integer k such that the product of 2205 x k is a perfect square ?	"a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 2205 = 3 ^ 2 * 7 ^ 7 * 5 , so if k = 5 then 2205 k = ( 3 * 7 * 5 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power ...	a ) 9 / 7 , b ) 5 , c ) 11.25 , d ) 81 , e ) 990	b	add(const_3, const_4)	add(const_3,const_4)\|	general
the function f ( p ) represents the number of ways that prime numbers can be uniquely summed to form a certain number p such that p = a + b + c + d … where those summed variables are each prime and a ≤ b ≤ c ≤ d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 1...	so we can start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d	a ) 40 , b ) 7 , c ) 35 % , d ) 55 % , e ) 200	b	add(divide(12, const_4), const_4)	divide(n11,const_4)\|add(#0,const_4)	general
in what time will a train 175 m long cross an electric pole , it its speed be 144 km / hr ?	"speed = 144 * 5 / 18 = 40 m / sec time taken = 175 / 40 = 4.37 sec . answer : c"	a ) 4 years , b ) 67 % , c ) 4.37 sec , d ) 5120 , e ) 6	c	divide(175, multiply(144, const_0_2778))	multiply(n1,const_0_2778)\|divide(n0,#0)\|	physics
a student chose a number , multiplied it by 5 , then subtracted 275 from the result and got 135 . what was the number he chose ?	"let x be the number he chose , then 5 ⋅ x − 275 = 135 5 x = 410 x = 82 correct answer b"	a ) 110 , b ) 70 , c ) 40 , d ) 2.56 % , e ) 82	e	divide(add(135, 275), 5)	add(n1,n2)\|divide(#0,n0)\|	general
in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?	"let c be the capacity of the can . ( 3 / 5 ) * ( c - 6 ) + 6 = ( 2 / 3 ) * c 9 c - 54 + 90 = 10 c c = 36 the answer is a ."	a ) 36 , b ) 4 sec , c ) 280 , d ) 36 days , e ) $ 0.40	a	add(add(multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 3), 6), multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 2))	multiply(n2,n4)\|multiply(n1,n3)\|multiply(n0,n4)\|subtract(#1,#2)\|divide(#0,#3)\|multiply(n0,#4)\|multiply(n1,#4)\|add(n2,#5)\|add(#7,#6)\|	general
susan drives from city a to city b . after two hours of driving she noticed that she covered 80 km and calculated that , if she continued driving at the same speed , she would end up been 15 minutes late . so she increased her speed by 10 km / hr and she arrived at city b 36 minutes earlier than she planned . find the ...	let xx be the distance between a and b . since susan covered 80 km in 2 hours , her speed was v = 802 = 40 v = 802 = 40 km / hr . if she continued at the same speed she would be 1515 minutes late , i . e . the planned time on the road is x 40 − 1560 x 40 − 1560 hr . the rest of the distance is ( x − 80 ) ( x − 80 ) km ...	a ) 250 , b ) . 2 , c ) 10.28 % , d ) 16 , e ) 16.2 %	a	add(divide(subtract(add(subtract(divide(36, const_60), divide(80, add(divide(80, const_2), 10))), const_2), divide(15, const_60)), subtract(divide(const_1, divide(80, const_2)), divide(const_1, add(divide(80, const_2), 10)))), const_100)	divide(n3,const_60)\|divide(n0,const_2)\|divide(n1,const_60)\|add(n2,#1)\|divide(const_1,#1)\|divide(n0,#3)\|divide(const_1,#3)\|subtract(#0,#5)\|subtract(#4,#6)\|add(#7,const_2)\|subtract(#9,#2)\|divide(#10,#8)\|add(#11,const_100)	physics
a train running at the speed of 40 km / hr crosses a pole in 9 sec . what is the length of the train ?	"speed = 40 * 5 / 18 = 100 / 9 m / sec length of the train = speed * time = 100 / 9 * 9 = 100 m answer : a"	a ) 16 , b ) 66 , c ) 54 , d ) 100 m , e ) 22	d	multiply(divide(multiply(40, const_1000), const_3600), 9)	multiply(n0,const_1000)\|divide(#0,const_3600)\|multiply(n1,#1)\|	physics
what is the remainder if 7 ^ 16 is divided by 100 ?	"7 ^ 16 can be written as ( 7 ^ 4 ) ^ 4 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 4 by 100 , the reminder is 1 ^ 4 = 1 answer : d"	a ) 90 , b ) 5940 , c ) 29 , d ) 2 ^ 11 - 1 , e ) 1	e	subtract(divide(100, const_2), multiply(7, 7))	divide(n2,const_2)\|multiply(n0,n0)\|subtract(#0,#1)\|	general
