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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in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 27 to the thrice of the remainder . the dividend is | "divisor = ( 6 * 3 ) + 27 = 45 5 * quotient = 45 quotient = 9 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 9 ) + 6 = 186 . c )" | a ) 74 , b ) 78 , c ) 186 , d ) 92 , e ) 98 | c | add(multiply(add(multiply(6, const_3), 27), divide(add(multiply(6, const_3), 27), 5)), 6) | multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)| | general |
the sum of two numbers is 64 , and one of them is 12 more than the other . what are the two numbers ? | "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 64 : word problem = 64 the line over x + 12 is a grouping symbol called a vinculum . it saves... | a ) 26 - 38 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63 | a | divide(subtract(64, 12), const_2) | subtract(n0,n1)|divide(#0,const_2)| | general |
two whole numbers whose sum is 36 can not be in the ratio | b ) 3 : 4 | a ) 2 : 4 , b ) 3 : 4 , c ) 3 : 6 , d ) 1 : 3 , e ) 3 : 36 | b | divide(divide(subtract(divide(36, const_2), const_10), const_2), add(divide(36, const_2), const_10)) | divide(n0,const_2)|add(#0,const_10)|subtract(#0,const_10)|divide(#2,const_2)|divide(#3,#1)| | other |
if x β 2 + 3 β 4 = 9 β 4 , what is the value of x ? | "x β 2 + 3 β 4 = 9 β 4 let ' s multiply both sides by 4 . 2 x + 3 = 9 2 x = 6 x = 3 the answer is d ." | a ) β 2 , b ) β 1 , c ) 1 , d ) 3 , e ) 5 | d | divide(9, 4) | divide(n3,n2)| | general |
a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is | "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then βΉ = βΊ ( x + 24 ) + 2 = 2 ( x + 2 ) βΉ = βΊ x + 26 = 2 x + 4 x = 22 . answer d" | a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none | d | divide(subtract(24, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
two mechanics were working on your car . one can complete the given job in 4 hours , but the new guy takes eight hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ? | "rate ( 1 ) = 1 / 4 rate ( 2 ) = 1 / 8 combined = 3 / 8 work done in 2 days = 3 / 4 work left = 1 / 4 rate * time = work left 1 / 8 * time = 1 / 4 time = 2 a" | a ) 2 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 17 / 5 | a | max(divide(subtract(const_1, multiply(add(divide(const_1, add(const_4, const_2)), divide(const_1, 4)), const_2)), divide(const_1, 4)), const_3) | add(const_2,const_4)|divide(const_1,n0)|divide(const_1,#0)|add(#2,#1)|multiply(#3,const_2)|subtract(const_1,#4)|divide(#5,#1)|max(#6,const_3)| | physics |
yearly subscription to professional magazines cost a company $ 940.00 . to make a 30 % cut in the magazine budget , how much less must be spent ? | "total cost 940 940 * 30 / 100 = 282 so the cut in amount is 282 the less amount to be spend is 940 - 282 = 658 answer : e" | a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 658 | e | multiply(divide(subtract(const_100, 30), const_100), 940.00) | subtract(const_100,n1)|divide(#0,const_100)|multiply(n0,#1)| | general |
water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 9 meters . what is value of the radius in meters ? | 10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 9 ) which is about 1 / 9 r = 1 / 3 the answer is b . | a ) 1 / 2 , b ) 1 / 3 , c ) 1.5 , d ) 3 , e ) 6 | b | divide(multiply(10, 0.31), 9) | multiply(n0,n2)|divide(#0,n3) | physics |
what is 10 - 8 + 6 - 4 + . . . + ( - 16 ) ? | "the expression considers all even numbers between 10 and - 16 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 , - 14 , and - 16 . now , the first term is positive and the next term is subtracted . so , the required expre... | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | d | subtract(6, 8) | subtract(n2,n1)| | general |
how many 7 in between 1 to 90 ? | "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 19 7 ' s between 1 to 90 answer : a" | a ) 19 , b ) 20 , c ) 22 , d ) 23 , e ) 24 | a | divide(90, multiply(7, 1)) | multiply(n0,n1)|divide(n2,#0)| | general |
for a race a distance of 224 meters can be covered by p in 16 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 / 16 = 14 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 16 seconds therefore , distance covered by p in that time = 14 m / s x 16 seconds = 224 metres answer : c" | a ) 232 m , b ) 238 m , c ) 224 m , d ) 331 m , e ) 236 m | c | subtract(224, multiply(16, speed(224, 32))) | speed(n0,n2)|multiply(n1,#0)|subtract(n0,#1)| | physics |
a merchant has selected two items to be placed on sale , one of which currently sells for 25 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ? | "expensive item = $ 100 ; cheap item = $ 75 ; we must increase $ 75 to $ 100 , so by $ 25 , which is approximately 30 % increase : ( 100 - 75 ) / 75 = 1 / 3 = ~ 0.33 answer : c ." | a ) 52 % , b ) 40 % , c ) 30 % , d ) 20 % , e ) 10 % | c | multiply(divide(divide(25, const_100), subtract(const_1, divide(25, const_100))), const_100) | divide(n0,const_100)|subtract(const_1,#0)|divide(#0,#1)|multiply(#2,const_100)| | general |
if the wheel is 15 cm then the number of revolutions to cover a distance of 1540 cm is ? | "2 * 22 / 7 * 15 * x = 1540 = > x = 16 answer : e" | a ) 11 , b ) 14 , c ) 18 , d ) 12 , e ) 16 | e | divide(1540, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 15)) | multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)| | physics |
you enter a weight loss challenge game and manage to lose 14 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ? | "( 100 % - 14 % ) * ( 100 % + 2 % ) = 0.86 * 1.02 = 12.28 % the weigh in records your weight loss at 12.28 % ! the answer is e" | a ) 13 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12.28 % | e | multiply(subtract(const_1, multiply(subtract(const_1, divide(14, const_100)), add(const_1, divide(2, const_100)))), const_100) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|subtract(const_1,#4)|multiply(#5,const_100)| | gain |
