Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 16 weavers in 16 days ? | "1 weaver can weave 1 mat in 4 days . 16 weavers can weave 16 mats in 4 days . 16 weavers can weave 64 mats in 16 days . the answer is c ." | a ) 16 , b ) 32 , c ) 64 , d ) 96 , e ) 128 | c | multiply(16, multiply(16, divide(4, multiply(4, 4)))) | multiply(n0,n0)|divide(n0,#0)|multiply(n3,#1)|multiply(n3,#2)| | gain |
a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 65 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ? | lets say x ounces of p is mixed with q . = > 65 - x ounces of q is present in the mixture ( as the total = 65 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 65 - x ) = 15 = > x = 25 = > 65 - 25 = 40 ounces of q is present in the mixture . answer is d . | a ) 16 , b ) 20 , c ) 32 , d ) 40 , e ) 48 | d | divide(subtract(15, multiply(divide(20, const_100), 65)), subtract(divide(25, const_100), divide(20, const_100))) | divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#0)|subtract(#1,#0)|subtract(n3,#2)|divide(#4,#3) | general |
if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability q that n is divisible by 3 ? | "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ." | a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0 | d | divide(add(3, const_2), multiply(const_4, const_4)) | add(n0,const_2)|multiply(const_4,const_4)|divide(#0,#1)| | general |
a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 330 m long platform ? | "e 45 min let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 330 ) / 36 * 5 / 18 = 45 min ." | a ) 37 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min | e | divide(add(330, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36)) | multiply(n0,const_0_2778)|multiply(n1,#0)|add(n2,#1)|divide(#2,#0)| | physics |
if 3 < x < 6 < y < 10 , then what is the greatest possible positive integer difference of x and y ? | "3 < x < 6 < y < 10 ; 3 < x y < 10 3 + y < x + 10 y - x < 7 . positive integer difference is 6 ( for example y = 9.5 and x = 3.5 ) answer : d ." | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | subtract(subtract(10, 3), const_1) | subtract(n2,n0)|subtract(#0,const_1)| | general |
what is 10 - 8 + 6 - 4 + . . . + ( - 14 ) ? | the expression considers all even numbers between 10 and - 14 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , and - 14 now , the first term is positive and the next term is subtracted . so , the required expression beco... | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) - 2 | e | subtract(6, 8) | subtract(n2,n1) | general |
the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 1000 . what is the manager ' s monthly salary ? | "explanation : manager ' s monthly salary rs . ( 2500 * 21 - 1500 * 20 ) = rs . 22500 . answer : c" | a ) rs . 16003 , b ) rs . 16029 , c ) rs . 22500 , d ) rs . 16108 , e ) rs . 16011 | c | subtract(multiply(add(1500, 1000), add(20, const_1)), multiply(1500, 20)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
stacy and heather are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the tw... | "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 30 - 2.4 = 17.6 time taken = distance / speed = 27.6 / 11 = 2.5 hrs heather wi... | a ) 15 mile , b ) 14 mile , c ) 11 mile , d ) 10 mile , e ) 12.5 mile | e | multiply(divide(subtract(30, multiply(24, divide(add(1, 5), const_60))), add(5, add(1, 5))), 5) | add(n1,n2)|add(n2,#0)|divide(#0,const_60)|multiply(n3,#2)|subtract(n0,#3)|divide(#4,#1)|multiply(n2,#5)| | physics |
for a race a distance of 224 meters can be covered by p in 8 seconds and q in 32 seconds . by what distance does p defeat q eventually ? | "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 8 = 28 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 24 seconds therefore , distance covered by p in that time = 28 m / s x 24 seconds = 672 metres answer : a" | a ) 672 m , b ) 6738 m , c ) 634 m , d ) 671 m , e ) 636 m | a | subtract(224, multiply(8, speed(224, 32))) | speed(n0,n2)|multiply(n1,#0)|subtract(n0,#1)| | physics |
in a single throw of a die , what is the probability of getting a number greater than 4 ? | s = { 1,2 , 3,4 , 5,6 } e = { 5,6 } probability = 2 / 6 = 1 / 3 answer is a | a ) 1 / 3 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7 | a | divide(const_2, add(4, const_2)) | add(n0,const_2)|divide(const_2,#0) | probability |
the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 6 year . find what was the original average age of the class ? | let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 34 â ‡ ’ 40 y + 384 = 34 y + 408 â ‡ ’ 6 y = 24 â ˆ ´ y = 4 e | a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 4 | e | divide(subtract(multiply(12, subtract(40, 6)), multiply(12, 32)), 6) | multiply(n1,n2)|subtract(n0,n3)|multiply(n1,#1)|subtract(#2,#0)|divide(#3,n3) | general |
a car takes 6 hours to cover a distance of 180 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 6 distance = 280 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 180 / 9 = 20 kmph b )" | a ) 10 kmph , b ) 20 kmph , c ) 15 kmph , d ) 30 kmph , e ) 25 kmph | b | divide(180, divide(multiply(6, 3), 2)) | multiply(n0,n2)|divide(#0,n3)|divide(n1,#1)| | physics |
5 n + 2 > 12 and 7 n - 19 < 44 ; n must be between which numbers ? | 5 n + 2 > 12 5 n > 10 n > 2 7 n - 19 < 44 7 n < 63 n < 9 so n must be between 2 and 9 2 < n < 9 correct answer c | a ) 1 and 8 , b ) 2 and 6 , c ) 2 and 9 , d ) 2 and 7 , e ) 2 and 9 | c | add(multiply(const_2, const_10), divide(add(44, 19), 7)) | add(n4,n5)|multiply(const_10,const_2)|divide(#0,n3)|add(#2,#1) | general |
