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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what is the sum of all even numbers from 1 to 901 ? | "explanation : 900 / 2 = 450 450 * 451 = 202950 answer : b" | a ) 122821 , b ) 202950 , c ) 281199 , d ) 122850 , e ) 128111 | b | divide(multiply(1, 901), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general |
the lcm and hcf of two numbers are 100 and 10 respectively . find the larger of the two numbers if their sum is 110 . | "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 100 * 10 = 1000 so the answer which we are looking for has to be a factor of 1000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 1000 . and then take the highest number as the answe... | a ) 100 , b ) 12 , c ) 35 , d ) 466 , e ) 56 | a | divide(multiply(100, 10), 110) | multiply(n0,n1)|divide(#0,n2)| | physics |
a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 3 girls and 1 boy ? | "sample space = 2 ^ 4 = 16 . favourable events = { bbgg } , { bgbg } , { bggb } , { ggbb } , { gbgb } , { gbbg } . { bggg } , { gbbb ) probability = 8 / 16 = 1 / 2 . ans ( e ) ." | a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 1 / 2 | e | subtract(3, multiply(divide(factorial(const_3.0), factorial(const_2.0)), power(divide(3, 1), 4))) | divide(n2,const_2.0)|factorial(const_3.0)|factorial(n3)|divide(#1,#2)|power(#0,n0)|multiply(#3,#4)|subtract(n2,#5)| | general |
what will be the compound interest on a sum of rs . 40,000 after 3 years at the rate of 12 % p . a . ? | "amount = [ 40000 * ( 1 + 12 / 100 ) 3 ] = 40000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 56197.12 c . i . = ( 56197.12 - 40000 ) = rs : 16197.12 answer : e" | a ) s : 10123.19 , b ) s : 10123.29 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 16197.12 | e | subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(12, const_100)), 3)), multiply(multiply(const_4, const_100), const_100)) | divide(n2,const_100)|multiply(const_100,const_4)|add(#0,const_1)|multiply(#1,const_100)|power(#2,n1)|multiply(#3,#4)|subtract(#5,#3)| | gain |
a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? | orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : ... | a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220 | b | subtract(divide(subtract(multiply(12, 370), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8)), subtract(370, divide(subtract(multiply(12, 370), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtrac... | multiply(n0,n2)|multiply(const_1000,const_3)|multiply(const_100,const_3)|multiply(const_10,const_2)|subtract(n0,n1)|add(#1,#2)|add(#5,#3)|subtract(#0,#6)|divide(#7,#4)|subtract(n2,#8)|subtract(#8,#9) | general |
if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 81 , how much does one shirt cost ? | "3 j + 2 s = 69 2 j + 3 s = 81 - - - - - - - - - - - - - - - - 5 j + 5 s = 150 - - - - ( divide by 5 ) - - - > j + s = 30 3 j + 2 s = j + 2 ( j + s ) = j + 60 = 69 - - - > j = 9 3 * 9 + 2 s = 69 27 + 2 s = 69 2 s = 42 s = 21 answer : d" | a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 21 , e ) $ 16.80 | d | divide(subtract(multiply(81, 3), multiply(69, 2)), subtract(multiply(3, 3), multiply(2, 2))) | multiply(n0,n5)|multiply(n1,n2)|multiply(n0,n0)|multiply(n1,n1)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)| | general |
a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference ? | "total circuit = 27 / 3 = 9 total feet squirrel travels = 9 * 3 = 27 feet answer : c" | a ) 10 feet , b ) 12 feet , c ) 27 feet , d ) 15 feet , e ) 18 feet | c | multiply(divide(27, 3), 3) | divide(n1,n0)|multiply(n2,#0)| | geometry |
how many zeroes are there at the end of the number n , if n = 60 ! + 120 ! ? | the number of zeroes at the end of 60 ! will be less than the number of zeroes at the end of 120 ! hence it is sufficient to calculate the number of zeroes at the end of 60 ! the number of zeroes = [ 60 / 5 ] + [ 60 / 25 ] + [ 60 / 125 ] = 12 + 2 + 0 = 14 the answer is b . | a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20 | b | add(divide(60, add(const_4, const_1)), const_2) | add(const_1,const_4)|divide(n0,#0)|add(#1,const_2) | general |
if x is a sum of all even integers on the interval 13 . . . 61 and y is their number , what is the gcd ( x , y ) ? | "x = 14 + 16 + . . . + 60 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 60 ) / 2 * 24 = 37 * 24 . gcd of 24 and 37 * 22 is 24 . answer : d ." | a ) 1 , b ) 13 , c ) 26 , d ) 24 , e ) 1014 | d | multiply(add(subtract(13, const_10), const_2), add(subtract(13, const_10), const_2)) | subtract(n0,const_10)|add(#0,const_2)|multiply(#1,#1)| | general |
a train leaves delhi at 11 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ? | "d = 30 * 3 = 90 rs = 40 β 30 = 10 t = 90 / 10 = 9 d = 40 * 9 = 360 km answer : a" | a ) 360 , b ) 288 , c ) 600 , d ) 888 , e ) 121 | a | multiply(divide(multiply(30, add(const_3, 2)), subtract(40, 30)), 40) | add(n2,const_3)|subtract(n3,n1)|multiply(n1,#0)|divide(#2,#1)|multiply(n3,#3)| | physics |