a large box contains 17 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?	"the number of chocolate bars is equal to 17 * 25 = 425 correct answer c"	a ) 1 , b ) $ 32500 , c ) 18 days , d ) 425 , e ) 400	d	multiply(17, 25)	multiply(n0,n1)\|	general
what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?	explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d	a ) 3.6 km , b ) 11.25 sec , c ) 3000000 , d ) 6 , e ) 21 hours	d	divide(6, const_1)	divide(n2,const_1)	general
jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 6 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?	"u / i = 6 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 30 : 18 : 2 i . e . u : b = 30 : 2 answer : option b"	a ) 43983 , b ) 1800 , c ) 70 , d ) 5 inches', ' , e ) 30 : 2	e	divide(multiply(6, 5), multiply(1, 2))	multiply(n0,n2)\|multiply(n1,n3)\|divide(#0,#1)\|	other
a man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 3 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman...	when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 3 * 15 / 60 ...	a ) 63 , b ) 2 , c ) 3200 , d ) 50', ' , e ) 450	b	multiply(const_60, divide(multiply(divide(3, const_60), subtract(15, 9)), 9))	divide(n2,const_60)\|subtract(n1,n0)\|multiply(#0,#1)\|divide(#2,n0)\|multiply(#3,const_60)	physics
in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 20 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , b...	"since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats ....	a ) 12 % , b ) 113 m 2 , c ) 9 / 25 , d ) 44 . , e ) 420 gallons', '	a	multiply(divide(subtract(add(multiply(divide(20, const_100), 2), multiply(divide(80, const_100), 3)), add(subtract(3, multiply(divide(80, const_100), 3)), subtract(2, multiply(divide(20, const_100), 2)))), add(3, 2)), const_100)	add(n0,n1)\|divide(n3,const_100)\|divide(n2,const_100)\|multiply(n1,#1)\|multiply(n0,#2)\|add(#3,#4)\|subtract(n0,#4)\|subtract(n1,#3)\|add(#6,#7)\|subtract(#5,#8)\|divide(#9,#0)\|multiply(#10,const_100)\|	other
a school has received 50 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to c...	"let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 50 % of total amount . so total amount = 16000 * 100 / 50 remaining amount is 50 % of total amount . 50 % of total amount = 16000 * ( 100 / 50 ) * ( 50 / 100 ) = 16000 this amount has to be divided by 50 ( remaining people are 5...	a ) $ 320 , b ) 80 % , c ) 49 , d ) 6 , e ) 70	a	divide(multiply(divide(multiply(divide(40, const_100), 400), divide(50, const_100)), divide(40, const_100)), divide(50, const_100))	divide(n2,const_100)\|divide(n0,const_100)\|multiply(n1,#0)\|divide(#2,#1)\|multiply(#3,#0)\|divide(#4,#1)\|	general
the sides of a square region , measured to the nearest centimeter , are 10 centimeters long . the least possible value of the actual area of the square region is	"though there might be some technicalities concerning the termnearest ( as 9.5 is equidistant from both 9 and 10 ) the answer still should be : 9.5 ^ 2 = 90.25 . answer : e"	a ) 90.25 sq cm , b ) 1000 m , c ) 100 days , d ) 89 % , e ) 16 / 625	a	power(subtract(subtract(10, const_0_25), const_0_25), const_2)	subtract(n0,const_0_25)\|subtract(#0,const_0_25)\|power(#1,const_2)\|	geometry
p software has coding line 5 % more than n , n software has coding line 1 / 2 more than m . m software has 100 lines of coding . find p lines .	"m s / w has 100 line of code n s / w has = 100 + 100 * 1 / 2 = 150 line of code p s / w 5 % more n ' code 150 + 7.5 = 157.5 or 158 line of code answer : e"	a ) 158 , b ) 23 , c ) 1.46 % , d ) 44800 , e ) 26250	a	add(100, divide(100, 2))	divide(n3,n2)\|add(n3,#0)\|	general
in a garden , there are 10 rows and 15 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is	"explanation : each row contains 15 plants . there are 14 gapes between the two corner trees ( 14 x 2 ) metres and 1 metre on each side is left . therefore length = ( 28 + 2 ) m = 30 m . answer : b"	a ) $ 600 , b ) rs . 5.10 , c ) 30 m , d ) 16 , e ) 27 / 20	c	add(add(multiply(subtract(15, const_1), 2), divide(10, 2)), divide(10, 2))	divide(n0,n2)\|subtract(n1,const_1)\|multiply(n2,#1)\|add(#0,#2)\|add(#3,#0)\|	physics