the price of a consumer good increased by pp % during 20122012 and decreased by 1212 % during 20132013 . if no other change took place in the price of the good and the price of the good at the end of 20132013 was 1010 % higher than the price at the beginning of 20122012 , what was the value of pp ? | as per question = > price was simple 10 percent greater hence x [ 1 + 10 / 100 ] must be the final price . equating the two we get = > x [ 110 / 100 ] = x [ 1 + p / 100 ] [ 88 / 100 ] = > 44 p + 4400 = 5500 = > 44 p = 1100 = > p = 1100 / 44 = > 100 / 4 = > 25 . so p must be 25 answer : d | a ) − 2 % , b ) 2 % , c ) 22 % , d ) 25 % , e ) can not be determined | d | multiply(const_100, subtract(divide(add(const_1, divide(const_10, const_100)), subtract(const_1, divide(const_12, const_100))), const_1)) | divide(const_10,const_100)|divide(const_12,const_100)|add(#0,const_1)|subtract(const_1,#1)|divide(#2,#3)|subtract(#4,const_1)|multiply(#5,const_100) | general |
two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer . | "assume the integers to be x and y , where x < y given x / y = 1 / 4 - ( i ) or y = 4 x and x + 6 / y = 1 / 2 - ( ii ) or y = 2 x + 12 substituting the value of y from ( i ) , 4 x = 2 x + 12 x = 6 hence y = 4 * 6 = 24 answer d" | a ) 4 , b ) 6 , c ) 12 , d ) 24 , e ) 30 | d | multiply(divide(multiply(2, 6), subtract(4, 2)), 4) | multiply(n2,n4)|subtract(n1,n4)|divide(#0,#1)|multiply(n1,#2)| | other |
in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 12 days , working 16 hours a day , the number of men required is : | "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 16 : 8 : : 12 : x = > 12 x 16 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 12 x 16 ) = > x = 5 answer : b" | a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9 | b | divide(divide(multiply(multiply(12, 8), 10), 16), 12) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n4)|divide(#2,n3)| | physics |
what is the unit digit in ( 4137 ) 754 ? | "explanation : unit digit in ( 4137 ) 754 = unit digit in { [ ( 4137 ) 4 ] 188 x ( 4137 ) 2 } = unit digit in { 292915317923361 x 17114769 } = ( 1 x 9 ) = 9 c" | a ) 6 , b ) 5 , c ) 9 , d ) 13 , e ) 15 | c | reminder(power(4137, const_2), const_10) | power(n0,const_2)|reminder(#0,const_10)| | general |
find the volume , curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm . | volume = ∏ r 2 h = ( ( 22 / 7 ) x ( 7 / 2 ) x ( 7 / 2 ) x 40 ) = 1540 cm ^ 3 . . curved surface area = 2 ∏ rh = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x 40 ) = 880 cm ^ 2 . total surface area = 2 ∏ rh + 2 ∏ r 2 = 2 ∏ r ( h + r ) = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x ( 40 + 3.5 ) ) cm 2 = 957 cm ^ 2 answer is b | ['a ) 952 cm ^ 2', 'b ) 957 cm ^ 2', 'c ) 954 cm ^ 2', 'd ) 958 cm ^ 2', 'e ) none of them'] | b | add(multiply(multiply(power(divide(7, const_2), const_2), const_pi), const_2), multiply(multiply(7, const_pi), 40)) | divide(n0,const_2)|multiply(n0,const_pi)|multiply(n1,#1)|power(#0,const_2)|multiply(#3,const_pi)|multiply(#4,const_2)|add(#5,#2) | geometry |
how many positive integers less than 5,000 are evenly divisible by neither 15 nor 23 ? | "integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 23 5000 / 23 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 23 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 23 = 333 + 238 - 47 = 524 now subtract tha... | a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349 | c | divide(factorial(subtract(add(const_4, 15), const_1)), multiply(factorial(15), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general |
find the sum the difference between the compound and s . i . on a certain sum of money for 4 years at 20 % per annum is rs . 50 of money ? | "p = 50 ( 100 / 20 ) 4 = > p = 1000 answer : a" | a ) 1000 , b ) 6000 , c ) 5000 , d ) 8000 , e ) 1900 | a | multiply(multiply(divide(50, multiply(20, 4)), const_100), multiply(20, 4)) | multiply(n0,n1)|divide(n2,#0)|multiply(#1,const_100)|multiply(#2,#0)| | general |
jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 52,000 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 * 52,000 i . e . rs . 26,000 answer : b" | a ) rs . 27,000 , b ) rs . 26,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these | b | 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 |
an investment yields an interest payment of $ 234 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ? | let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 234 = > p = ( 234 * 4 * 10 ^ 2 ) / 3 = 78 * 4 * 10 ^ 2 = 312 * 10 ^ 2 = 31200 answer d | a ) $ 28,300 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 31,200 , e ) $ 35,100 | d | multiply(divide(234, divide(9, multiply(const_3, const_4))), const_100) | multiply(const_3,const_4)|divide(n1,#0)|divide(n0,#1)|multiply(#2,const_100) | gain |
the mass of 1 cubic meter of a substance is 400 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters ) | "density is mass divided by volume . so density of the given substance will be mass / volume = 400 kg / 1 m ^ 3 = 400 kg / m ^ 3 or 1 g / 2.5 cm ^ 3 = 0.4 g / cm ^ 3 . next , ask yourself if 400,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 0... | a ) 0.8 , b ) 1.25 , c ) 8.0 , d ) 2.5 , e ) 80.0 | d | subtract(divide(power(const_100, const_3), multiply(400, 1,000)), const_2) | multiply(n1,n4)|power(const_100,const_3)|divide(#1,#0)|subtract(#2,const_2)| | geometry |
a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 80 , how many horses are there ? | "legs 16 * 4 = 64 now half on their horses so remaining on the walk so 8 men 8 men has 16 legs so , 16 + 64 = 80 legs walking answer : d" | a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | d | divide(80, add(const_4, divide(const_2, const_2))) | divide(const_2,const_2)|add(#0,const_4)|divide(n0,#1)| | general |