if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly twice in 2 consecutive flips ? | "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 = 4 ways for 2 h tt , thus probability is = p ( tt ) = 1 / 4 = . 25 answer : b" | a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666 | b | multiply(power(divide(const_1, const_2), 2), 2) | divide(const_1,const_2)|power(#0,n0)|multiply(n0,#1)| | general |
how many multiples of 8 are less than 7600 , and also multiples of 19 ? | "lcm of 8 & 19 = 152 tried dividing 7600 by 152 got quotient 50 ' so c is answer" | a ) 104 , b ) 100 , c ) 50 , d ) 89 , e ) 90 | c | add(divide(subtract(19, 7600), 8), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | general |
in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,7 ) , ( 12,7 ) , ( 2,3 ) , ( 9,3 ) ? | "area of parallelogram = b * h . base = distance in x coordinates between ( 2,3 ) and ( 9,3 ) = 7 height = difference in y coordinates between ( 5,7 ) and ( 2,3 ) = 3 . area = 7 * 3 = 21 . answer : a" | a ) 21 , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 . | a | add(const_3, const_2) | add(const_2,const_3)| | geometry |
on dividing 265 by a number , the quotient is 12 and the remainder is 1 . find the divisor . | "d = ( d - r ) / q = ( 265 - 1 ) / 12 = 264 / 12 = 22 e )" | a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22 | e | floor(divide(265, 12)) | divide(n0,n1)|floor(#0)| | general |
of the 12,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ? | "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will b... | a ) 14.3 % , b ) 13.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 % | b | multiply(multiply(divide(divide(divide(2, 7), 2), add(divide(divide(2, 7), 2), subtract(const_1, divide(2, 7)))), const_100), const_3) | divide(n1,n2)|divide(#0,n1)|subtract(const_1,#0)|add(#1,#2)|divide(#1,#3)|multiply(#4,const_100)|multiply(#5,const_3)| | general |
given two sets a = { 11 , 44 , 55 } and b = { 01 } , if one number is chosen from each set at random , what is the probability that the sum of both numbers is an even number | one way to look at it : the number from set a can be anything . the number selected from set b will determine whether the sum is odd or even . for example , if a 4 is selected from set a , we need a 0 from set b to get an even sum . if a 5 is selected from set a , we need a 1 from set b to get an even sum . and so on .... | a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 7 , d ) 1 / 2 , e ) 3 | d | divide(divide(add(11, 44), const_2), 55) | add(n0,n1)|divide(#0,const_2)|divide(#1,n2) | general |
what is the least value of x , so that 2 x 4472 is divisible by 9 | "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 4 + 4 + 7 + 2 = 19 + x least value of x may be ' 8 ' , so that the total 19 + 8 = 27 is divisible by 9 . answer : option b" | a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 2 | b | divide(divide(divide(lcm(2, 4472), 4472), const_4), const_4) | lcm(n0,n1)|divide(#0,n1)|divide(#1,const_4)|divide(#2,const_4)| | general |
a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 230 per month . what is his monthly salary ? | "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 Γ’ β¬ β 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 230 = > 5750 answer : b" | a ) 5000 , b ) 5750 , c ) 2878 , d ) 2990 , e ) 2771 | b | divide(multiply(230, const_100), subtract(const_100, add(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(20, const_100))))) | divide(n1,const_100)|multiply(n2,const_100)|subtract(const_100,n0)|multiply(#0,#2)|add(#3,#2)|subtract(const_100,#4)|divide(#1,#5)| | general |
one hour after adrienne started walking the 60 miles from x to y , william started walking from x to y as well . adrienne walks 3 miles per hour and william walks 1 mile per hour faster than adrienne . how far from x will william be when he catches up to adrienne ? | first , determine how far adrienne has walked in the one hour . she has walked three miles which means she is three miles ahead of william when he sets off . william walks at four miles / hour which means that every hour , william will get one mile closer to adrienne . if he gets one mile closer every hour , it will ta... | a ) 8 miles , b ) 9 miles , c ) 10 miles , d ) 11 miles , e ) 12 miles | d | stream_speed(multiply(3, add(3, 1)), 1) | add(n1,n2)|multiply(n1,#0)|stream_speed(#1,n2) | physics |
a shipment of 250 smartphones contains 76 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ? | "probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = ( 76 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 75 ( we already picked one ) defective phones is = ( 75 / 249 ) combined probability of series of events ... | a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3 | c | divide(multiply(76, subtract(76, const_1)), multiply(250, subtract(250, const_1))) | subtract(n1,const_1)|subtract(n0,const_1)|multiply(n1,#0)|multiply(n0,#1)|divide(#2,#3)| | other |