if tim had lunch at $ 50.50 and he gave 10 % tip , how much did he spend ?	"the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 10 / 100 ) * 50.50 = $ 5.05 total spent 50.50 + 5.05 = $ 55.55 correct answer d"	a ) 38 , b ) 55 % , c ) 25 % , d ) $ 55.55 , e ) $ 500	d	add(50.50, divide(multiply(50.50, 10), const_100))	multiply(n0,n1)\|divide(#0,const_100)\|add(n0,#1)\|	gain
a 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .	"relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 240 / 9 = 500 / 9 x = 260 ans is 260 m answer : a"	a ) 5 / 1 , b ) 32.8 % , c ) 120 , d ) 260 m , e ) 70	d	subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 240)	add(n1,n2)\|multiply(#0,const_0_2778)\|multiply(n3,#1)\|subtract(#2,n0)\|	physics
company a imported 12,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?	answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 10 % brass widgets leads to 4 % blue brass widgets out of the total 10,550 widgets . 12,000 / 100 * ...	a ) 8 : 5 , b ) 480 , c ) 80 % , d ) 55 % , e ) 6	b	multiply(multiply(multiply(multiply(divide(10, const_100), divide(40, const_100)), divide(add(10, const_2), 10)), const_100), const_100)	add(n1,const_2)\|divide(n1,const_100)\|divide(n3,const_100)\|divide(#0,n1)\|multiply(#1,#2)\|multiply(#3,#4)\|multiply(#5,const_100)\|multiply(#6,const_100)	gain
mr . das decided to walk down the escalator of a mall . he found that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stair she would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time h...	here when he step down 26 steps he has 30 seconds for remaining steps . if he step down 34 stairs he has only 18 sec . 30 - 18 = 12 12 secs for 8 steps . . 18 secs for 12 steps . 12 + 34 = 46 so ans is 46 . . answer : b	a ) 6 , b ) 32.8 % , c ) 3.6 , d ) 5 / 4 , e ) 44800	a	subtract(add(multiply(divide(subtract(34, 26), subtract(30, 18)), 30), 26), multiply(const_4, const_10))	multiply(const_10,const_4)\|subtract(n2,n0)\|subtract(n1,n3)\|divide(#1,#2)\|multiply(n1,#3)\|add(n0,#4)\|subtract(#5,#0)	physics
solution x is 30 % chemical a and 70 % chemical b by volume . solution y is 40 % chemical a and 60 % chemical b by volume . if a mixture of x and y is 36 % chemical a , what percent of the mixture is solution x ?	"the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.36 ( x + y ) x = 2 y / 3 x / ( x + y ) = ( 2 y / 3 ) / ( 5 y / 3 ) = 2 / 5 = 40 % . the answer is c ."	a ) 1.6 . , b ) 40 % , c ) 240 meters , d ) 15 , e ) 600	b	multiply(divide(divide(subtract(40, 36), subtract(36, 30)), add(divide(subtract(40, 36), subtract(36, 30)), const_1)), const_100)	subtract(n2,n4)\|subtract(n4,n0)\|divide(#0,#1)\|add(#2,const_1)\|divide(#2,#3)\|multiply(#4,const_100)\|	gain
jim ’ s taxi service charges an initial fee of $ 2.45 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?	"let the fixed charge of jim ’ s taxi service = 2.45 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.45 + ( 3.6 / . 4 ) * . 35 = 2.45 + 9 * . 35 = 5.6 $ answer e"	a ) $ 5.6 , b ) 25 , c ) 80 , d ) 1 : 1 , e ) 6	a	add(2.45, multiply(0.35, divide(3.6, divide(2, 5))))	divide(n2,n3)\|divide(n4,#0)\|multiply(n1,#1)\|add(n0,#2)\|	general
a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all...	let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , y...	a ) 43 square meters , b ) 100775 , c ) 3 % , d ) 22.5 % , e ) 308	d	multiply(divide(divide(subtract(24, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100)	add(const_2,const_3)\|divide(const_100,#0)\|divide(#1,const_2)\|divide(#2,const_2)\|add(#2,#3)\|subtract(n0,#4)\|divide(#5,const_2)\|divide(#6,#1)\|multiply(#7,const_100)	general
on selling 9 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :	"( c . p . of 9 balls ) - ( s . p . of 9 balls ) = ( c . p . of 5 balls ) c . p . of 4 balls = s . p . of 9 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 4 = rs . 180 . answer : option e"	a ) 4 : 5 , b ) 2500 , c ) 151 / 31 , d ) 6 , e ) s . 180	e	divide(720, subtract(9, 5))	subtract(n0,n2)\|divide(n1,#0)\|	gain