in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.865 per pound ? | using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.865 0.9 β 0.1 x = 0.865 x = 0.35 thus ratio of both flours is 1 : 2 b | a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 3 : 1 | b | divide(0.865, add(0.8, 0.9)) | add(n0,n1)|divide(n2,#0) | general |
a rectangular block 12 cm by 20 cm by 36 cm is cut into an exact number of equal cubes . find the least possible number of cubes ? | "volume of the block = 12 * 20 * 36 = 8640 cm ^ 3 side of the largest cube = h . c . f of 12 , 20,36 = 4 cm volume of the cube = 4 * 4 * 4 = 64 cm ^ 3 number of cubes = 8640 / 64 = 135 answer is a" | a ) 135 , b ) 10 , c ) 15 , d ) 40 , e ) 22 | a | divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add(multiply(const_3, const_1000), multiply(36, const_10))), divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add... | multiply(const_1000,const_3)|multiply(n2,const_10)|multiply(const_2,const_3)|rectangle_area(const_1000,const_360)|add(#0,#1)|divide(#3,const_10)|multiply(#2,const_1000)|subtract(#5,#6)|add(#4,#7)|divide(#8,const_10)|divide(#8,#9)| | geometry |
the average of 45 results is 10 . the average of first 22 of them is 16 and that of last 22 is 20 . find the 23 result ? | "23 th result = sum of 45 results - sum of 44 results 10 * 45 - 16 * 22 + 20 * 22 = 450 - 352 + 440 = 538 answer is c" | a ) 600 , b ) 480 , c ) 538 , d ) 650 , e ) 560 | c | subtract(subtract(multiply(45, 10), multiply(22, 20)), multiply(22, 16)) | multiply(n0,n1)|multiply(n2,n5)|multiply(n2,n3)|subtract(#0,#1)|subtract(#3,#2)| | general |
an escalator moves towards the top level at the rate of 15 ft . sec and its length is 200 feet . if a person walks on the moving escalator at the rate of 5 feet per second towards the top level , how much time does he take to cover the entire length . | "explanation : time taken to cover the entire length = tot . dist / resultant speed = 200 / ( 15 + 5 ) = 10 sec answer : b" | a ) 5 sec , b ) 10 sec , c ) 20 sec , d ) 15 sec , e ) 25 sec | b | divide(200, add(15, 5)) | add(n0,n2)|divide(n1,#0)| | gain |
4 barrels of water have an average capacity of 8 gallons . what is the maximum possible capacity of the smallest barrel e if the median is 10 gallons ? | suppose 4 barrels are b 1 , b 2 , b 3 , b 4 in ascending capacity . ( b 1 + b 2 + b 3 + b 4 ) / 4 = 8 b 1 + b 2 + b 3 + b 4 = 32 median is 10 . . . . . . . as the no . of terms are even i . e 4 , median = ( b 2 + b 3 ) / 2 = = > b 2 + b 3 = 20 now we have b 1 + b 4 = 32 - 20 = 12 only the following possible cases can b... | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | subtract(subtract(add(multiply(8, const_2), multiply(4, const_2)), const_12), 10) | multiply(n1,const_2)|multiply(n0,const_2)|add(#0,#1)|subtract(#2,const_12)|subtract(#3,n2) | general |
the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1200 , then what is the income of p 1 ? | "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x β 3 y = 1200 β¦ ( i ) and 4 x β 2 y = 1200 β¦ β¦ . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1200 - > x = 600 p 1 β s income = rs 5 * 600 = r... | a ) s . 800 , b ) s . 2400 , c ) s . 3000 , d ) s . 3200 , e ) s . 4200 | c | multiply(subtract(multiply(divide(1200, 2), 3), 1200), 5) | divide(n6,n1)|multiply(n4,#0)|subtract(#1,n6)|multiply(n2,#2)| | other |
in a two - digit number , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is : | let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 sum of digits = x + ( x + 2 ) = 2 x + 2 ( 11 x + 2 ) ( 2 x + 2 ) = 144 2 x 2 + 26 x - 140 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 hence , required number = 11 x + 2 = 24 . answer : a | a ) 24 , b ) 26 , c ) 42 , d ) 46 , e ) 48 | a | add(multiply(add(10, const_1), 2), 2) | add(n0,const_1)|multiply(n1,#0)|add(n1,#1) | general |
what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 70 ? | "put in simple words , we need to find the highest power of 2 in 100 ^ 70 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 70 = ( 2 ^ 2 * 5 ^ 2 ) ^ 70 = 2 ^ 140 * 5 ^ 140 answer : b" | a ) 120 , b ) 140 , c ) 130 , d ) 150 , e ) 160 | b | subtract(100, subtract(power(2, divide(100, 70)), const_1)) | divide(n1,n2)|power(n0,#0)|subtract(#1,const_1)|subtract(n1,#2)| | general |
a certain box has 12 cards and each card has one of the integers from 1 to 12 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on... | "the average of the numbers is 6.5 the total number of ways to choose 2 cards from 12 cards is 12 c 2 = 66 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 1,5 } , { 2,3 } , { 2,4 } the probability is 6 / 66 = 1 / 11 the answer is a ." | a ) 1 / 11 , b ) 2 / 23 , c ) 3 / 34 , d ) 4 / 45 , e ) 5 / 56 | a | divide(const_4, divide(factorial(12), multiply(factorial(2), factorial(subtract(12, 2))))) | factorial(n0)|factorial(n3)|subtract(n0,n3)|factorial(#2)|multiply(#1,#3)|divide(#0,#4)|divide(const_4,#5)| | general |
the average of first five multiples of 4 is ? | "average = 4 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 60 / 5 = 12 . answer : e" | a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 12 | e | add(4, const_1) | add(n0,const_1)| | general |
priya takes a trip and drives 5 hours from town x to town z at a rate of 50 miles per hour . on her way back , priya drives 60 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take scott to drive from town z to town y ? | distance from x to z = 5 hr * 50 mph = 250 miles hence distance from y to z = 1 / 2 * 250 = 125 time = 125 / 60 = 2.08 hrs imo : c | a ) 3.0 , b ) 2.25 , c ) 2.08 , d ) 1.75 , e ) 2.0 | c | divide(divide(multiply(5, 50), const_2), 60) | multiply(n0,n1)|divide(#0,const_2)|divide(#1,n2) | physics |
in a ratio which is equal to 4 : 6 , if the antecedent is 50 , then the consequent is ? | we have 4 / 6 = 50 / x 4 x = 50 * 6 x = 75 consequent = 75 answer is a | a ) 75 , b ) 85 , c ) 64 , d ) 51 , e ) 45 | a | add(50, divide(50, const_2)) | divide(n2,const_2)|add(n2,#0) | other |