if 48 machine can finish a job in 80 days , then how many more machines would be needed to finish the job in one - fifth less time ? | "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 t... | a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16 | d | subtract(divide(multiply(48, 80), multiply(divide(const_3, const_4), 80)), 48) | divide(const_3,const_4)|multiply(n0,n1)|multiply(n1,#0)|divide(#1,#2)|subtract(#3,n0)| | general |
a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is | "explanation : number of bricks = courtyard area / 1 brick area = ( 2500 Γ 160020 Γ 10 ) = 20000 answer : option c" | a ) 16000 , b ) 18000 , c ) 20000 , d ) 22000 , e ) 24000 | c | divide(multiply(multiply(25, const_100), multiply(16, const_100)), multiply(20, 10)) | multiply(n0,const_100)|multiply(n1,const_100)|multiply(n2,n3)|multiply(#0,#1)|divide(#3,#2)| | physics |
a train 108 m long is moving at a speed of 50 km / hr . it crosses a train 112 m long coming from opposite direction in 6 seconds . what is the speed of the second train ? | explanation : total distance = 108 + 112 = 220 m time = 6 s relative speed = distance / time = 220 / 6 m / s = 110 / 3 m / s = ( 110 / 3 ) Γ ( 18 / 5 ) km / hr = 132 km / hr = > 50 + speed of second train = 132 km / hr = > speed of second train = 132 - 50 = 82 km / hr answer : option a | a ) 82 kmph , b ) 76 kmph , c ) 44 kmph , d ) 58 kmph , e ) 56 kmph | a | multiply(const_3_6, subtract(divide(add(112, 108), 6), multiply(const_0_2778, 50))) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,n3)|subtract(#2,#1)|multiply(#3,const_3_6) | physics |
john found that the average of 15 numbers is 40 . if 14 is added to each number then the mean of number is ? | ( x + x 1 + . . . x 14 ) / 15 = 40 54 option a | a ) 54 , b ) 45 , c ) 65 , d ) 78 , e ) 64 | a | add(40, 14) | add(n1,n2) | general |
the perimeter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 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 . perimeter of the rectangle = 2 ( 18 + 14 ) = 64 cm perimeter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circumference of the semicircle = 1 / 2 ( β ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 25.14 cm to two decimal places answer : e" | a ) 23.57 , b ) 23.54 , c ) 23.5 , d ) 24.55 , e ) 25.14 | e | floor(divide(circumface(divide(divide(multiply(const_2, add(14, 18)), const_4), const_2)), const_2)) | add(n0,n1)|multiply(#0,const_2)|divide(#1,const_4)|divide(#2,const_2)|circumface(#3)|divide(#4,const_2)|floor(#5)| | geometry |
when 6 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ? | "explanation : let the number be 26 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 6 = a / 30 = > a = 180 answer : b" | a ) 32 , b ) 180 , c ) 60 , d ) 27 , e ) 11 | b | divide(const_3.0, divide(divide(const_1, multiply(const_3, add(const_2, 6))), const_2)) | add(const_2,const_3)|multiply(#0,const_3)|divide(const_1,#1)|divide(#2,const_2)|divide(n0,#3)| | general |
danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 31 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point betwe... | "danny ' s time is 31 minutes . the time to reach halfway is 15.5 minutes . steve ' s time is 62 minutes . the time to reach halfway is 31 minutes . the time difference is 31 - 15.5 = 15.5 minutes the answer is a ." | a ) 15.5 minutes , b ) 31 minutes , c ) 35 minutes , d ) 62 minutes , e ) 93 minutes | a | divide(31, const_2) | divide(n0,const_2)| | physics |
in a group of 140 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ? | "number of people whose age is less than 20 is given by 140 - 90 = 50 probability p that a person selected at random from the group is less than 20 is given by 50 / 140 = 0.35 correct answer a" | a ) 0.35 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85 | a | divide(subtract(140, 90), 140) | subtract(n0,n1)|divide(#0,n0)| | general |
if radius of a circle is reduced by 10 % , then how much % of its area will be reduced ? | let initial radius = a then , area = Ο a ^ 2 . new radius = 90 % of a = 9 a / 10 . new area = Ο * 81 a ^ 2 / 100 = 81 / 100 Ο a ^ 2 reduce in area = [ Ο a ^ 2 - 81 / 100 Ο a ^ 2 ] = 19 / 100 Ο a ^ 2 % reduce = [ ( 19 * Ο a ^ 2 / 100 ) * ( 1 * 100 / Ο a ^ 2 ) ] % = 19 % answer b | ['a ) 10 %', 'b ) 19 %', 'c ) 20 %', 'd ) 36 %', 'e ) 30 %'] | b | multiply(subtract(const_1, power(divide(subtract(const_100, 10), const_100), const_2)), const_100) | subtract(const_100,n0)|divide(#0,const_100)|power(#1,const_2)|subtract(const_1,#2)|multiply(#3,const_100) | geometry |
a rope of which a calf is tied is increased from 12 m to 21 m , how much additional grassy ground shall it graze ? | "Ο ( 212 β 122 ) = 933.4 answer : a" | a ) 933.4 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 1312 | a | multiply(subtract(power(21, const_2), power(const_10, const_2)), divide(add(multiply(12, const_2), const_2), add(const_4, const_3))) | add(const_3,const_4)|multiply(const_10,const_2)|power(n1,const_2)|power(n0,const_2)|add(#1,const_2)|subtract(#2,#3)|divide(#4,#0)|multiply(#6,#5)| | general |