boy sells a book for rs . 630 he gets a loss of 10 % , to gain 10 % , what should be the sp ?	"cost price = 630 / 90 x 100 = 700 to gain 10 % = 700 x 10 / 100 = 70 sp = cp + gain = 700 + 70 = 770 answer : d"	a ) 10000 , b ) 2 . , c ) 770 , d ) 32 , e ) 33.3 %	c	add(divide(630, subtract(const_1, divide(10, const_100))), multiply(divide(630, subtract(const_1, divide(10, const_100))), divide(10, const_100)))	divide(n1,const_100)\|divide(n2,const_100)\|subtract(const_1,#0)\|divide(n0,#2)\|multiply(#3,#1)\|add(#3,#4)\|	gain
a and b can do a piece of work in 11 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?	"c = 1 / 5 – 1 / 11 = 6 / 55 = > 9.2 days answer : d"	a ) 10 / 3 , b ) 31 , c ) 103.4 % , d ) 9.2 days , e ) 40 %	d	inverse(subtract(5, divide(5, 11)))	divide(n1,n0)\|subtract(n1,#0)\|inverse(#1)\|	physics
a train 310 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?	"speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 310 * 3 / 55 ] sec = 17 sec answer : d"	a ) 3 , b ) 17 , c ) 21 , d ) 1 , e ) 4 : 5	b	multiply(const_3600, divide(divide(310, const_1000), add(60, 6)))	add(n1,n2)\|divide(n0,const_1000)\|divide(#1,#0)\|multiply(#2,const_3600)\|	physics
how many odd factors does 210 have ?	start with the prime factorization : 210 = 2 * 3 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 , 1 } plus 1 to each = { 2 , 2 , 2 } product = 2 * 2 * 2 = 8 therefore , there are 8 odd factors of 210 . in case you are curious , they are { 1 , ...	a ) 32.8 % , b ) 40 , c ) 62.5 % , d ) 8 , e ) 28.57 %	d	add(add(add(const_4, const_2), const_1), const_1)	add(const_2,const_4)\|add(#0,const_1)\|add(#1,const_1)	other
sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every d...	"7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 350 - - > x = 1.715 . 1.25 x = ~ 2.14 . answer : c ."	a ) 24 , b ) $ 2.14 , c ) 300 , d ) 32 kmph , e ) 240000	b	multiply(divide(add(multiply(multiply(32, divide(75, const_100)), multiply(add(const_4, 1), const_2)), 350), add(multiply(subtract(multiply(add(const_4, 1), const_2), 3), 32), multiply(multiply(divide(add(const_100, 25), const_100), 3), 32))), divide(add(const_100, 25), const_100))	add(n5,const_4)\|add(n1,const_100)\|divide(n2,const_100)\|divide(#1,const_100)\|multiply(n3,#2)\|multiply(#0,const_2)\|multiply(#4,#5)\|multiply(n4,#3)\|subtract(#5,n4)\|add(n0,#6)\|multiply(n3,#8)\|multiply(n3,#7)\|add(#10,#11)\|divide(#9,#12)\|multiply(#13,#3)\|	gain
what is the greatest prime factor of 2 ^ 8 - 1 ?	"2 ^ 8 - 1 = ( 2 ^ 4 - 1 ) ( 2 ^ 4 + 1 ) = 15 * 17 the answer is c ."	a ) 16 , b ) 40 % , c ) 12 kmph , d ) 2 , e ) 17	e	floor(divide(2, divide(8, const_2)))	divide(n1,const_2)\|divide(n0,#0)\|floor(#1)\|	general
if x , y , and z are positive integers and 2 x = 3 y = 4 z , then the least possible value of x + y + z is	"given 2 x = 3 y = 5 z x + y + z in terms of x = x + ( 2 x / 3 ) + ( 2 x / 5 ) = 31 x / 15 now checking with each of the answers and see which value gives a minimum integer value . a x = 15 / 31 * 40 , not an integer b , c , d can be ruled out similarly . e is minimum value as x = 15 * 31 / 31 = 15 answer is e"	a ) 40 , b ) 48 , c ) 25 , d ) 7 , e ) 31	e	add(subtract(divide(multiply(multiply(2, 3), 4), 2), divide(multiply(multiply(2, 3), 4), 3)), divide(multiply(multiply(2, 3), 4), 4))	multiply(n0,n1)\|multiply(n2,#0)\|divide(#1,n2)\|divide(#1,n0)\|divide(#1,n1)\|subtract(#3,#4)\|add(#2,#5)\|	general
right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 7 ≤ x ≤ 1 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet ...	"we have the rectangle with dimensions 9 * 7 ( 9 horizontal dots and 7 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 7 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot...	a ) 174 cm , b ) 3 / 5 , c ) 3024 , d ) 50', ' , e ) 150	c	multiply(multiply(7, subtract(7, const_1)), multiply(9, 7))	multiply(n0,n3)\|subtract(n0,const_1)\|multiply(n0,#1)\|multiply(#2,#0)\|	geometry