shekar scored 76 , 65 , 82 , 67 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ? | "explanation : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 hence average = 75 answer : c" | a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90 | c | divide(add(add(add(add(76, 65), 82), 67), 85), add(const_1, const_4)) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | general |
an escalator moves towards the top level at the rate of 12 ft . sec and its length is 210 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length . | "time taken to cover the entire length = tot . dist / resultant speed = 210 / ( 12 + 2 ) = 15 sec answer : a" | a ) 15 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec | a | divide(210, add(12, 2)) | add(n0,n2)|divide(n1,#0)| | gain |
two employees x and y are paid a total of rs . 800 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ? | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 800 but x = 120 % of y = 120 y / 100 = 12 y / 10 β΄ 12 y / 10 + y = 800 β y [ 12 / 10 + 1 ] = 800 β 22 y / 10 = 800 β 22 y = 8000 β y = 8000 / 22 = rs . 363.63 e )" | a ) s . 200.63 , b ) s . 250.63 , c ) s . 290.63 , d ) s . 300.63 , e ) s . 363.63 | e | divide(multiply(800, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4)| | general |
elena β s bread recipe calls for 5 ounces of butter for each 7 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ? | solving through algebra route : 5 b + 7 f = x amount if we multiply this equation with 4 we get : 20 b + 28 f = 4 x therefore , we got 20 ounces of butter and 4 x amount of quantity when we use 28 ounces of floor . ans : e | a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28 | e | multiply(7, 4) | multiply(n1,n2) | general |
tom left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ? | in order not to lose money because of the change tom ' s total commission must beat least $ 75000 - $ 45000 = $ 30000 , so total sales must beat least $ 30000 / 0.15 = $ 200000 . which means that he must makeat least $ 200000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d . | a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600 | d | divide(subtract(75000, 45000), multiply(divide(15, const_100), 750)) | divide(n2,const_100)|subtract(n0,n1)|multiply(n3,#0)|divide(#1,#2) | general |
there are 192 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ? | "you had the answer almost right . the x = 84 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 84 + set ab = 84 + 23 = 17 c" | a ) 72 , b ) 85 , c ) 107 , d ) 98 , e ) 108 | c | subtract(add(subtract(192, 59), 23), 49) | subtract(n0,n2)|add(n3,#0)|subtract(#1,n1)| | other |
a family travelled for 12 hours . they covered the first half of the distance at 35 kmph and remaining half of the distance at 40 kmph . find the distance travelled by the family ? | let the distance travelled be x km . total time = ( x / 2 ) / 35 + ( x / 2 ) / 40 = 12 = > x / 70 + x / 80 = 12 = > ( 8 x + 7 x ) / 560 = 12 = > x = 560 km answer : e | a ) 270 km , b ) 890 km , c ) 684 km , d ) 320 km , e ) 560 km | e | divide(multiply(multiply(35, const_2), multiply(40, const_2)), subtract(multiply(multiply(40, const_2), const_1), multiply(multiply(35, const_2), const_1))) | multiply(n1,const_2)|multiply(n2,const_2)|multiply(#0,#1)|multiply(#1,const_1)|multiply(#0,const_1)|subtract(#3,#4)|divide(#2,#5) | physics |
of the 250 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren β t full - time and haven β t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ... | "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 1... | a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100 | e | subtract(subtract(250, 80), 20) | subtract(n0,n1)|subtract(#0,n3)| | general |
the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 360 . find the principal ? | "p = 360 ( 100 / 5 ) ^ 2 = > p = 9000 answer : c" | a ) 2277 , b ) 2667 , c ) 9000 , d ) 2766 , e ) 1811 | c | divide(360, 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 |
the average of 6 integers is 63 , and none of these integers is greater than 100 . if the average of 3 of the integers is 65 , what is the least possible value of one of the other two integers ? | when it comes to averages , we know thataverage value = ( sum of n values ) / n we can rewrite this into a useful formula : sum of n values = ( average value ) ( n ) the average of five integers is 63 so , the sum of all 5 integers = ( 63 ) ( 6 ) = 378 the average of three of the integers is 65 so , the sum of the 3 in... | a ) 45 , b ) 62 , c ) 75 , d ) 83 , e ) 90 | d | subtract(subtract(multiply(6, 63), multiply(3, 65)), 100) | multiply(n0,n1)|multiply(n3,n4)|subtract(#0,#1)|subtract(#2,n2) | general |
in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . what is the duration of the flight ? | "explanation : let the duration of the flight be x hours . then 600 / x β 600 / x + 1 / 2 = 200 600 / x β 1200 / 2 x + 1 = 200 x ( 2 x + 1 ) = 3 2 x 2 + x β 3 = 0 = > ( 2 x + 3 ) ( x β 1 ) = 0 neglecting the negative value for x we get x = 1 option d" | a ) 3 hours , b ) 2.4 hours , c ) 1.4 hours , d ) 1 hour , e ) none of these | d | divide(600, divide(multiply(200, 30), const_10)) | multiply(n1,n2)|divide(#0,const_10)|divide(n0,#1)| | general |
what is the tens digit of 7 ^ 1415 ? | "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1415 = 4 * 353 + 3 the ten ' s digit will be 4 . answer e" | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | floor(divide(reminder(power(7, reminder(1415, add(const_4, const_1))), const_100), const_10)) | add(const_1,const_4)|reminder(n1,#0)|power(n0,#1)|reminder(#2,const_100)|divide(#3,const_10)|floor(#4)| | general |
the ratio of 2 numbers is 3 : 4 and their h . c . f . is 4 . their l . c . m . is ? | "let the numbers be 3 x and 4 x their h . c . f . = 4 so the numbers are 3 * 4 , 4 * 4 = 12,16 l . c . m . = 48 answer is c" | a ) 20 , b ) 24 , c ) 48 , d ) 36 , e ) 60 | c | sqrt(divide(4, add(power(4, 3), add(power(2, 3), power(3, const_2))))) | power(n0,n1)|power(n1,n1)|power(n2,const_2)|add(#0,#1)|add(#3,#2)|divide(n3,#4)|sqrt(#5)| | other |