in a school with 640 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is | sol . let the number of grils be x . then , number of boys = ( 640 - x ) . then , ( 11 3 / 4 Γ 640 ) β 11 x + 12 ( 640 - x ) β x = 7680 - 7520 β 160 . answer a | a ) 160 , b ) 200 , c ) 250 , d ) 350 , e ) none | a | subtract(multiply(12, 640), multiply(add(11, divide(9, 12)), 640)) | divide(n4,n1)|multiply(n0,n1)|add(n2,#0)|multiply(n0,#2)|subtract(#1,#3) | general |
if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 33 , what is the value of x ? | "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 33 x = 31 correct option : b" | a ) 30 , b ) 31 , c ) 32 , d ) 32 , e ) 37 | b | subtract(multiply(4, const_2), multiply(2, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general |
two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 4 days ? | "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 4 days = 4 ( 1 / 18 ) = 2 / 9 . answer e" | a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 9 | e | multiply(4, add(divide(const_1, 30), divide(const_1, 45))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)| | physics |
30 pens and 75 pencils were purchased for 690 . if the average price of a pencil was 2.00 , find the average price of a pen . | "since average price of a pencil = 2 β΄ price of 75 pencils = 150 β΄ price of 30 pens = ( 690 β 150 ) = 540 β΄ average price of a pen = 540 β 60 = 18 answer c" | a ) 10 , b ) 11 , c ) 18 , d ) 13 , e ) 14 | c | divide(subtract(690, multiply(75, 2.00)), 30) | multiply(n1,n3)|subtract(n2,#0)|divide(#1,n0)| | general |
if the price of a tv is first decreased by 20 % and then increased by 45 % , then the net change in the price will be : | "explanation : solution : let the original price be rs . 100 . new final price = 145 % of ( 80 % of 100 ) = rs . 145 / 100 * 80 / 100 * 100 = rs . 116 . . ' . increase = 16 % answer : d" | a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 16 % increase , e ) none of these | d | subtract(divide(multiply(subtract(const_100, 20), add(const_100, 45)), const_100), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(#3,const_100)| | general |
two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team e . if team a ' s average speed was 5 mph greater than team e ' s , what was team e ' s average mph ? | this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of que... | a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25 | d | divide(divide(300, 5), 3) | divide(n0,n2)|divide(#0,n1) | physics |
what is the square root of 4,624 ? | "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 68 * 68 = 4,624 4624 divided by x = 68 x = 68 ( c ) 68" | a ) a ) 18 , b ) b ) 9 , c ) c ) 68 , d ) d ) 62 , e ) e ) 81 | c | circle_area(divide(4,624, multiply(const_2, const_pi))) | multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)| | other |
a and b can do a piece of work in 40 days and 50 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ? | "explanation : ( a + b ) β s 10 days work = 10 [ 1 / 40 + 1 / 50 ] = 10 [ 5 + 4 / 200 ] = 9 / 20 a complete remaining work in 9 / 20 * 40 = 18 total work = 10 + 18 = 28 days answer : option a" | a ) 28 days , b ) 60 days , c ) 20 days , d ) 30 days , e ) 40 days | a | divide(subtract(10, add(divide(10, 50), divide(10, 40))), divide(10, 50)) | divide(n2,n1)|divide(n2,n0)|add(#0,#1)|subtract(n2,#2)|divide(#3,#0)| | physics |
sahil purchased a machine at rs 13000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it . | explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 13000 + 5000 + 1000 = 19000 150 % of 19000 = 150 / 100 * 19000 = 28500 option d | a ) rs . 22000 , b ) rs . 24500 , c ) rs . 26500 , d ) rs . 28500 , e ) none of these | d | add(add(add(13000, 5000), 1000), multiply(divide(add(add(13000, 5000), 1000), const_100), 50)) | add(n0,n1)|add(n2,#0)|divide(#1,const_100)|multiply(n3,#2)|add(#1,#3) | gain |
the area of a square field is a square feet and the perimeter is p feet . if 6 a = 6 ( 2 p + 9 ) , what is the perimeter of the field , in feet ? ( here a = a ^ 2 ) | you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with d you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 6 a = 6 ( 2 p + 9 )... | ['a ) 28', 'b ) 36', 'c ) 40', 'd ) 56', 'e ) 84'] | b | multiply(const_4, 9) | multiply(n3,const_4) | geometry |
how many numbers from 10 to 43 are exactly divisible by 3 ? | "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 . 11 numbers . 10 / 3 = 3 and 43 / 3 = 14 = = > 14 - 3 = 11 . therefore 11 digits b )" | a ) 13 , b ) 11 , c ) 16 , d ) 17 , e ) 18 | b | add(divide(subtract(multiply(floor(divide(43, 3)), 3), multiply(add(floor(divide(10, 3)), const_1), 3)), 3), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | general |