a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?	c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 .	a ) 40 % , b ) 7 , c ) 13 , d ) 2 , e ) 90	e	add(divide(multiply(480, 10), const_60), 10)	multiply(n0,n2)\|divide(#0,const_60)\|add(n2,#1)	general
when n is divided by 48 , the remainder is 6 . what is the remainder when 4 n is divided by 8 ?	"let n = 6 ( leaves a remainder of 6 when divided by 48 ) 4 n = 4 ( 6 ) = 24 , which leaves a remainder of 0 when divided by 8 . answer a"	a ) 100 % , b ) rs . 20985 , c ) 78 , d ) 0 , e ) 0.45 %	d	subtract(6, reminder(4, 8))	reminder(n2,n3)\|subtract(n1,#0)\|	general
find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ?	if sum of the digits is divisible by 3 , the number is divisible by 3 . therefore , required number of non - negative integers is equal to count of numbers less than 10000 which are divisible by 3 . such numbers are ( 3 , 6 , 9 , . . . , 9999 ) ( arithmetic progression with first term = 3 , last term = 9999 , common di...	a ) 1 , b ) 40 , c ) $ 214.16 , d ) 3334 , e ) 50 %	d	add(floor(divide(10000, 3)), const_1)	divide(n0,n1)\|floor(#0)\|add(#1,const_1)	general
a , b and c can do a work in 7 , 14 and 21 days respectively . they completed the work and got rs . 242 . what is the share of c ?	"the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = rs . 44 \ answer : b"	a ) 49 hr , b ) 127 , c ) 44 , d ) 4.2 , e ) 855	c	multiply(242, divide(inverse(14), add(inverse(21), add(inverse(7), inverse(14)))))	inverse(n1)\|inverse(n0)\|inverse(n2)\|add(#1,#0)\|add(#3,#2)\|divide(#0,#4)\|multiply(n3,#5)\|	physics
the present population of a town is 4320 . population increase rate is 20 % p . a . find the population of town before 2 years ?	"p = 4320 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 4320 / ( 1 + 20 / 100 ) ^ 2 = 4320 / ( 6 / 5 ) ^ 2 = 3000 ( approximately ) answer is d"	a ) 6 : 15 , b ) 1 / 6 , c ) 36', ' , d ) 36.3 , e ) 3000	e	add(4320, divide(multiply(4320, 20), const_100))	multiply(n0,n1)\|divide(#0,const_100)\|add(n0,#1)\|	gain
if 12 men and 16 boys can do a piece of work in 7 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy .	"12 m + 16 b - - - - - 7 days 13 m + 24 b - - - - - - - 4 days 84 m + 112 b = 52 m + 96 b 32 m = 16 b = > 2 m = b m : b = 1 : 2 answer : b"	a ) 1 : 2 , b ) 9 , c ) $ 154.1 , d ) 7500 , e ) 32 square inches	a	divide(subtract(multiply(4, 24), multiply(7, 16)), subtract(multiply(7, 12), multiply(4, 13)))	multiply(n4,n5)\|multiply(n1,n2)\|multiply(n0,n2)\|multiply(n3,n5)\|subtract(#0,#1)\|subtract(#2,#3)\|divide(#4,#5)\|	physics
two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 6 days ?	"a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 6 days = 6 ( 1 / 18 ) = 1 / 3 . answer c"	a ) 1 / 12 , b ) 54 min , c ) 50 % , d ) 1405.25 , e ) 1 / 3	e	multiply(6, add(divide(const_1, 30), divide(const_1, 45)))	divide(const_1,n0)\|divide(const_1,n1)\|add(#0,#1)\|multiply(n2,#2)\|	physics
a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 432,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?	"number of boxes = total volume / volume of one box = 432,000 / ( 8 * 10 * 12 ) = 450 one box costs 7.50 , so 450 box will cost = 450 * 7.5 = 3375 e is the answer"	a ) 200 , b ) 100 , c ) 46 , d ) $ 3,375 , e ) 3.5	d	divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 7.50), const_1000)	multiply(const_100,const_3)\|multiply(n0,n1)\|multiply(n0,n1)\|add(#0,#1)\|multiply(n2,#2)\|add(#3,const_4)\|multiply(#5,const_1000)\|divide(#6,#4)\|multiply(n3,#7)\|divide(#8,const_1000)\|	general
in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate .	"solution : let the arrangement be , b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 4 ! ways . required number of ways , = 4 ! * 4 ! = 576 . answer : option d"	a ) 576 , b ) 1 / 104 , c ) 1 / 216 , d ) 3 , e ) 6	a	multiply(factorial(4), factorial(4))	factorial(n0)\|factorial(n1)\|multiply(#0,#1)\|	probability