54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is : | "explanation : let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = > 12 x = 240 = > x = 20 . bigger part = ( 54 - x ) = 34 . answer : b ) 34" | a ) 33 , b ) 34 , c ) 26 , d ) 28 , e ) 19 | b | subtract(54, divide(subtract(780, multiply(54, 10)), subtract(22, 10))) | multiply(n0,n1)|subtract(n2,n1)|subtract(n3,#0)|divide(#2,#1)|subtract(n0,#3)| | general |
a cistern is filled by pipe a in 10 hours and the full cistern can be leaked out by an exhaust pipe b in 15 hours . if both the pipes are opened , in what time the cistern is full ? | "time taken to full the cistern = ( 1 / 10 - 1 / 15 ) hrs = 1 / 30 = 30 hrs answer : b" | a ) 50 hrs , b ) 30 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs | b | divide(const_1, subtract(divide(const_1, 10), divide(const_1, 15))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)| | physics |
all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 45 th boy . total number of boys in the class ? | "as half the circle shape consist of 45 - 10 = 35 boys , so total number of boys in full circle = 2 * 35 = 70 answer : d" | a ) 65 , b ) 68 , c ) 72 , d ) 70 , e ) 58 | d | multiply(subtract(45, 10), const_2) | subtract(n1,n0)|multiply(#0,const_2)| | general |
how many integers between 2000 and 3000 that have distinct digits and increase from left to right ? | since the numbers must be distinct and increasing from left to right , the only arrangements we could come - up with are : 245 _ - - > 4 246 _ - - > 3 247 _ - - > 2 248 _ - - > 1 256 _ - - > 3 257 _ - - > 2 258 _ - - > 1 267 _ - - > 2 268 _ - - > 1 number of integers = 20 b | a ) 10 , b ) 20 , c ) 60 , d ) 120 , e ) 600 | b | divide(factorial(multiply(divide(2000, const_1000), divide(3000, const_1000))), multiply(factorial(divide(3000, const_1000)), factorial(divide(3000, const_1000)))) | divide(n0,const_1000)|divide(n1,const_1000)|factorial(#1)|multiply(#0,#1)|factorial(#3)|multiply(#2,#2)|divide(#4,#5) | general |
the speed of a car is 70 km in the first hour and 90 km in the second hour . what is the average speed of the car ? | "s = ( 70 + 90 ) / 2 = 80 kmph answer : b" | a ) 79 kmph , b ) 80 kmph , c ) 34 kmph , d ) 23 kmph , e ) 14 kmph | b | divide(add(70, 90), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed z ? | "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this z we get x = 8 . b ." | a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16 | b | divide(add(divide(96, 16), sqrt(add(multiply(multiply(divide(divide(96, 16), add(const_1, divide(50, const_100))), 4), 4), power(divide(96, 16), const_2)))), const_2) | divide(n0,n2)|divide(n3,const_100)|add(#1,const_1)|power(#0,const_2)|divide(#0,#2)|multiply(n1,#4)|multiply(#5,n1)|add(#6,#3)|sqrt(#7)|add(#0,#8)|divide(#9,const_2)| | physics |
the length of the bridge , which a train 475 metres long and travelling at 90 km / hr can cross in 30 seconds , is : | "speed = [ 90 x 5 / 18 ] m / sec = [ 25 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 475 + x ) / 30 = 25 = > 475 + x = 750 = > x = 275 answer : e" | a ) 200 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) 275 m | e | subtract(multiply(divide(multiply(90, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 475) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 90 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ? | "typical dosage is dose : weight : : 2 : 15 . now if weight is 90 ( multiplying factor is 6 : ( 90 / 15 ) ) then typical dosage would be 2 * 6 = 12 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 12 ) * 100 = 16.67 % e is the answer ." | a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 16.7 % | e | multiply(divide(subtract(multiply(divide(2, 15), 90), 18), multiply(divide(2, 15), 90)), const_100) | divide(n2,n3)|multiply(n1,#0)|subtract(#1,n0)|divide(#2,#1)|multiply(#3,const_100)| | gain |
sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 80 ps per meter is ? | "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.80 = rs . 200 answer : d" | a ) 287 , b ) 369 , c ) 125 , d ) 200 , e ) 361 | d | divide(multiply(80, rectangle_perimeter(sqrt(divide(multiply(3750, 2), 3)), divide(3750, sqrt(divide(multiply(3750, 2), 3))))), const_100) | multiply(n1,n2)|divide(#0,n0)|sqrt(#1)|divide(n2,#2)|rectangle_perimeter(#3,#2)|multiply(n3,#4)|divide(#5,const_100)| | physics |
what is the smallest positive integer x , such that 1152 x is a perfect cube ? | we need to make 1152 x a perfect cube , hence we need to have the powers a multiple of 3 1152 = 2 ^ 7 * 3 ^ 2 the minimum value of x for which 1152 x is a perfect cube = 2 ^ 2 * 3 = 12 correct option : d | a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18 | d | floor(add(power(1152, divide(const_1, const_3)), const_2)) | divide(const_1,const_3)|power(n0,#0)|add(#1,const_2)|floor(#2) | geometry |
an association of mathematics teachers has 1,600 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ? | total umber of members = 1600 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1600 ) * 100 = 19.6 % answer e | a ) 75 % , b ) 58 % , c ) 42 % , d ) 14.5 % , e ) 19.6 % | e | multiply(divide(multiply(divide(60, const_100), 525), multiply(const_100, power(const_4, const_2))), const_100) | divide(n2,const_100)|power(const_4,const_2)|multiply(n1,#0)|multiply(#1,const_100)|divide(#2,#3)|multiply(#4,const_100) | gain |
a no . when divided by 125 gives a remainder 40 , what remainder will be obtainedby dividingthe same no . 15 ? | "125 + 40 = 165 / 15 = 11 ( remainder ) b" | a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14 | b | divide(add(125, 40), 15) | add(n0,n1)|divide(#0,n2)| | general |