working together , printer a and printer b would finish the task in 30 minutes . printer a alone would finish the task in 50 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ? | "30 * a + 30 * b = x pages in 30 mins printer a will print = 30 / 50 * x pages = 3 / 5 * x pages thus in 30 mins printer printer b will print x - 3 / 5 * x = 2 / 5 * x pages also it is given that printer b prints 3 more pages per min that printer a . in 30 mins printer b will print 90 more pages than printer a thus 3 /... | a ) 200 , b ) 400 , c ) 600 , d ) 800 , e ) 900 | b | multiply(divide(3, subtract(divide(const_60.0, 30), const_1)), const_60) | divide(n1,n0)|subtract(#0,const_1)|divide(const_4.0,#1)|multiply(#2,const_60)| | physics |
train speed 36 kph . dist travelled in 3 minutes in meters | 36 kmph = 10 m / sec d = 10 * 180 = 1800 meters answer : c | a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000 | c | multiply(multiply(36, divide(3, const_60)), const_1000) | divide(n1,const_60)|multiply(n0,#0)|multiply(#1,const_1000) | physics |
300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 65 % of the customers t... | "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 65 % = 117 responded as satisfied , so remaining satisfied are 120 - 117 = 3 so 3 is what percentage of 300 - 1 % so the answer should be a" | a ) 1 , b ) 25 , c ) 35 , d ) 45 , e ) 75 | a | multiply(divide(subtract(multiply(divide(40, 100), 300), multiply(divide(65, 100), multiply(300, divide(60, 100)))), 300), 100) | divide(n3,n2)|divide(n4,n2)|divide(n1,n2)|multiply(n0,#0)|multiply(n0,#2)|multiply(#1,#4)|subtract(#3,#5)|divide(#6,n0)|multiply(#7,n2)| | general |
in a company of 148 employees , 92 are females . a total of 78 employees have advanced degrees and the rest have a college degree only . if 31 employees are males with college degree only , how many employees are females with advanced degrees ? | "the number of males is 148 - 92 = 56 . the number of males with advanced degrees is 56 - 31 = 25 . the number of females with advanced degrees is 78 - 25 = 53 . the answer is d ." | a ) 50 , b ) 51 , c ) 52 , d ) 53 , e ) 54 | d | subtract(78, subtract(subtract(148, 92), 31)) | subtract(n0,n1)|subtract(#0,n3)|subtract(n2,#1)| | geometry |
a cycle is bought for rs . 900 and sold for rs . 1260 , find the gain percent ? | "900 - - - - 360 100 - - - - ? = > 40 % answer : c" | a ) 39 % , b ) 20 % , c ) 40 % , d ) 74 % , e ) 83 % | c | multiply(divide(subtract(1260, 900), 900), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a van takes 6 hours to cover a distance of 288 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 distence = 288 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 288 / 9 = 32 kmph c | a ) 50 kmph , b ) 60 kmph , c ) 32 kmph , d ) 80 kmph , e ) 90 kmph | c | divide(288, multiply(divide(3, 2), 6)) | divide(n2,n3)|multiply(n0,#0)|divide(n1,#1) | physics |
a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 30 sec . what is the length of the goods train ? | "speed = 72 * 5 / 18 = 20 m / sec . time = 30 sec . let the length of the train be x meters . then , ( x + 250 ) / 30 = 20 x = 350 m . answer : c" | a ) 299 , b ) 277 , c ) 350 , d ) 270 , e ) 281 | c | subtract(multiply(multiply(divide(72, const_3600), const_1000), 30), 250) | divide(n0,const_3600)|multiply(#0,const_1000)|multiply(n2,#1)|subtract(#2,n1)| | physics |
the ratio of the adjacent angles of a parallelogram is 8 : 10 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ? | "the measures of the adjacent angles of a parallelogram add up to be 180 Β° given so , 8 x + 10 x = 180 Β° or , 18 x = 180 Β° or , x = 10 Β° hence the angles of the parallelogram are 80 Β° and 100 Β° further it is given we know sum of all the four angles of a quadrilateral is 360 Β° so , 5 y + 6 y + 7 y + 12 y = 360 Β° or , 5 ... | a ) 168 Β° , b ) 228 Β° , c ) 156 Β° , d ) 224 Β° , e ) 164 Β° | e | multiply(divide(multiply(add(multiply(multiply(8, const_2), const_10), const_100), const_2), add(add(add(5, 6), 7), 12)), 10) | add(n2,n3)|multiply(const_2,n0)|add(n4,#0)|multiply(#1,const_10)|add(#3,const_100)|add(n5,#2)|multiply(#4,const_2)|divide(#6,#5)|multiply(n1,#7)| | other |
if the price of a certain computer increased 30 percent from d dollars to 364 dollars , then 2 d = | before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 364 ( given ) i . e . d = 364 / 1.3 = $ 280 i . e . 2 d = 2 * 280 = 560 answer : option e | a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 560 | e | multiply(divide(364, divide(add(const_100, 30), const_100)), 2) | add(n0,const_100)|divide(#0,const_100)|divide(n1,#1)|multiply(n2,#2) | general |
find the value of 72518 x 9999 = m ? | "72518 x 9999 = 72518 x ( 10000 - 1 ) = 72518 x 10000 - 72518 x 1 = 725180000 - 72518 = 725107482 e" | a ) 456578972 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 725107482 | e | multiply(subtract(9999, const_4), 72518) | subtract(n1,const_4)|multiply(#0,n0)| | general |