two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 4 ½ hours if they are walking in the same direction ?	"rs = 5 ¾ - 4 ½ = 1 ¼ t = 4 ½ h . d = 5 / 4 * 9 / 2 = 45 / 8 = 5 5 / 8 km answer : c"	a ) 1.8 , b ) 5 5 / 8 km , c ) 130 cm , d ) 40 % , e ) 391	b	add(multiply(add(4, divide(const_1, const_2)), subtract(add(5, divide(const_3, 4)), add(4, divide(const_1, const_2)))), const_2)	divide(const_1,const_2)\|divide(const_3,n0)\|add(n2,#0)\|add(n1,#1)\|add(n0,#0)\|subtract(#3,#4)\|multiply(#2,#5)\|add(#6,const_2)\|	physics
kavi spends 50 % of his monthly salary on food and saves 80 % of the remaining amount . if his monthly salary is rs . 19000 , how much money does he save every month ?	explanation : kavi ' s monthly income = rs . 19,000 he spends 50 % on food . the total money spent on food = 50 / 100 * 19000 = rs . 9500 now , his monthly remaining income = rs . 19000 – rs . 9500 = rs . 9500 out of rs . 9500 , he saves 40 % . amount saved = 40 / 100 * 9500 = rs . 3800 answer : d	a ) $ 0.50 , b ) rs . 3800 , c ) 9 / 20 , d ) 4 , e ) 175.5 cm	b	divide(divide(multiply(divide(multiply(19000, 50), const_100), 80), const_100), const_2)	multiply(n0,n2)\|divide(#0,const_100)\|multiply(n1,#1)\|divide(#2,const_100)\|divide(#3,const_2)	gain
a man can row upstream at 40 kmph and downstream at 52 kmph , and then find the speed of the man in still water ?	"us = 40 ds = 52 m = ( 40 + 52 ) / 2 = 46 answer : d"	a ) 80 % , b ) 44.9091 , c ) 8200 , d ) 46 , e ) 125	d	divide(add(40, 52), const_2)	add(n0,n1)\|divide(#0,const_2)\|	physics
a can do a piece of work in 10 days and b alone can do it in 20 days . how much time will both take to finish the work ?	"this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 10 x 20 / ( 10 + 20 ) = 200 / 30 = 6.666 days answer : c"	a ) 46 seconds , b ) 4 : 5 , c ) 6.666 , d ) 67 % , e ) 125 %	c	divide(const_1, add(divide(const_1, 10), divide(const_1, 20)))	divide(const_1,n0)\|divide(const_1,n1)\|add(#0,#1)\|divide(const_1,#2)\|	physics
a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,600 to 3,000 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?	"to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 100 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 120 total weight will be = 120 * 1600 = 192000 pounds , which is lesser than the maximum weight allowed ....	a ) 11190 , b ) 1070 , c ) 120 , d ) 227.04 mtrs , e ) $ 120	c	divide(multiply(multiply(100, const_2), const_1000), add(add(add(add(add(add(const_1000, const_100), const_100), const_100), const_100), const_100), const_100))	add(const_100,const_1000)\|multiply(n0,const_2)\|add(#0,const_100)\|multiply(#1,const_1000)\|add(#2,const_100)\|add(#4,const_100)\|add(#5,const_100)\|add(#6,const_100)\|divide(#3,#7)\|	general
the simple interest on rs . 10 for 4 months at the rate of 3 paise per rupeeper month is	"sol . s . i . = rs . [ 10 * 3 / 100 * 4 ] = rs . 1.20 answer a"	a ) 1.2 , b ) 33.33 % , c ) 1528 , d ) 8.12 % , e ) 17	a	divide(multiply(multiply(10, 4), 3), const_100)	multiply(n0,n1)\|multiply(n2,#0)\|divide(#1,const_100)\|	gain
two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 48 seconds . find the length of the faster train ?	"relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 48 * 10 = 480 m . the length of the faster train = 480 m . answer : e"	a ) 15 % , b ) 480 , c ) 0.85 , d ) 49 , e ) $ 35	b	multiply(divide(subtract(72, 36), const_3_6), 48)	subtract(n0,n1)\|divide(#0,const_3_6)\|multiply(n2,#1)\|	physics
a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all...	"let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats ...	a ) 1 / 3 , b ) 14', ' , c ) 25 % , d ) 2000 , e ) 16.5 m 2	c	multiply(divide(divide(subtract(25, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100)	add(const_2,const_3)\|divide(const_100,#0)\|divide(#1,const_2)\|divide(#2,const_2)\|add(#2,#3)\|subtract(n0,#4)\|divide(#5,const_2)\|divide(#6,#1)\|multiply(#7,const_100)\|	general