the area of a triangle will be when a = 3 m , b = 4 m , c = 5 m , a , b , c being lengths of respective sides ? | s = ( 3 + 4 + 5 ) / 2 = 6 answer : b | a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1 | b | divide(add(add(3, 4), 5), 4) | add(n0,n1)|add(n2,#0)|divide(#1,n1)| | geometry |
a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.5 per box per month for the record storage , what is the total amount that the company pays each month for record storage ? | "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.5 = 300 answer : b" | a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 2,400 | b | multiply(0.5, divide(1.08, divide(divide(divide(multiply(multiply(15, 12), 10), const_100), const_100), const_100))) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|divide(n3,#4)|multiply(n4,#5)| | general |
if 7 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ? | "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 7 c 2 for vertical 8 c 2 total parallelogram is 7 c 2 * 8 c 2 = 21 * 28 = 588 answer : a" | a ) 588 , b ) 263 , c ) 120 , d ) 160 , e ) 1260 | a | multiply(divide(multiply(7, subtract(7, const_1)), const_2), divide(multiply(8, subtract(8, const_1)), const_2)) | subtract(n0,const_1)|subtract(n1,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)|divide(#3,const_2)|multiply(#4,#5)| | physics |
if the a radio is sold for rs 490 and sold for rs 465.50 . find loss percentage . | cost price = rs 490 , selling price = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . loss % = [ ( 24.50 / 490 ) * 100 ] % = 5 % answer is b | a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) none of them | b | multiply(divide(subtract(490, 465.5), 490), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100) | gain |
if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first flip but not on the last 4 flips ? | "p ( htttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is d ." | a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 64 | d | power(divide(1, 2), 5) | divide(n0,n1)|power(#0,n2)| | probability |
a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 50000 . find his total income ? | "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 50000 100 % = 50000 * 100 / 5 = $ 1000000 answer is d" | a ) a ) 452000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 1000000 , e ) e ) 652000 | d | multiply(divide(50000, subtract(const_100, add(add(multiply(20, 3), 30), 5))), const_100) | multiply(n0,n1)|add(n2,#0)|add(n3,#1)|subtract(const_100,#2)|divide(n4,#3)|multiply(#4,const_100)| | gain |
the average ( arithmetic mean ) of the even integers from 0 to 60 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 30 inclusive ? | "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 60 is 60 / 2 = 30 the average of the even numbers from 0 to 30 is 30 ... | a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | b | subtract(divide(add(30, 0), const_2), divide(add(60, 0), const_2)) | add(n2,n3)|add(n0,n1)|divide(#0,const_2)|divide(#1,const_2)|subtract(#2,#3)| | general |
a train 200 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 10 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 60 + 10 = 70 km / hr . = 70 * 5 / 18 = 175 / 9 m / sec . time taken to pass the men = 200 * 9 / 175 = 10 sec . answer : c" | a ) 5 , b ) 6 , c ) 10 , d ) 9 , e ) 5 | c | divide(200, multiply(add(60, 10), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
what is the least number which should be added to 2697 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ? | "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2697 by 60 , the remainder is 57 . the number to be added = 60 - 57 = 3 . the answer is a ." | a ) 3 , b ) 11 , c ) 19 , d ) 27 , e ) 35 | a | add(3, add(4, add(6, add(5, multiply(5, const_2))))) | multiply(n1,const_2)|add(n1,#0)|add(n2,#1)|add(n3,#2)|add(n4,#3)| | general |
on dividing number by 357 , we get 39 as remainder . on dividing the same number by 17 , what will be the remainder ? | "let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x 2 = ( 5 k + 3 ) 2 = ( 25 k 2 + 30 k + 9 ) = 5 ( 5 k 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . answer : c" | a ) 0 , b ) 3 , c ) 5 , d ) 11 , e ) 13 | c | reminder(39, 17) | reminder(n1,n2)| | general |
how many even number in the range between 10 to 150 inclusive are not divisible by 3 | "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 150 using ap formula , we can say 150 = 10 + ( n - 1 ) * 2 or n = 71 . for 6 , 12,18 , . . . 96 using ap formula , we can say 150 = 12 + ( n ... | a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 47 | e | subtract(divide(subtract(subtract(150, 10), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(150, const_2), multiply(3, const_4)), 3), 3), 3), const_2)) | multiply(n2,const_4)|subtract(n1,n0)|subtract(n1,const_2)|subtract(#1,const_2)|subtract(#2,#0)|divide(#3,const_2)|subtract(#4,n2)|subtract(#6,n2)|divide(#7,n2)|divide(#8,const_2)|subtract(#5,#9)| | general |
a is twice as good as b . and together they finish a piece of work in 20 days . in how many days will a alone finish the work | "( a ' s 1 day work ) : ( b ' s 1 day work ) = 2 : 1 a + b 1 day work = 1 / 20 a ' s 1 day work = ( 1 / 20 ) * ( 2 / 3 ) = 1 / 30 a alone can finish the work in 30 days answer is a" | a ) 30 , b ) 25 , c ) 12 , d ) 10 , e ) 32 | a | inverse(multiply(divide(inverse(20), add(const_2, const_1)), const_2)) | add(const_1,const_2)|inverse(n0)|divide(#1,#0)|multiply(#2,const_2)|inverse(#3)| | physics |
a tradesman sold an article at a loss of 20 % . if the selling price had been increased by $ 100 , there would have been a gain of 5 % . what was the cost price of the article ? | "let c . p . be $ x then , ( 105 % of x ) - ( 80 % of x ) = 100 or 25 % of x = 100 x / 4 = 100 x = 400 c . p . = $ 400 correct option is d" | a ) $ 100 , b ) $ 200 , c ) $ 300 , d ) $ 400 , e ) $ 500 | d | divide(100, divide(add(20, 5), const_100)) | add(n0,n2)|divide(#0,const_100)|divide(n1,#1)| | gain |