a 140 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ? | "1 : 2 / 5 = 5 : 2 2 / 7 * 140 = 40 answer : e" | a ) 35 , b ) 20 , c ) 47 , d ) 36 , e ) 40 | e | subtract(140, divide(140, add(divide(2, 5), const_1))) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)| | physics |
the sum of 3 consecutive numbers is definitely : | "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : c" | a ) positive , b ) divisible by 2 . , c ) divisible by 3 , d ) divisible by 4 . , e ) divisible by 5 | c | add(add(power(add(add(divide(subtract(subtract(3, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(3, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(3, const_10), const_2), const_4), const_2), power(add(di... | subtract(n0,const_10)|subtract(#0,const_2)|divide(#1,const_4)|add(#2,const_2)|power(#2,const_2)|add(#3,const_2)|power(#3,const_2)|add(#5,const_2)|add(#4,#6)|power(#5,const_2)|power(#7,const_2)|add(#9,#10)|add(#11,#8)| | physics |
a tree is 12 m tall and casts an an 8 m long shadow . at the same time , a flag pole caste a 100 m long shadow . how long is the flag pole ? | answer β΅ 8 m shadow means original height = 12 m β΄ 1 m shadow means original height = 12 / 8 m β΄ 100 m shadow means original height = ( 12 / 8 ) x 100 m = ( 6 / 4 ) x 100 = 6 x 25 = 150 m correct option : a | a ) 150 m , b ) 200 m , c ) 125 m , d ) 115 m , e ) none | a | multiply(100, divide(12, 8)) | divide(n0,n1)|multiply(n2,#0) | physics |
in a division sum , the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is : | "diver = ( 4 * 3 ) + 2 = 14 4 * quotient = 14 quotient = 3.5 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 3.5 ) + 4 = 53 a" | a ) 53 , b ) 58 , c ) 51 , d ) 60 , e ) 62 | a | add(multiply(add(multiply(4, const_3), 2), divide(add(multiply(4, const_3), 2), 3)), 4) | multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)| | general |
if x is equal to the sum of the integers from 20 to 30 , inclusive , and y is the number of even integers from 20 to 30 , inclusive , what is the value of x + y ? | "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 20 + ( 11 - 1 ) * 1 } = 11 * 25 = 275 = x number of even number = ( 30 - 20 ) / 2 + 1 = 6 = y x + y = 275 + 6 = 281 b" | a ) 171 , b ) 281 , c ) 361 , d ) 461 , e ) 561 | b | add(multiply(divide(add(20, 30), const_2), add(subtract(30, 20), const_1)), add(divide(subtract(30, 20), const_2), const_1)) | add(n0,n1)|subtract(n1,n0)|add(#1,const_1)|divide(#1,const_2)|divide(#0,const_2)|add(#3,const_1)|multiply(#2,#4)|add(#5,#6)| | general |
the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 36 . what is the rate of interest per annum ? | "$ 36 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 36 x = 0.06 the answer is b ." | a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 % | b | sqrt(36) | sqrt(n2)| | gain |
there are 60 slots around a circle , numbered 1 to 60 . a man starts fromthe first slot and jumps to the 5 th slot . from there he jumps to the 9 th slot andso on . in which slot will he land in his 2200 th jump ? | every 15 th jump , he comes back to 1 st position so , 2200 / 15 = remainder 10 hence 10 th position is 41 st slot answer : c | ['a ) 1', 'b ) 5', 'c ) 41', 'd ) 45', 'e ) 46'] | c | multiply(subtract(divide(2200, 60), floor(divide(2200, 60))), 60) | divide(n5,n0)|floor(#0)|subtract(#0,#1)|multiply(n0,#2) | geometry |
a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? | "net part filled in 1 hour = ( 1 / 3 - 1 / 6 ) = 1 / 6 the cistern will be filled in 6 / 1 hrs i . e . , 6 hrs . answer : d" | a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 6 hrs , e ) 5 hrs | d | divide(const_1, subtract(divide(const_1, 3), divide(const_1, 6))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)| | physics |
in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 3000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ? | "winner - looser 55 % - 45 % if 3000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 3,000 people compose 10 % of all voters , which means that the total number of votes is 30,000 . answer : e ." | a ) 23000 , b ) 22000 , c ) 20000 , d ) 25000 , e ) 30000 | e | divide(3000, divide(10, const_100)) | divide(n0,const_100)|divide(n1,#0)| | gain |
a departmental store has 9 managers and 18 associates . the 9 managers have an average salary of $ 1300 . the 18 associates have an average salary of $ 12000 . what is the average salary for the departmental store ? | number of managers is 9 their average salary is $ 1300 number of associates is 18 their average salary is $ 12,000 total salary of managers is 9 * 1300 = $ 11700 total salary of associates is 18 * 12,000 = $ 96,000 total salary for the departmental store is 96,000 + 11700 = 107700 average salary for the departmental st... | a ) $ 3556.25 , b ) $ 3988.89 , c ) $ 3836.56 , d ) $ 3745.56 , e ) $ 3428.56 | b | subtract(multiply(floor(divide(divide(divide(add(multiply(9, 1300), multiply(18, 12000)), add(9, 18)), const_2), const_1000)), const_1000), add(const_10, const_1)) | add(n0,n1)|add(const_1,const_10)|multiply(n0,n3)|multiply(n1,n5)|add(#2,#3)|divide(#4,#0)|divide(#5,const_2)|divide(#6,const_1000)|floor(#7)|multiply(#8,const_1000)|subtract(#9,#1) | general |
how many different positive integers are factors of 256 ? | "16 Γ 16 = 4 ^ 2 Γ 4 ^ 2 so total factors = ( 3 + 1 ) ( 3 + 1 ) = 16 answer : d" | a ) 4 , b ) 6 , c ) 8 , d ) 16 , e ) 18 | d | add(power(const_2, const_2), const_2) | power(const_2,const_2)|add(#0,const_2)| | other |
find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 ? | "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c" | a ) 240 / 1576 , b ) 240 / 1542 , c ) 240 / 1547 , d ) 240 / 1528 , e ) 240 / 1529 | c | multiply(divide(divide(5, 34), divide(7, 48)), divide(2, 13)) | divide(n2,n3)|divide(n4,n5)|divide(n0,n1)|divide(#0,#1)|multiply(#3,#2)| | other |