what is the units digit of ( 63 ^ 4 ) ( 41 ^ 7 ) ( 99 ^ 9 ) ?	"the units digit of 63 ^ 4 is the units digit of 3 ^ 4 which is 1 . the units digit of 41 ^ 7 is the units digit of 1 ^ 7 which is 1 . the units digit of 99 ^ 9 is the units digit of 9 ^ 9 which is 9 . note the pattern : 9 ^ 1 = 9 , 9 ^ 2 = 81 , 9 ^ 3 = 729 , . . . the units digit alternates between 9 and 1 . the units...	a ) 144 min , b ) 10780 , c ) 762 , d ) 9 , e ) 4.5 sec	d	divide(add(multiply(factorial(63), factorial(4)), multiply(factorial(63), factorial(7))), 63)	factorial(n0)\|factorial(n1)\|factorial(n3)\|multiply(#0,#1)\|multiply(#0,#2)\|add(#3,#4)\|divide(#5,n0)\|	general
if - 4 and - 8 are negative integers , then - 4 * - 8 + 2 is	answer : c	a ) 40 , b ) 8 , c ) 34 , d ) 10 years , e ) 8 / 25	c	add(multiply(negate(4), negate(8)), 2)	negate(n0)\|negate(n1)\|multiply(#0,#1)\|add(n4,#2)	general
the maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :	"explanation : required number of students = h . c . f of 1234 and 874 = 2 . answer : b"	a ) 180 m , b ) 82 , c ) 2 , d ) rs . 440 , e ) 612	c	gcd(1234, 874)	gcd(n0,n1)\|	general
a boatman selling a boat along river flow . if he sell boat in steal water at 3 m / sec and flow of river is 2 m / sec . how much time he will take to sell 100 m .	net speed = 3 + 2 = 5 m / sec distance = 100 m time = 100 / 5 = 20 sec answer d	a ) 0.225 , b ) 20 , c ) 106 , d ) 30 , e ) 39	b	divide(100, add(3, 2))	add(n0,n1)\|divide(n2,#0)	physics
a man can row his boat with the stream at 12 km / h and against the stream in 8 km / h . the man ' s rate is ?	explanation : ds = 12 us = 8 s = ? s = ( 12 - 8 ) / 2 = 2 kmph answer : a	a ) 600 , b ) 45 , c ) - 14 , d ) 2 kmph , e ) 60000	d	divide(subtract(12, 8), const_2)	subtract(n0,n1)\|divide(#0,const_2)	gain
jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 60,000 after completion of one year . what will be madhu ' s share of profit ?	"30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 60,000 i . e . rs . 30,000 answer : c"	a ) rs . 30,000 , b ) 0 , c ) rs . 25,000 , d ) 1 / 12 , e ) 1750 m	a	multiply(add(multiply(multiply(multiply(const_4, 2), multiply(add(2, const_3), 2)), const_100), multiply(multiply(add(2, const_3), const_100), const_100)), divide(divide(multiply(add(2, const_3), 2), 2), multiply(const_4, const_3)))	add(n1,const_3)\|multiply(n1,const_4)\|multiply(const_3,const_4)\|multiply(#0,n1)\|multiply(#0,const_100)\|divide(#3,n1)\|multiply(#1,#3)\|multiply(#4,const_100)\|divide(#5,#2)\|multiply(#6,const_100)\|add(#9,#7)\|multiply(#10,#8)\|	gain
if the average ( arithmetic mean ) of a and b is 120 , and the average of b and c is 150 , what is the value of a − c ?	"a + b = 240 b + c = 300 a - c = - 60 . imo option a ."	a ) − 60 , b ) rs 66.66 , c ) 25 , d ) 30 , e ) 786858	a	subtract(multiply(150, const_2), multiply(120, const_2))	multiply(n1,const_2)\|multiply(n0,const_2)\|subtract(#0,#1)\|	general
a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 30 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?	"25 % of 2 litres = 0.5 litres 30 % of 6 litres = 1.8 litres therefore , total quantity of alcohol is 2.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 23 % answer : a"	a ) 150 m , b ) 500 , c ) 23 % . , d ) 629 , e ) 0	c	multiply(divide(add(multiply(divide(25, const_100), 2), multiply(divide(30, const_100), 6)), 10), const_100)	divide(n1,const_100)\|divide(n3,const_100)\|multiply(n0,#0)\|multiply(n2,#1)\|add(#2,#3)\|divide(#4,n5)\|multiply(#5,const_100)\|	general
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 3 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 3 x years from now , age will be 15 + 3 * 4 = 27 option e"	a ) 14 : 00 , b ) 1 / 12 , c ) 27 , d ) 129 , e ) 5625	c	subtract(multiply(multiply(4, 3), 4), divide(subtract(14, const_1), const_2))	multiply(n0,n4)\|subtract(n1,const_1)\|divide(#1,const_2)\|multiply(n0,#0)\|subtract(#3,#2)\|	general