a shop keeper marked 20 % above the cost price and offered 15 % discount then find it ' s net profit ? | net profit = 20 - 15 + ( 20 * ( - 15 ) / 100 ) = 2 % answer is a | a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 % | a | subtract(subtract(add(const_100, 20), divide(multiply(add(const_100, 20), 15), const_100)), const_100) | add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(#3,const_100) | gain |
if 0.5 % of a = 65 paise , then the value of a is ? | answer ∵ 0.5 / 100 of a = 65 / 100 ∴ a = rs . ( 65 / 0.5 ) = rs . 130 correct option : a | a ) rs . 130 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none | a | divide(65, 0.5) | divide(n1,n0) | gain |
suppose a , b , and c are positive integers with a < b < c such that 1 / a + 1 / b + 1 / c = 1 . what is a + b + c ? | first note that we must have 1 / a < 1 , so a > 1 . since 1 / a > 1 / b > 1 / c , we must also have 1 / a > 1 / 3 ; so a < 3 . thus , a / 2 . now 1 / b + 1 / c = 1 / 2 where 2 < b < c . similar to before , 1 / b > 1 / 4 , so b < 4 . thus , b = 3 . with a = 2 and b = 3 we have 1 / 2 + 1 / 3 + 1 / c = 1 , which is satisf... | a ) 1 , b ) 4 , c ) 9 , d ) 11 , e ) no such integers exist | d | add(multiply(add(add(1, 1), 1), add(1, 1)), add(add(1, 1), add(add(1, 1), 1))) | add(n0,n0)|add(n0,#0)|add(#0,#1)|multiply(#1,#0)|add(#2,#3) | general |
what is the smallest number which when diminished by 24 , is divisible 5 , 10 , 15 and 20 ? | "required number = ( lcm of 5 , 10 , 15 and 20 ) + 24 = 60 + 24 = 84 option b" | a ) 276 , b ) 84 , c ) 88 , d ) 90 , e ) 342 | b | add(lcm(lcm(5, 10), lcm(15, 20)), 24) | lcm(n1,n2)|lcm(n3,n4)|lcm(#0,#1)|add(n0,#2)| | general |
a 6 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point ? | the longer wire will form a square with an area more than 1 if the wire is cut at a point within two meters of either end . the probability of this is 4 / 6 = 2 / 3 . the answer is a . | ['a ) 2 / 3', 'b ) 3 / 4', 'c ) 4 / 5', 'd ) 5 / 6', 'e ) 6 / 7'] | a | divide(square_perimeter(1), 6) | square_perimeter(n1)|divide(#0,n0) | geometry |
in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 42 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ? | "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 42 , s... | a ) 70 , b ) 245 , c ) 150 , d ) 300 , e ) 350 | d | divide(42, multiply(divide(subtract(const_100, 30), const_100), divide(20, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|divide(#1,const_100)|multiply(#2,#0)|divide(n2,#3)| | gain |
a goods train runs at the speed of 72 km / hr and crosses a 300 m long platform in 26 sec . what is the length of the goods train ? | "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 300 ) / 26 = 20 x = 220 m . answer : e" | a ) 382 , b ) 782 , c ) 278 , d ) 270 , e ) 220 | e | subtract(multiply(multiply(divide(72, const_3600), const_1000), 26), 300) | divide(n0,const_3600)|multiply(#0,const_1000)|multiply(n2,#1)|subtract(#2,n1)| | physics |
two sets of 3 consecutive positive integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ? | "a = ( 2 , 3,4 ) , sum of this = 9 b = ( 4 , 5,6 ) , sum of this = 15 , the differenct between 15 - 9 = 6 hence , 6 is the answer i . e . c" | a ) 4 , b ) 7 , c ) 6 , d ) 12 , e ) it can not be determined from the information given . | c | subtract(multiply(3, const_10), multiply(const_4, 3)) | multiply(n0,const_10)|multiply(n0,const_4)|subtract(#0,#1)| | general |
the average mark of the students of a class in a particular exam is 60 . if 5 students whose average mark in that exam is 44 are excluded , the average mark of the remaining will be 80 . find the number of students who wrote the exam ? | "let the number of students who wrote the exam be x . total marks of students = 60 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 60 x - ( 5 * 44 ) = 80 ( x - 5 ) 180 = 20 x = > x = 9 answer : d" | a ) 12 , b ) 10 , c ) 7 , d ) 9 , e ) 8 | d | divide(subtract(multiply(80, 5), multiply(5, 44)), subtract(80, 60)) | multiply(n1,n3)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | general |
in how many years will a sum of money doubles itself at 18 % per annum on simple interest ? | "p = ( p * 18 * r ) / 100 r = 5.5 % answer : b" | a ) 5.9 % , b ) 5.5 % , c ) 6 % , d ) 6.4 % , e ) 7.5 % | b | divide(const_100, 18) | divide(const_100,n0)| | gain |
how many pieces of 75 cm can be cut from a rope 55.5 meters long ? | "explanation : total pieces of 75 cm that can be cut from a rope of 55.5 meters long is = ( 55.5 meters ) / ( 75 cm ) = ( 55.5 meters ) / ( 0.75 meters ) = 74 answer : e" | a ) 30 , b ) 40 , c ) 60 , d ) none , e ) 74 | e | divide(55.5, 75) | divide(n1,n0)| | physics |
a merchant gains or loses , in a bargain , a certain sum . in a second bargain , he gains 380 dollars , and , in a third , loses 70 . in the end he finds he has gained 250 dollars , by the 3 together . how much did he gain or lose bv the first ? | in this sum , as the profit and loss are opposite in their nature , they must be distinguished by contrary signs . if the profit is marked + , the loss must be - . let x = the sum required . then according to the statement x + 380 - 70 = 250 and x = - 60 . answer c | a ) 80 , b ) 60 , c ) - 60 , d ) - 70 , e ) none | c | subtract(250, subtract(380, 70)) | subtract(n0,n1)|subtract(n2,#0) | general |