a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 70 % more recliners . what is the percentage increase of the gross ? | say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 70 % more ie . , 170 recliners hence her sales tields 170 * 80 = $ 13600 increase in sales = 13600 - 10000 = $ 3600 so % increase = 3600 * 100 / 10000 = 36 ... | a ) 10 % , b ) 15 % , c ) 20 % , d ) 36 % , e ) 50 % | d | subtract(multiply(multiply(subtract(const_1, divide(20, const_100)), add(const_1, divide(70, const_100))), const_100), const_100) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(#5,const_100) | general |
the least number , which when divided by 12 , 31 , 20 and 54 leaves in each case a remainder of 8 is : | "required number = ( l . c . m . of 12 , 31 , 20 , 54 ) + 8 = 16740 + 8 = 16748 . answer : c" | a ) 448 , b ) 488 , c ) 16748 , d ) 548 , e ) 560 | c | multiply(54, const_10) | multiply(n3,const_10)| | general |
timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey . if he made no stops during the trip and his average speed for the entire journey was 40 mph , for what fraction of the total time did he drive at 50 mph ? | we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire journey was 40 mph , then he drove at 50 mph for a longer duration of time . 10 30 10 - - 40 - - - - - - 50 this shows that you can divide the entire journ... | a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 3 / 4 , e ) 3 / 5 | d | divide(divide(subtract(40, 10), subtract(50, 40)), const_4) | subtract(n2,n0)|subtract(n1,n2)|divide(#0,#1)|divide(#2,const_4) | general |
a certain car uses 12 gallons of gasoline in traveling 420 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car β s gas mileage be increased ? | "420 / 10 = 42 the difference is 42 - 35 = 7 . answer d" | a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 10 | d | subtract(divide(420, 10), divide(420, 12)) | divide(n1,n2)|divide(n1,n0)|subtract(#0,#1)| | physics |
in august , a cricket team that played 120 matches won 26 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ? | "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 31.2 + x by solving we get x = 65 answer : c" | a ) 40 , b ) 52 , c ) 65 , d ) 80 , e ) 98 | c | divide(subtract(multiply(divide(52, const_100), 120), multiply(divide(26, const_100), 120)), subtract(const_1, divide(52, const_100))) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(const_1,#0)|subtract(#2,#3)|divide(#5,#4)| | general |
the average weight of a , b and c is 65 kg . if the average weight of a and b be 60 kg and that of b and c be 70 kg , then the weight of a is : | "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 65 x 3 ) = 195 Γ’ β¬ Β¦ . ( i ) a + b = ( 60 x 2 ) = 120 Γ’ β¬ Β¦ . ( ii ) b + c = ( 70 x 2 ) = 140 Γ’ β¬ Β¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 260 Γ’ β¬ Β¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = ... | a ) 55 kg , b ) 65 kg , c ) 75 kg , d ) 45 kg , e ) 63 kg | a | subtract(add(multiply(60, const_2), multiply(70, const_2)), multiply(65, const_3)) | multiply(n1,const_2)|multiply(n2,const_2)|multiply(n0,const_3)|add(#0,#1)|subtract(#3,#2)| | general |
a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ? | "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 = > 4 days answer a" | a ) 4 , b ) 3 , c ) 5 , d ) 2 , e ) 1 | a | inverse(add(inverse(28), add(inverse(7), inverse(14)))) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4)| | physics |
if a ^ 2 + b ^ 2 = 15 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 | "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 15 - 20 = - 5 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 15 + 20 = 35 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 35 - 5 = 30 d" | a ) 10 , b ) 20 , c ) 60 , d ) 30 , e ) 70 | d | add(multiply(sqrt(15), const_10), const_3) | sqrt(n2)|multiply(#0,const_10)|add(#1,const_3)| | general |
a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 105 , then how much amount should c pay as his share of rent ? | "a : b : c = 10 Γ 7 : 12 Γ 5 : 15 Γ 3 = 2 Γ 7 : 12 Γ 1 : 3 Γ 3 = 14 : 12 : 9 amount that c should pay = 105 Γ 9 / 35 = 3 Γ 9 = 27 answer is b ." | a ) 35 , b ) 27 , c ) 25 , d ) 15 , e ) 55 | b | multiply(105, divide(multiply(15, 3), add(add(multiply(10, 7), multiply(12, 5)), multiply(15, 3)))) | multiply(n4,n5)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|add(#3,#0)|divide(#0,#4)|multiply(n6,#5)| | general |
mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 80 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least ... | d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 80 , t = t d = 80 t since they went the same distance : 50 t + 50 / 4 = 80 t 30 t = 50 / 4 = 50 / 120 * 60 = 25 min t = 25 min d | a ) 35 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | d | multiply(const_60, divide(multiply(50, divide(15, const_60)), subtract(80, 50))) | divide(n1,const_60)|subtract(n2,n0)|multiply(n0,#0)|divide(#2,#1)|multiply(#3,const_60) | physics |
in a recent head - to - head run - off election , 18,000 absentee ballets were cast . 3 / 7 of the absentee ballets were thrown out and 2 / 9 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ? | "4 / 7 * 7 / 9 ( total absentee votes ) = 4 / 9 ( total votes ) = 4 / 9 * 18000 = 8000 answer is d" | a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000 | d | multiply(divide(divide(subtract(subtract(multiply(multiply(2, const_4), const_1000), multiply(multiply(multiply(2, const_4), const_1000), divide(3, 7))), multiply(subtract(multiply(multiply(2, const_4), const_1000), multiply(multiply(multiply(2, const_4), const_1000), divide(3, 7))), divide(2, 9))), const_1000), const_... | divide(n1,n2)|divide(n3,n4)|multiply(n3,const_4)|multiply(#2,const_1000)|multiply(#0,#3)|subtract(#3,#4)|multiply(#1,#5)|subtract(#5,#6)|divide(#7,const_1000)|divide(#8,const_4)|multiply(#9,n3)| | general |
how many multiples of 2 are there between 10 and 100 ( both are inclusive ) ? | the answer is ( 100 - 10 ) / 2 + 1 = 46 answer is d | a ) 2 , b ) 7 , c ) 6 , d ) 46 , e ) 3 | d | add(divide(subtract(100, 10), 2), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1) | other |