ratio of two numbers x and y is 2 : 5 . if x is increased by 50 % and y is increased by 8 then the new ratio becomes 3 : 10 . what is the ratio 3 y : ( x + 6 ) | "let : x = 2 n y = 5 n 3 n / ( 5 n + 5 ) = 3 / 10 30 n = 3 * ( 5 n + 5 ) n = 1 so , x = 2 ; y = 5 3 y / ( x + 6 ) = 15 / 8 answer = a" | a ) 15 : 8 , b ) 8 : 15 , c ) 2 : 5 , d ) 5 : 2 , e ) 13 : 6 | a | divide(multiply(3, multiply(divide(8, subtract(multiply(divide(add(const_100, 50), const_100), 10), divide(5, 2))), divide(5, 2))), add(divide(8, subtract(multiply(divide(add(const_100, 50), const_100), 10), divide(5, 2))), 6)) | add(n2,const_100)|divide(n1,n0)|divide(#0,const_100)|multiply(n5,#2)|subtract(#3,#1)|divide(n3,#4)|add(n7,#5)|multiply(#5,#1)|multiply(#7,n6)|divide(#8,#6)| | general |
the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnut purchased if you paid $ 19 ? | "a is the number of dozen of doughnuts at a price of $ 6 / dozen 1 + 6 a = 19 a = 3 the total number of doughnuts purchased - - > 1 + 3 * 12 = 37 answer : e" | a ) 24 , b ) 25 , c ) 35 , d ) 36 , e ) 37 | e | multiply(divide(19, 6), const_12) | divide(n2,n1)|multiply(#0,const_12)| | general |
factory x ' s bulbs work for over 4000 hours in 59 % of cases , whereas factory y ' s bulbs work for over 4000 hours in 65 % of cases . it is known that factory x supplies 60 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 4000 hours ? | "for x , 60 % of 59 % will work . for y , 40 % of 65 % will work . * 40 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.60 ( 0.59 ) = . 354 0.40 ( 0.65 ) = 0.26 the combined probability then is 35.4 + 26.00 = 61.4 % ans b" | a ) 66.4 % , b ) 61.4 % , c ) 77.4 % , d ) 65 % , e ) 53.9 % | b | divide(add(59, 65), const_2) | add(n1,n3)|divide(#0,const_2)| | physics |
walking 6 / 7 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ? | speed ratio = 1 : 6 / 7 = 7 : 6 time ratio = 6 : 4 1 - - - - - - - - 6 4 - - - - - - - - - ? = > 24 m answer : e | a ) 28 m , b ) 20 m , c ) 22 m , d ) 23 m , e ) 24 m | e | multiply(4, 6) | multiply(n0,n2) | gain |
if 6 a = 7 b = 20 , then 84 ab = | "6 a * 7 b = 20 * 20 = 400 42 ab = 400 i . e . 84 ab = 800 answer : option d" | a ) 50 , b ) 100 , c ) 625 , d ) 800 , e ) 1250 | d | multiply(84, multiply(divide(20, 6), divide(20, 7))) | divide(n2,n0)|divide(n2,n1)|multiply(#0,#1)|multiply(n3,#2)| | general |
a 180 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ? | "s = 180 / 6 * 18 / 5 = 108 kmph answerb" | a ) 109 , b ) 108 , c ) 109 , d ) 106 , e ) 101 | b | multiply(divide(180, 6), const_3_6) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
a is twice efficient as b and together they do the same work in as much time as c and d together . if c and d can complete the work in 20 and 30 daysrespectively , working alone , then in how many days a can complete the work individually : | explanation : a + b = c + d | | | | ratio of efficiency 10 x + 5 x 9 x + 6 x | ________| | _________| 15 x 15 x therefore , ratio of efficiency of a : c = 10 : 9 therefore , ratio of days taken by a : c = 9 : 10 therefore , number of days taken by a = 18 days answer : b | a ) 12 days , b ) 18 days , c ) 24 days , d ) 30 days , e ) none of these | b | multiply(divide(subtract(subtract(30, 20), const_1), subtract(30, 20)), 20) | subtract(n1,n0)|subtract(#0,const_1)|divide(#1,#0)|multiply(n0,#2) | physics |
a $ 500 investment and a $ 1,500 investment have a combined yearly return of 19 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ? | "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 19 ) = ( 500 Γ’ Λ β 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 23 % ( option c ) answer : c" | a ) 9 % , b ) 10 % , c ) 23 % , d ) 21 % , e ) 22 % | c | multiply(divide(subtract(multiply(add(500, multiply(const_3, 500)), divide(19, const_100)), multiply(500, divide(7, const_100))), multiply(const_3, 500)), const_100) | divide(n2,const_100)|divide(n4,const_100)|multiply(n0,const_3)|add(n0,#2)|multiply(n0,#1)|multiply(#3,#0)|subtract(#5,#4)|divide(#6,#2)|multiply(#7,const_100)| | gain |
it is well known that a triangle β s area is β ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , such that a , b , c are the lengths of sides of the triangle . if the triangle has 300 , 300 , and 300 as the side β s lengths , what is the triangle β s area ? | it is well known that a triangle β s area is β ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , - > p = ( 300 + 300 + 300 ) / 2 = 450 , area = β ( 450 ( 450 - 300 ) ( 450 - 300 ) ( 450 - 300 ) ) = 38,971 . therefore , the answer is e . | a ) 34,200 , b ) 36,200 , c ) 38,200 , d ) 42,200 , e ) 38,971 | e | divide(sqrt(multiply(multiply(multiply(subtract(divide(add(add(300, 300), 300), 2), 300), subtract(divide(add(add(300, 300), 300), 2), 300)), subtract(divide(add(add(300, 300), 300), 2), 300)), divide(add(add(300, 300), 300), 2))), const_1000) | add(n1,n1)|add(n1,#0)|divide(#1,n0)|subtract(#2,n1)|multiply(#3,#3)|multiply(#4,#3)|multiply(#2,#5)|sqrt(#6)|divide(#7,const_1000) | general |