population is 20000 . pop increases by 10 % every year , then the pop after 3 years is ? | population after 1 st year = 20000 * 10 / 100 = 2000 = = = > 20000 + 2000 = 22000 population after 2 nd year = 22000 * 10 / 100 = 2200 = = = > 22000 + 2200 = 24200 population after 3 rd year = 24200 * 10 / 100 = 2420 = = = > 24200 + 2420 = 26620 answer : d | a ) 26630 , b ) 26640 , c ) 36620 , d ) 26620 , e ) 26820 | d | add(add(add(20000, multiply(20000, divide(10, const_100))), multiply(add(20000, multiply(20000, divide(10, const_100))), divide(10, const_100))), multiply(add(add(20000, multiply(20000, divide(10, const_100))), multiply(add(20000, multiply(20000, divide(10, const_100))), divide(10, const_100))), divide(10, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|multiply(#2,#0)|add(#2,#3)|multiply(#4,#0)|add(#4,#5) | gain |
find the number of different prime factors of 6440 | "explanation : l . c . m of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2 , 5 , 7,23 number of different prime factors is 4 . answer : option a" | a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6 | a | add(const_2, const_2) | add(const_2,const_2)| | other |
a train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ? | "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 31 = 620 m . so , length of platform = 620 - 3... | a ) 240 meters , b ) 260 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined | b | subtract(multiply(divide(multiply(72, const_1000), const_3600), 31), multiply(divide(multiply(72, const_1000), const_3600), 18)) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|multiply(n2,#1)|subtract(#2,#3)| | physics |
wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 5 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability... | p ( 1 and not 2 ) = 5 / 8 * ( 1 - 3 / 5 ) = 1 / 4 answer : a . | a ) 1 / 4 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22 | a | multiply(divide(5, 8), subtract(const_1, divide(3, 5))) | divide(n0,n1)|divide(n3,n0)|subtract(const_1,#1)|multiply(#0,#2) | probability |
what is the remainder when 7 ^ 74 - 5 ^ 74 is divided by 12 ? | "easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 12 * 4 + 1 ) ^ 37 - ( 12 * 2 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : b" | a ) 1 , b ) 0 , c ) 2 , d ) 3 , e ) none of these | b | reminder(multiply(74, 7), 5) | multiply(n0,n1)|reminder(#0,n2)| | general |
joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 35 . he was allowed to drop his lowest score . after doing so , his average test score improved to 40 . what is the lowest test score that was dropped ? | the arithmetic mean of 4 equally weighted tests was 35 . so what we can assume is that we have 4 test scores , each 35 . he dropped his lowest score and the avg went to 40 . this means that the lowest score was not 35 and other three scores had given the lowest score 5 each to make it up to 35 too . when the lowest sco... | a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80 | a | subtract(multiply(35, 4), multiply(40, const_3)) | multiply(n0,n1)|multiply(n2,const_3)|subtract(#0,#1) | general |
there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 10 days more ? | "760 - - - - 22 760 - - - - 20 x - - - - - 10 x * 10 = 760 * 20 x = 1520 760 - - - - - - - 760 answer : b" | a ) 220 , b ) 760 , c ) 990 , d ) 880 , e ) 660 | b | subtract(divide(multiply(760, subtract(22, const_2)), 10), 760) | subtract(n1,const_2)|multiply(n0,#0)|divide(#1,n2)|subtract(#2,n0)| | physics |
the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 15 metres ? | "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 15 / 5 = 3 seconds . answer : c" | a ) 5 , b ) 10 , c ) 3 , d ) 12 , e ) 6 | c | divide(15, multiply(add(15, 3), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)| | physics |
a dishonest dealer professes to sell goods at the cost price but uses a weight of 723 grams per kg , what is his percent ? | "723 - - - 277 100 - - - ? = > 38.3 % answer : a" | a ) 38.3 % , b ) 25 % , c ) 77 % , d ) 99 % , e ) 12 % | a | subtract(multiply(divide(const_100, 723), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100) | add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)| | gain |
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 800 more than d , what is b ' s share ? | "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 800 x = 800 . b ' s share = rs . 2 x = rs . ( 2 x 800 ) = rs . 1600 . answer = a" | a ) rs . 1600 , b ) rs . 1500 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above | a | multiply(multiply(subtract(4, 3), 800), 3) | subtract(n2,n3)|multiply(n4,#0)|multiply(n3,#1)| | general |
an error 4 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ? | "percentage error in calculated area = ( 4 + 4 + ( 4 ã — 4 ) / 100 ) % = 8.16 % answer : c" | a ) 4.05 % , b ) 4.02 % , c ) 8.16 % , d ) 3 % , e ) 2 % | c | divide(multiply(subtract(square_area(add(const_100, 4)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | gain |
if the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 5 , what is the ratio of apples to cucumbers ? | "apples : bananas = 4 : 3 bananas : cucumbers = 1 : 5 = 3 : 15 so if i have bananas , i ' d have 4 apples and 15 cucumbers apples : cucumbers = 4 : 15 answer : a" | a ) 4 : 15 , b ) 1 : 3 , c ) 2 : 5 , d ) 4 : 5 , e ) 7 : 6 | a | divide(divide(4, 3), 5) | divide(n0,n1)|divide(#0,n3)| | other |
if ( t - 8 ) is a factor of t ^ 2 - kt - 40 , then k = | "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 1 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ... | a ) 16 , b ) 1 , c ) 2 , d ) 6 , e ) 14 | b | add(const_10, 2) | add(n1,const_10)| | general |
a certain number when divided by 95 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? | "explanation : 95 + 25 = 120 / 15 = 8 ( remainder ) d" | a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9 | d | reminder(25, 15) | reminder(n1,n2)| | general |