if 25 % of a number exceeds 8 % of it by 11.9 , then find the number ? | "use the elimination method to find the correct option . of all the options only 70 fits 25 % of 70 = 17.5 8 % of 70 = 5.6 17.5 - 5.6 = 11.9 required number is 70 . answer : b" | a ) 76 , b ) 70 , c ) 55 , d ) 65 , e ) 22 | b | add(divide(11.9, divide(subtract(25, 8), const_100)), 8) | subtract(n0,n1)|divide(#0,const_100)|divide(n2,#1)|add(n1,#2)| | gain |
in a 20 litre mixture ratio of milk and water is 3 : 1 . how much milk should added so that mixture ratio become 4 : 1 ? | amount of milk = 20 Γ 3 / 4 = 15 litre and water = 5 litre let x litre milk to be added then 15 + x / 5 = 4 / 1 = 15 + x = 20 , x = 5 answer e | a ) 3 , b ) 2 , c ) 8 , d ) 6 , e ) 5 | e | subtract(multiply(multiply(20, divide(1, add(1, 3))), 4), multiply(20, divide(3, 4))) | add(n1,n2)|divide(n1,n3)|divide(n2,#0)|multiply(n0,#1)|multiply(n0,#2)|multiply(n3,#4)|subtract(#5,#3) | general |
the price of an item is discounted 5 percent on day 1 of a sale . on day 2 , the item is discounted another 5.00001 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ? | "let initial price be 100 price in day 1 after 5 % discount = 95 price in day 2 after 5 % discount = 90.25 price in day 3 after 10 % discount = 81.23 so , price in day 3 as percentage of the sale price on day 1 will be = 81.23 / 95 * 100 = > 85.5 % answer will definitely be ( e )" | a ) 80 % , b ) 82.5 % , c ) 83 % , d ) 84 % , e ) 85.5 % | e | add(multiply(divide(divide(10, const_100), subtract(1, divide(1, 5))), const_100), 2) | divide(n5,const_100)|divide(n1,n0)|subtract(n1,#1)|divide(#0,#2)|multiply(#3,const_100)|add(n2,#4)| | gain |
a 14 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ? | "1 : 2 / 5 = 5 : 2 2 / 7 * 14 = 4 answer : e" | a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 4 | e | subtract(14, divide(14, add(divide(2, 5), const_1))) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)| | physics |
what is the smallest positive perfect square that is divisible by 9 , 15 , and 25 ? | "the number needs to be divisible by 3 ^ 2 , 3 * 5 , and 5 ^ 2 . the smallest such perfect square is 3 ^ 2 * 5 ^ 2 = 225 the answer is b ." | a ) 100 , b ) 225 , c ) 900 , d ) 1,600 , e ) 4,900 | b | add(multiply(multiply(multiply(9, power(const_3, const_2)), 15), const_2), multiply(15, 25)) | multiply(n1,n2)|power(const_3,const_2)|multiply(n0,#1)|multiply(n1,#2)|multiply(#3,const_2)|add(#4,#0)| | geometry |
a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? | a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.50 for the f... | a ) 15.6 , b ) 18.1 , c ) 17.5 , d ) 18.7 , e ) 19.1 | b | add(2.5, multiply(subtract(divide(8, divide(1, 5)), 1), 0.4)) | divide(n1,n2)|divide(n6,#0)|subtract(#1,n1)|multiply(n3,#2)|add(n0,#3) | general |
water is poured into a tank so that the tank is being filled at the rate of 5 cubic feet per hour . if the empty rectangular tank is 10 feet long , 6 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ? | the volume the tank is : length * width * depth = 10 * 6 * 5 = 300 cubic feet . 300 cubic feet / 5 cubic feet per hour = 60 hours . it will take 60 hours to fill the tank . the answer is e . | ['a ) 40', 'b ) 45', 'c ) 50', 'd ) 55', 'e ) 60'] | e | divide(volume_rectangular_prism(10, 6, 5), 5) | volume_rectangular_prism(n0,n1,n2)|divide(#0,n0) | physics |
a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 69 km downstream . | "speed of boat in still water = 13 km / hr speed of the stream = 6 km / hr speed downstream = ( 13 + 6 ) = 19 km / hr time taken to travel 69 km downstream = 69 Γ’ Β β 19 = 17 Γ’ Β β 4 = 3.6 hours answer is a" | a ) 3.6 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr | a | divide(69, add(13, 6)) | add(n0,n1)|divide(n2,#0)| | physics |
a string of 50 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.05 , what is the probability that the string of light bulbs will fail during the time period t ? | the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 50 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.05 = 0.95 the the probability that n... | a ) 0.05 , b ) ( 0.05 ) ^ 50 , c ) 1 - ( 0.96 ) ^ 50 , d ) 1 - ( 0.95 ) ^ 50 , e ) ( 0.95 ) ^ 50 | d | subtract(const_1, power(subtract(const_1, 0.05), 50)) | subtract(const_1,n1)|power(#0,n0)|subtract(const_1,#1) | probability |
a sum was put at simple interest at a certain rate for 7 years had it been put at 2 % higher rate , it would have fetched 140 more . find the sum . | "difference in s . i . = p Γ t / 100 ( r 1 β r 2 ) β 140 = p Γ 7 x 2 / 100 ( β΅ r 1 - r 2 = 2 ) β p = 140 Γ 100 / 7 Γ 2 = 1000 answer c" | a ) 500 , b ) 750 , c ) 1000 , d ) 1250 , e ) 1500 | c | divide(140, multiply(divide(2, const_100), 7)) | divide(n1,const_100)|multiply(n0,#0)|divide(n2,#1)| | gain |
zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 8 questions , if sterling had answered 2 ... | "i got two equations : 3 x - 2 y = 25 x + y = 8 3 x - 2 ( 8 - x ) = 25 3 x - 16 + 2 x = 25 5 x = 41 x = 8.2 or between 8 and 9 . 9 ans c )" | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | c | divide(add(subtract(multiply(2, subtract(8, 2)), multiply(3, 2)), 31), add(3, 2)) | add(n0,n2)|multiply(n0,n2)|subtract(n1,n2)|multiply(n2,#2)|subtract(#3,#1)|add(n3,#4)|divide(#5,#0)| | general |
a positive number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ? | "sq rt ( 7 x / 3 ) = x = > 7 x / 3 = x ^ 2 = > x = 7 / 3 ans - a" | a ) 7 / 3 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2 | a | divide(7, 3) | divide(n0,n1)| | general |
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is : | "let the total number of workers be x . then , 8000 x = ( 18000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 84000 = x = 42 . answer : c" | a ) 23 , b ) 19 , c ) 42 , d ) 20 , e ) 21 | c | add(7, divide(multiply(7, subtract(18000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | general |