in the fifth grade at parkway elementary school there are 450 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? | "total students = 450 boys = 320 , girls = 130 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 130 - 35 = 95 . correct option : d" | a ) 69 . , b ) 73 . , c ) 81 . , d ) 95 . , e ) 108 . | d | subtract(subtract(450, 320), subtract(250, divide(multiply(250, 86), const_100))) | multiply(n2,n3)|subtract(n0,n1)|divide(#0,const_100)|subtract(n2,#2)|subtract(#1,#3)| | gain |
excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ? | "explanation : t = 16 / 48 * 60 = 20 answer : option c" | a ) a ) 40 , b ) b ) 30 , c ) c ) 20 , d ) d ) 10 , e ) e ) 5 | c | subtract(const_60, multiply(const_60, divide(32, 48))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | physics |
at a kennel with 80 dogs , 45 of the dogs wear tags and 40 wear flea collars . if 6 of the dogs wear both , then how many of the dogs wear neither a collar nor tags ? | dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 ) dogs wear neither a collar nor tags = 80 - 79 dogs wear neither a collar nor tags = 80 - 79 hence , answer will be 1 answer : a | a ) 1 , b ) 6 , c ) 34 , d ) 79 , e ) 85 | a | subtract(80, subtract(add(45, 40), 6)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1) | other |
the ratio 9 : 5 expressed as a percent equals | "solution 9 : 5 = 9 / 5 = ( 9 / 5 x 100 ) % . = 180 % . answer c" | a ) 12.5 % , b ) 40 % , c ) 180 % , d ) 125 % , e ) none | c | multiply(divide(9, 5), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
the sum of all two digit numbers divisible by 7 is | "required numbers are 14 , 21,28 . . . . . 98 this is an a . p . in which a = 14 , d = 7 and l = 98 . let the number of terms in it be n . then t = 98 so a + ( n - 1 ) d = 98 . 14 + ( n - 1 ) * 7 = 98 , 14 + 7 n - 7 = 98 7 + 7 n = 98 7 n = 98 - 7 n = 91 / 7 then n = 13 . required sum = n / 2 ( a + l ) = 13 / 2 ( 14 + 9... | a ) 910 , b ) 510 , c ) 728 , d ) 628 , e ) 810 | c | multiply(divide(divide(subtract(multiply(7, add(const_10, const_1)), multiply(const_1, 7)), subtract(multiply(7, const_2), multiply(const_1, 7))), const_2), add(multiply(7, const_2), multiply(7, add(const_10, const_1)))) | add(const_1,const_10)|multiply(n0,const_2)|multiply(n0,const_1)|multiply(n0,#0)|subtract(#1,#2)|add(#1,#3)|subtract(#3,#2)|divide(#6,#4)|divide(#7,const_2)|multiply(#5,#8)| | general |
a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 115 . find the divisor ? | "easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 115 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 367 d * some integer = 367 checking all options only ( d ) syncs with it . answer d" | a ) 370 , b ) 365 , c ) 380 , d ) 367 , e ) 460 | d | subtract(multiply(241, const_2), 115) | multiply(n0,const_2)|subtract(#0,n1)| | general |
find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 65 = x ? | e ) 5 | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | floor(add(reminder(add(subtract(multiply(divide(47, const_100), 1442), multiply(divide(36, const_100), 1412)), 65), const_10), const_1)) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n3,#1)|subtract(#2,#3)|add(n4,#4)|reminder(#5,const_10)|add(#6,const_1)|floor(#7) | general |
the edges of three metal cubes are 1 cm , 2 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ? | "the total volume is 1 ^ 3 + 2 ^ 3 + 4 ^ 3 = 73 the edge of the new cube is the cube root of 73 which is about 4.2 cm . the answer is b ." | a ) 3.8 , b ) 4.2 , c ) 4.6 , d ) 5.0 , e ) 5.4 | b | power(add(power(4, 2), add(1, power(2, const_3))), const_0_33) | power(n1,n1)|power(n2,const_3)|add(n0,#0)|add(#2,#1)|power(#3,const_0_33)| | physics |
every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that... | "` ` dog ' ' = ( 4 + 15 + 7 ) * 3 = 78 . the answer is c ." | a ) 72 , b ) 75 , c ) 78 , d ) 81 , e ) 84 | c | multiply(add(add(subtract(multiply(2, const_10), 2), 1), multiply(2, const_10)), 3) | multiply(n1,const_10)|subtract(#0,n1)|add(n0,#1)|add(#2,#0)|multiply(n2,#3)| | general |
the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 21 . what is the last numbers ? | "a + b + c = 18 b + c + d = 15 a + d = 21 a β d = 3 a + d = 21 2 d = 18 d = 9 answer : e" | a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9 | e | subtract(subtract(multiply(3, 6), add(subtract(21, 6), 3)), 6) | multiply(n1,n3)|subtract(n6,n3)|add(n1,#1)|subtract(#0,#2)|subtract(#3,n3)| | general |
15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours . then how many sugar cubes of 5 grams each , will 20 ants move in 3 hours ? | d 15 ants move 600 / 5 = 120 sugar cubes of 10 grams in 1 hour . 5 grams sugar cubes will take less time to move . thus if weight of the sugar cube is 5 grams , 15 ants will move 120 x 10 / 5 = 240 sugar cubes in 1 hour . more ants , more sugar cubes they can move . 20 ants will move 240 x 20 / 15 = 320 sugar cubes in ... | ['a ) 360', 'b ) 480', 'c ) 720', 'd ) 960', 'e ) 1000'] | d | divide(multiply(multiply(divide(divide(multiply(600, 10), 5), 15), 20), 3), 5) | multiply(n1,n2)|divide(#0,n3)|divide(#1,n0)|multiply(n5,#2)|multiply(n6,#3)|divide(#4,n3) | physics |