p alone can complete a job in 4 days . the work done by q alone in one day is equal to one - third of the work done by p alone in one day . in how many days can the work be completed if p and q work together ? | p ' s rate is 1 / 4 q ' s rate is 1 / 12 the combined rate is 1 / 4 + 1 / 12 = 1 / 3 if they work together , the job will take 3 days . the answer is d . | a ) 1.5 , b ) 2.0 , c ) 2.5 , d ) 3.0 , e ) 3.5 | d | divide(const_1, add(divide(const_1, 4), divide(divide(const_1, 4), const_3))) | divide(const_1,n0)|divide(#0,const_3)|add(#0,#1)|divide(const_1,#2) | physics |
a man ' s speed with the current is 12 km / hr and the speed of the current is 2 km / hr . the man ' s speed against the current is | "man ' s rate in still water = ( 12 - 2 ) km / hr = 10 km / hr . man ' s rate against the current = ( 10 - 2 ) km / hr = 8 km / hr . answer : a" | a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | a | subtract(subtract(12, 2), 2) | subtract(n0,n1)|subtract(#0,n1)| | gain |
in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 242 runs ? | "required run rate = [ 242 - ( 3.2 * 10 ) ] / 40 = 210 / 40 = 5.25 answer : b" | a ) 6.25 , b ) 5.25 , c ) 6.29 , d ) 6.39 , e ) 6.13 | b | divide(subtract(242, multiply(10, 3.2)), 40) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain |
the population of a bacteria colony doubles every day . if it was started 8 days ago with 4 bacteria and each bacteria lives for 12 days , how large is the colony today ? | "4 ^ 8 ( 2 ) = 131072 the answer is d ." | a ) 512 , b ) 768 , c ) 1024 , d ) 131072 , e ) 409600 | d | subtract(power(4, add(8, const_1)), const_1) | add(n0,const_1)|power(n1,#0)|subtract(#1,const_1)| | physics |
a coin is tossed six times . what is the probability that there is at the least one tail ? | let p ( t ) be the probability of getting least one tail when the coin is tossed six times . = there is not even a single tail . i . e . all the outcomes are heads . = 1 / 64 ; p ( t ) = 1 - 1 / 64 = 63 / 64 answer : a | a ) 63 / 64 , b ) 31 / 37 , c ) 31 / 18 , d ) 31 / 10 , e ) 31 / 19 | a | multiply(multiply(divide(const_1, const_2), multiply(multiply(multiply(divide(const_1, const_2), divide(const_1, const_2)), divide(const_1, const_2)), divide(const_1, const_2))), const_1) | divide(const_1,const_2)|multiply(#0,#0)|multiply(#0,#1)|multiply(#0,#2)|multiply(#0,#3)|multiply(#4,const_1) | probability |
how many 3 x 3 x 3 cubes could fit in a 10 x 24 x 16 box ? | the answer is d ) 142 . the 10 x 24 x 16 box has an area of 3840 . if you divide it by 27 ( the total of the 3 x 3 x 3 smaller cube ) you get 142.2 . this means you could fit 142 whole cubes in the larger box . | a ) 150 , b ) 145 , c ) 138 , d ) 142 , e ) 175 | d | volume_rectangular_prism(10, 24, 16) | volume_rectangular_prism(n3,n4,n5)| | geometry |
how many positive integers less than 5,000 are there in which the sum of the digits equals 5 ? | "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x... | a ) 64 , b ) 62 , c ) 63 , d ) 61 , e ) 56 | e | divide(factorial(subtract(add(const_4, 5), const_1)), multiply(factorial(5), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general |
what is the rate percent when the simple interest on rs . 5000 amount to rs . 2500 in 5 years ? | "interest for 1 year = 2500 / 5 = 500 interest on rs 5000 p / a = 500 interest rate = 500 / 5000 * 100 = 10 % answer : c" | a ) 9 % , b ) 8 % , c ) 10 % , d ) 10.5 % , e ) 7.5 % | c | divide(multiply(const_100, 2500), multiply(5000, 5)) | multiply(n1,const_100)|multiply(n0,n2)|divide(#0,#1)| | gain |
on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction q of the total distance did... | if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or... | a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7 | e | subtract(divide(lcm(const_2, const_3), 2.8), const_2) | lcm(const_2,const_3)|divide(#0,n1)|subtract(#1,const_2)| | general |
given the two equations 3 x + 2 y = 16 and 5 x + 3 y = 26 , by how much does r exceed s ? | solve by simultaneous equations . my answer is e . x = 4 y = 2 | a ) 3 , b ) 4 , c ) 5 , d ) 1 , e ) 2 | e | divide(multiply(16, 2), 16) | multiply(n1,n2)|divide(#0,n2) | general |
the length of a rectangular floor is more than its breadth by 300 % . if rs . 423 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ? | "let the length and the breadth of the floor be l m and b m respectively . l = b + 400 % of b = l + 4 b = 5 b area of the floor = 423 / 3 = 141 sq m l b = 141 i . e . , l * l / 5 = 141 l 2 = 705 = > l = 26.6 m . answer : c" | a ) 24 , b ) 25 , c ) 26.6 m , d ) 26 , e ) 27 | c | multiply(sqrt(divide(divide(423, 3), const_3)), const_3) | divide(n1,n2)|divide(#0,const_3)|sqrt(#1)|multiply(#2,const_3)| | gain |
a can finish a work in 18 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day | "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 18 b ' s 1 day work = 1 / 9 [ because b take half time than a ] ... | a ) 1 \ 5 , b ) 1 \ 6 , c ) 1 \ 7 , d ) 1 \ 8 , e ) 1 \ 9 | b | add(divide(const_1, 18), multiply(divide(const_1, 18), const_2)) | divide(const_1,n0)|multiply(#0,const_2)|add(#0,#1)| | physics |
the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ? | "let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 10 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( â ˆ ) ( 14 ) = 1 / 2 ( 22 / 7 ) ( 14 ) = 308 / 14 = 22 cm to two decimal places answer : b" | a ) 22.51 , b ) 22.0 , c ) 22.15 , d ) 22.17 , e ) 22.63 | b | divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(18, 10)), const_2)), const_2) | rectangle_perimeter(n0,n1)|square_edge_by_perimeter(#0)|divide(#1,const_2)|circumface(#2)|divide(#3,const_2)| | geometry |