a company charges a fixed rental of rs . 350 per month . it allows 200 calls free per month . each call is charge at rs . 1.4 when the number of calls exceed 200 per month and it charges rs . 1.6 when the number of calls exceeds 400 per month and so on . a customer made 150 calls in february and 250 calls in march . by... | solution : charge per call in february = 350 / 150 = 7 / 3 = 2.33 charge per call in march = [ 350 + ( 50 * 1.4 ) ] / 250 = 420 / 250 = 42 / 25 = 1.68 % cheaper call rate in march = [ ( 2.33 - 1.68 ) / 2.33 ] * 100 = 28 % . answer : option a | a ) 28 % , b ) 25 % , c ) 18.5 % , d ) 16 % , e ) none of these | a | multiply(divide(subtract(divide(350, 150), divide(add(multiply(subtract(250, 200), 1.4), 350), 250)), divide(350, 150)), const_100) | divide(n0,n6)|subtract(n7,n1)|multiply(n2,#1)|add(n0,#2)|divide(#3,n7)|subtract(#0,#4)|divide(#5,#0)|multiply(#6,const_100) | general |
3 * 12 + 3 * 13 + 3 * 16 + 11 = ? | 3 * 12 + 3 * 13 + 3 * 16 + 11 = 36 + 39 + 48 + 11 = 134 the answer is c . | a ) 122 , b ) 126 , c ) 134 , d ) 148 , e ) 151 | c | add(add(add(multiply(3, 12), multiply(3, 13)), multiply(3, 16)), 11) | multiply(n0,n1)|multiply(n0,n3)|multiply(n0,n5)|add(#0,#1)|add(#3,#2)|add(n6,#4) | general |
a certain roller coaster has 7 cars , and a passenger is equally likely to ride in any 1 of the 7 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 7 times , what is the probability that the passenger will ride in each of the 7 cars ? | "if he is to ride 6 times and since he can choose any of the 6 cars each time , total number of ways is = 7 * 7 * 7 * 7 * 7 * 7 = 117649 now the number of ways if he is to choose a different car each time is = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 so the probability is = 5040 / 117649 = 720 / 16807 answer : d" | a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 720 / 16807 , e ) 1 | d | multiply(factorial(7), power(divide(1, 7), 7)) | divide(n1,n0)|factorial(n0)|power(#0,n0)|multiply(#1,#2)| | general |
what is the greatest of 3 consecutive integers whose sum is 18 ? | "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 18 ; = > 3 n = 15 ; = > n = 5 the greatest of the three numbers is therefore 5 + 2 = 7 answer : b" | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5 | b | add(divide(subtract(18, 3), 3), const_2) | subtract(n1,n0)|divide(#0,n0)|add(#1,const_2)| | physics |
a man can row his boat with the stream at 16 km / h and against the stream in 4 km / h . the man ' s rate is ? | "ds = 16 us = 4 s = ? s = ( 16 - 4 ) / 2 = 6 kmph answer : c" | a ) 1 kmph , b ) 3 kmph , c ) 6 kmph , d ) 7 kmph , e ) 5 kmph | c | divide(subtract(16, 4), const_2) | subtract(n0,n1)|divide(#0,const_2)| | gain |
a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 6.0 . if the company β s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ? | "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 6 $ then total value is 300 * 6.0 = 1800 . imo option e is correct answer . ." | a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 1,800 | e | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 6.0), 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 |
a certain quantity of 45 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ? | "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 45 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 45 ml and 25 ml is 20 ml per 100 ml of ... | a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4 | c | inverse(add(divide(subtract(35, 25), subtract(45, 35)), const_1)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|add(#2,const_1)|inverse(#3)| | other |
there are 16 bees in the hive , then 8 more fly . how many bees are there in all ? | 16 + 8 = 24 . answer is d . | a ) 7 , b ) 33 , c ) 12 , d ) 24 , e ) 25 | d | add(16, 8) | add(n0,n1)| | general |
let raj be 3 years older than ravi and hema be two years younger than ravi . raj is 3 times as old as rahul who is hema β s brother . the ratio of the ages of hema and her brother is 3 : 2 . find by how much percentage raj β s age is more than hema β s when raj will be 20 years old . | answer : 33.33 | a ) 33.33 , b ) 27.33 , c ) 28.38 , d ) 29.37 , e ) 28.31 | a | multiply(divide(add(3, const_2), add(subtract(multiply(3, divide(add(3, const_2), subtract(3, divide(3, 2)))), add(3, const_2)), subtract(20, multiply(3, divide(add(3, const_2), subtract(3, divide(3, 2))))))), const_100) | add(n0,const_2)|divide(n0,n3)|subtract(n0,#1)|divide(#0,#2)|multiply(n0,#3)|subtract(#4,#0)|subtract(n4,#4)|add(#5,#6)|divide(#0,#7)|multiply(#8,const_100) | general |
the salaries of a and b together amount to $ 6000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ? | "let a ' s salary is x b ' s salary = 6000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 6000 - x ) x = $ 4500 answer is d" | a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 4500 , e ) $ 5200 | d | subtract(6000, divide(6000, add(divide(subtract(const_100, 85), subtract(const_100, 95)), const_1))) | subtract(const_100,n2)|subtract(const_100,n1)|divide(#0,#1)|add(#2,const_1)|divide(n0,#3)|subtract(n0,#4)| | gain |
gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 50 and the turban . find the price of the turban . | "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 50 . thus , 3434 ( 90 + x ) = 50 + x or 270 + 3 x = 200 + 4 x or x = 70 answer : e" | a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 70 | e | subtract(multiply(divide(subtract(90, 50), subtract(const_12, 9)), const_12), 90) | subtract(n0,n2)|subtract(const_12,n1)|divide(#0,#1)|multiply(#2,const_12)|subtract(#3,n0)| | general |
the diagonal of a rectangle is cm and its area is 20 sq . cm . the perimeter of the rectangle must be : | explanation : ( or ) { \ color { black } l ^ { 2 } + b ^ { 2 } = 41 } also , { \ color { black } ( l + b ) ^ { 2 } = l ^ { 2 } + b ^ { 2 } + 2 lb } = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . answer : a ) 18 | ['a ) 18', 'b ) 77', 'c ) 625', 'd ) 276', 'e ) 191'] | a | multiply(const_2, sqrt(add(add(20, 20), add(add(20, 20), const_1)))) | add(n0,n0)|add(#0,const_1)|add(#0,#1)|sqrt(#2)|multiply(#3,const_2) | geometry |