jack and jill work at a hospital with 4 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?	"total number of ways to choose 2 out of 6 workers = 6 ! / 2 ! 4 ! = 15 number of ways to choose both jack and jill = 1 probability = 1 / 15 c should be the answer"	a ) 5 : 6 , b ) 16 days , c ) 4991 , d ) 110 , e ) 1 / 15	e	inverse(divide(factorial(6), multiply(factorial(2), factorial(4))))	factorial(n2)\|factorial(n1)\|factorial(n0)\|multiply(#1,#2)\|divide(#0,#3)\|inverse(#4)\|	physics
a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 35 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?	"find the product of the two increases : ( 1.4 ) * ( 1.35 ) which is 1.89 and a 89 % increase . d"	a ) 900 , b ) 210 , c ) 8 : 1 , d ) 89 % , e ) 3 : 2	d	multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(35, const_100))), const_100), const_1), const_100)	divide(n1,const_100)\|divide(n0,const_100)\|add(#0,const_1)\|add(#1,const_1)\|multiply(#3,const_100)\|multiply(#2,#4)\|divide(#5,const_100)\|subtract(#6,const_1)\|multiply(#7,const_100)\|	gain
what least number must be added to 9879 , so that the sum is completely divisible by 10 ?	"if we divide 9879 by 10 remainder is 9 10 - 9 = 1 answer : c"	a ) 89 % , b ) 1 , c ) $ 3.85 , d ) $ 24.88 , e ) 3	b	subtract(multiply(add(multiply(const_4, const_10), const_2), 10), 9879)	multiply(const_10,const_4)\|add(#0,const_2)\|multiply(n1,#1)\|subtract(#2,n0)\|	general
solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 150 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?	"we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 150 then y = 450 answer : d"	a ) 30 kmph , b ) 450 , c ) 104 meters', ' , d ) 2 : 1 , e ) 28 / 55	b	multiply(divide(subtract(25, 10), subtract(30, 25)), 150)	subtract(n3,n0)\|subtract(n1,n3)\|divide(#0,#1)\|multiply(n2,#2)\|	general
a cycle is bought for rs . 750 and sold for rs . 1080 , find the gain percent ?	"750 - - - - 180 100 - - - - ? = > 44 % answer : b"	a ) 28 , b ) 44 , c ) 150 , d ) 5.75 , e ) 1076	b	multiply(divide(subtract(1080, 750), 750), const_100)	subtract(n1,n0)\|divide(#0,n0)\|multiply(#1,const_100)\|	gain
a , b and c invested rs . 6500 , rs . 1300 and rs . 7800 respectively , in a partnership business . find the share of b in profit of rs . 11700 after a year ?	"explanation : 6500 : 1300 : 7800 5 : 1 : 6 1 / 12 * 11700 = 975 answer : d"	a ) 975 , b ) 174 , c ) 6 , d ) 36 , e ) $ 480	a	multiply(divide(6500, add(add(6500, 1300), 7800)), 11700)	add(n0,n1)\|add(n2,#0)\|divide(n0,#1)\|multiply(n3,#2)\|	gain
the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 65.0 . what is the quiz score of the student who dropped the class ?	"total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 65 = 975 so , the score of the person who left is 25 ( 1000 - 975 ) answer will be ( b )"	a ) 16 , b ) 25 , c ) 50 days , d ) 6 , e ) 93 / 10	b	subtract(multiply(16, 62.5), multiply(subtract(16, const_1), 65.0))	multiply(n0,n1)\|subtract(n0,const_1)\|multiply(n2,#1)\|subtract(#0,#2)\|	general
evaluate 35 % of 450 + 45 % of 350	"explanation : = ( 35 / 100 ) * 450 + ( 45 / 100 ) * 350 = 315 option c"	a ) 7 / 20 , b ) 315 , c ) 21 , d ) 10 , e ) 31.67 %	b	divide(35, divide(450, 35))	divide(n1,n0)\|divide(n0,#0)\|	gain
when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ?	"when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 8 - - > y = 66.7 . answer : c ."	a ) 104 meters', ' , b ) 8.4 , c ) 0.036 , d ) 88 , e ) 66.7	e	divide(8, subtract(96.12, floor(96.12)))	floor(n1)\|subtract(n1,#0)\|divide(n0,#1)\|	general
a bullock cart has to cover a distance of 80 km in 10 hrs . if it covers half of the journey in 3 / 5 th time . what should be its speed to cover the remaining distance in the time left .	a 10 kmph time left = 10 - 3 / 5 * 10 = 4 hr 10 km / h speed = 40 km / 4 hr = 10 kmph	a ) 10 kmph , b ) 100 % , c ) 2013 , d ) $ 65.00 , e ) 18	a	divide(divide(80, const_2), subtract(10, multiply(divide(10, 5), 3)))	divide(n0,const_2)\|divide(n1,n3)\|multiply(n2,#1)\|subtract(n1,#2)\|divide(#0,#3)	physics

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