the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 198,000 . what was the percent increase in the cost of the home ? | "increase = 198000 - 120000 = 78000 % increase = 78000 * 100 / 120000 = 65 % answer : option a" | a ) 65 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 % | a | multiply(divide(subtract(multiply(multiply(const_12, multiply(const_4, const_4)), const_1000), multiply(multiply(const_12, const_1000), const_10)), multiply(multiply(const_12, const_1000), const_10)), const_100) | multiply(const_4,const_4)|multiply(const_1000,const_12)|multiply(#0,const_12)|multiply(#1,const_10)|multiply(#2,const_1000)|subtract(#4,#3)|divide(#5,#3)|multiply(#6,const_100)| | general |
a is a working partner and b is a sleeping partner in a business . a puts in 80,000 and b 70,000 . a gets 25 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the profit if b get 14000 . | "let amount distributed between a and b is x ratio of capital between a and b is 8 : 7 if b get 14000 then x * 7 / 15 = 14000 x * 7 = 210000 x = 30000 let total profit = y y * 75 / 100 = 30000 y = 40000 answer d" | a ) 42000 , b ) 46000 , c ) 54000 , d ) 40000 , e ) none of these | d | add(divide(multiply(subtract(14000, divide(multiply(25, 14000), const_100)), add(const_2, const_3)), add(add(const_2, const_3), add(const_2, const_4))), divide(multiply(25, 14000), const_100)) | add(const_2,const_3)|add(const_2,const_4)|multiply(n2,n3)|add(#0,#1)|divide(#2,const_100)|subtract(n3,#4)|multiply(#0,#5)|divide(#6,#3)|add(#7,#4)| | gain |
how many integers are divisible by 5 between 10 ! and 10 ! + 20 inclusive ? | a - 7 10 ! is divisible by 5 there are 4 numbers between 10 ! and 10 ! + 20 that are divisible by 5 . hence 5 | a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | a | add(divide(20, 5), const_1) | divide(n3,n0)|add(#0,const_1) | general |
a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 150 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ? | "the distance between the nest and the ditch is 150 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 150 = 4500 . d = st 4500 / 1.5 = t , i think we can take 4500 meters as 4.5 km , then only we get t = 4.5 . ( 10... | a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5 | d | divide(divide(multiply(150, multiply(15, const_2)), const_1000), divide(15, const_10)) | divide(n1,const_10)|multiply(n1,const_2)|multiply(n0,#1)|divide(#2,const_1000)|divide(#3,#0)| | physics |
if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 9 m of the same rod ? | "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 9 : : 42.75 : x = > 11.25 x x = 9 x 42.75 = > x = ( 9 x 42.75 ) / 11.25 = > x = 34.2 answer : b" | a ) 22.8 kg , b ) 34.2 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these | b | divide(multiply(9, 42.75), 11.25) | multiply(n1,n2)|divide(#0,n0)| | physics |
if paint costs $ 3.20 per quart , and a quart covers 120 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ? | "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 120 = 5 cost will be 5 * 3.2 = $ 16 ans : b" | a ) $ 1.60 , b ) $ 16.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 196.00 | b | multiply(divide(3.20, 120), surface_cube(10)) | divide(n0,n1)|surface_cube(n2)|multiply(#0,#1)| | geometry |
if 3 / p = 6 & 3 / q = 18 then p - q = ? | "p = 3 / 6 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 1 / 2 ) - ( 1 / 6 ) = 1 / 3 answer : e" | a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 1 / 3 | e | subtract(divide(3, 6), divide(3, 18)) | divide(n0,n1)|divide(n0,n3)|subtract(#0,#1)| | general |
two trains 150 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? | "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 150 + 160 = 310 m . required time = 310 * 9 / 250 = 279 / 25 = 11.16 sec . answer : e" | a ) 10.16 sec , b ) 18.8 sec , c ) 14.8 sec , d ) 10.8 sec , e ) 11.16 sec | e | divide(add(150, 160), multiply(add(60, 40), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | physics |
a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors... | let # of colors needed be nn , then it must be true that n + c 2 n ≥ 12 n + cn 2 - # of ways to choose the pair of different colors from nn colors when order does n ' t matter ) - - > n + n ( n − 1 ) / 2 ≥ 12 - - > 2 n + n ( n − 1 ) ≥ 24 - - > n is an integer ( it represents # of colors ) n ≥ 5 - - > nmin = 5 answer : ... | a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24 | b | subtract(divide(factorial(subtract(divide(12, const_2), const_1)), multiply(factorial(const_3), factorial(const_2))), subtract(divide(12, const_2), const_1)) | divide(n0,const_2)|factorial(const_3)|factorial(const_2)|multiply(#1,#2)|subtract(#0,const_1)|factorial(#4)|divide(#5,#3)|subtract(#6,#4) | general |
the average of 5 numbers is 27 . if one number is excluded the average become 25 . the excluded number is : | solution excluded number = ( 27 × 5 ) - ( 25 × 4 ) = 135 - 100 = 35 . answer d | a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 37 | d | subtract(multiply(5, 27), multiply(subtract(5, const_1), 25)) | multiply(n0,n1)|subtract(n0,const_1)|multiply(n2,#1)|subtract(#0,#2) | general |
a train 200 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 = [ 200 * 3 / 55 ] sec = 11 sec answer : a" | a ) 11 , b ) 10 , c ) 5 , d ) 9 , e ) 8 | a | multiply(const_3600, divide(divide(200, const_1000), add(60, 6))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | physics |
a sum fetched a total simple interest of rs . 4016.25 at the rate of 9 % p . a . in 5 years . what is the sum ? | principal = ( 100 * 4016.25 ) / ( 9 * 5 ) = rs . 8925 . answer : d | a ) 3888 , b ) 2988 , c ) 2777 , d ) 8925 , e ) 288 | d | divide(divide(multiply(4016.25, const_100), 9), 5) | multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)| | gain |
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