an empty fuel tank with a capacity of 214 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ? | say there are a gallons of fuel a in the tank , then there would be 214 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 214 - a gallons of fuel b is 0.16 ( 214 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 214 - a ) = 30 - - > a = ... | a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 106 | e | divide(subtract(multiply(214, divide(16, const_100)), 30), subtract(divide(16, const_100), divide(12, const_100))) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|subtract(#0,#1)|subtract(#2,n3)|divide(#4,#3) | gain |
if 27.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ? | "students enrolled in biology are 27.5 % and therefore not enrolled are 72.5 % . so of 880 is 880 * . 225 = 638 answer is a 638" | a ) 638 , b ) 330 , c ) 550 , d ) 430 , e ) 880 | a | multiply(divide(880, const_100), subtract(const_100, 27.5)) | divide(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)| | other |
the ratio of local and international calls made by amy this week is 5 to 2 . if the ratio changes to 5 to 3 after amy makes 3 more international calls , how many local calls did amy make this week ? | the ratio of local and international calls made by amy this week is 5 to 2 let the current ratio be 5 x / 2 x the ratio changes to 5 to 3 after amy makes three more international calls 5 x / ( 2 x + 3 ) = 5 / 3 solving we get x = 3 initial ratio 15 : 6 ( 5 : 2 ) final ratio 15 : ( 6 + 3 ) = 15 : 9 = 5 : 3 so total numb... | a ) 3 , b ) 5 , c ) 10 , d ) 15 , e ) 21 | d | multiply(divide(3, subtract(3, 2)), 5) | subtract(n3,n1)|divide(n3,#0)|multiply(n0,#1) | other |
on a sum of money , the simple interest for 2 years is rs . 660 , while the compound interest is rs . 696.30 , the rate of interest being the same in both the cases . the rate of interest is : | "solution difference in c . i . and s . i . for 2 years = rs . ( 696.30 - 660 ) = rs . 36.30 . s . i . for one year = rs . 330 . β΄ s . i . on rs . 330 for 1 year = rs . 36.30 . β΄ rate ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer d" | a ) 10 % , b ) 10.5 % , c ) 12 % , d ) none of these , e ) can not be determined | d | divide(multiply(const_100, subtract(subtract(696.30, divide(660, 2)), divide(660, 2))), divide(660, 2)) | divide(n1,n0)|subtract(n2,#0)|subtract(#1,#0)|multiply(#2,const_100)|divide(#3,#0)| | gain |
what is the ratio between perimeters of two squares one having 4 times the diagonal then the other ? | "d = 4 d d = d a β 2 = 4 d a β 2 = d a = 4 d / β 2 a = d / β 2 = > 4 : 1 answer : d" | a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 4 : 1 , e ) 3 : 3 | d | divide(4, divide(4, 4)) | divide(n0,n0)|divide(n0,#0)| | geometry |
what is the distance covered by a train if it travels with a speed of 150 kmh for 8 hours ? | "distance = time x speed distance = 150 x 8 = 1200 answer : e" | a ) 1000 km , b ) 700 km , c ) 800 km , d ) 1400 km , e ) 1200 km | e | multiply(150, 8) | multiply(n0,n1)| | physics |
following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 12 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ? | "price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 12 / 1.5 = 8 total price = 8 + 8 = 16 c is the answer" | a ) 11 . , b ) 12 . , c ) 16 . , d ) 14 . , e ) 14.5 | c | add(divide(multiply(10, const_100), add(const_100, 25)), divide(multiply(12, const_100), add(const_100, 50))) | add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|multiply(n1,const_100)|divide(#2,#0)|divide(#3,#1)|add(#4,#5)| | general |
of the 120 passengers on flight 750 , 55 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ? | number of passengers on flight = 120 number of female passengers = . 5 * 120 = 66 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8... | a ) 44 , b ) 48 , c ) 50 , d ) 52 , e ) 58 | e | subtract(multiply(120, divide(55, const_100)), subtract(multiply(120, divide(10, const_100)), divide(multiply(120, divide(10, const_100)), 3))) | divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n0,#1)|divide(#3,n5)|subtract(#3,#4)|subtract(#2,#5) | gain |
if x ^ 2 + 1 / x ^ 2 = 9 , what is the value of x ^ 4 + 1 / x ^ 4 ? | "important : i notice that if we square x Β² , we get x β΄ , and if we square 1 / x Β² , we get 1 / x β΄ , so let ' s see what happens if we take the equation x Β² + 1 / x Β² = 9 andsquareboth sides : ( x Β² + 1 / x Β² ) Β² = 81 so , ( x Β² + 1 / x Β² ) ( x Β² + 1 / x Β² ) = 81 expand to get : x β΄ + 1 + 1 + 1 / x β΄ = 81 simplify : ... | a ) 10 , b ) 72 , c ) 79 , d ) 16 , e ) 18 | c | subtract(power(2, 2), 2) | power(n0,n0)|subtract(#0,n0)| | general |
a certain no . when divided by 65 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? | "explanation : 65 + 25 = 90 / 15 = 6 ( remainder ) c" | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9 | c | subtract(subtract(subtract(65, 25), const_4), const_2) | subtract(n0,n1)|subtract(#0,const_4)|subtract(#1,const_2)| | general |
a , b and c started a partnership business by investing rs . 24000 , rs . 32000 , rs . 36000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ? | "a : b : c = 24000 : 32000 : 36000 = 6 : 8 : 9 let total profit = p then p Γ£ β 9 / 23 = 36000 p = ( 36000 Γ£ β 23 ) / 9 = 92000 answer is d ." | a ) 70000 , b ) 60000 , c ) 80000 , d ) 92000 , e ) 50000 | d | add(add(multiply(divide(24000, 36000), 36000), multiply(divide(32000, 36000), 36000)), 36000) | divide(n0,n2)|divide(n1,n2)|multiply(n3,#0)|multiply(n3,#1)|add(#2,#3)|add(n3,#4)| | gain |
the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 60 / kg . how much did a kg of coffee cost in june ? | "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 60 = > x = 60 e" | a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60 | e | divide(60, multiply(subtract(const_1, divide(20, const_100)), add(divide(20, const_100), const_1))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|divide(n2,#4)| | general |
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