find the sum the difference between the compound and s . i . on a certain sum of money for 6 years at 10 % per annum is rs . 80 of money ? | "p = 80 ( 100 / 10 ) 6 = > p = 1500 answer : c" | a ) 1000 , b ) 1200 , c ) 4800 , d ) 3600 , e ) 8400 | c | multiply(multiply(divide(80, multiply(10, 6)), const_100), multiply(10, 6)) | multiply(n0,n1)|divide(n2,#0)|multiply(#1,const_100)|multiply(#2,#0)| | general |
a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 4 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes... | "the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 4 dollars - - > the profit from one mango = 1 / 4 - 1 / 5 = 1 / 20 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 5 - 1 / 6 = 1 / 30 dollars . the profit... | a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 5 | d | divide(subtract(divide(const_1, 4), divide(const_1, 5)), subtract(divide(const_1, 5), divide(const_1, multiply(const_2, const_4)))) | divide(const_1,n1)|divide(const_1,n0)|multiply(const_2,const_4)|divide(const_1,#2)|subtract(#0,#1)|subtract(#1,#3)|divide(#4,#5)| | other |
what is the positive difference between the sum of the squares of the first 6 positive integers and the sum of the prime numbers between the first square and fourth square ? | forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 + 6 ^ 2 = 91 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = ... | a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 50 | e | subtract(add(add(add(add(add(const_1, power(const_2, const_2)), power(const_3, const_2)), power(const_4, const_2)), power(add(const_4, const_1), const_2)), power(6, const_2)), add(add(add(const_4, const_3), 6), add(add(add(add(const_2, const_3), add(const_4, const_1)), add(const_4, const_3)), add(add(const_2, const_3),... | add(const_1,const_4)|add(const_3,const_4)|add(const_2,const_3)|power(const_2,const_2)|power(const_3,const_2)|power(const_4,const_2)|power(n0,const_2)|add(#3,const_1)|add(n0,#1)|add(#2,#0)|add(n0,#2)|power(#0,const_2)|add(#7,#4)|add(#9,#1)|add(#12,#5)|add(#13,#10)|add(#14,#11)|add(#8,#15)|add(#16,#6)|subtract(#18,#17) | general |
john makes $ 60 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ? | "increase = ( 20 / 60 ) * 100 = ( 2 / 6 ) * 100 = 33.33 % . b" | a ) 16 % , b ) 33.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 % | b | multiply(divide(subtract(80, 60), 60), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
find the area of a parallelogram with base 28 cm and height 32 cm . | "area of a parallelogram = base * height = 28 * 32 = 896 cm 2 answer : option e" | a ) 200 , b ) 384 , c ) 345 , d ) 244 , e ) 896 | e | multiply(28, 32) | multiply(n0,n1)| | geometry |
a can complete a work in 18 days and b can do the same work in 10 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ? | "the required answer = ( 18 - 3 ) * 5 / 18 = 150 / 18 = 8 days answer is b" | a ) 2 days , b ) 8 days , c ) 6 days , d ) 7 days , e ) 10 days | b | add(multiply(18, const_2.0), divide(18, 3)) | divide(n0,const_2.0)|multiply(n0,n2)|add(#0,#1)| | physics |
what is the range of all the roots of | x ^ 2 - 5 | = x ? | "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 5 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 5 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 5 or x = 1 i guess range is 5 -... | a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | a | sqrt(5) | sqrt(n1)| | general |
a man can swim in still water at 15 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ? | "m = 15 s = x ds = 15 + x us = 15 - x 15 + x = ( 15 - x ) 2 15 + x = 30 - 2 x 3 x = 15 x = 5 answer : b" | a ) 3.9 , b ) 5 , c ) 5.3 , d ) 1.5 , e ) 5.2 | b | divide(15, const_3) | divide(n0,const_3)| | general |
there are 134 toys coloured red and white in a box . two red toys are removed from the lot and now there are twice as many red ones as white ones . how many of red colour toys are there now ? | r + w = 134 two red toys are removed from the lot and now there are twice red ones as white ones r - 2 = 2 w sub 1 st one we get 134 - w - 2 = 2 w 132 = 3 w w = 44 r = 88 actually red will be 90 now 88 answer : d | a ) 76 , b ) 86 , c ) 90 , d ) 88 , e ) 78 | d | subtract(divide(add(multiply(134, const_2), const_2), const_3), const_2) | multiply(n0,const_2)|add(#0,const_2)|divide(#1,const_3)|subtract(#2,const_2) | general |
2224 Γ 9997 = ? | "c 22233328 2224 Γ 9997 = 2224 Γ ( 10000 - 3 ) = 2224 Γ 10000 - 2224 Γ 3 = 22240000 - 6672 = 22233328" | a ) 22244428 , b ) 22255538 , c ) 22233328 , d ) 22266628 , e ) 22233327 | c | multiply(divide(2224, 9997), const_100) | divide(n0,n1)|multiply(#0,const_100)| | 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 340 m long platform ? | "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 + 340 ) / 36 * 5 / 18 = 46 min . answer : d" | a ) 19 , b ) 27 , c ) 29 , d ) 46 , e ) 28 | d | divide(add(340, 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 |
a shopkeeper sells 20 % of his stock at 20 % profit ans sells the remaining at a loss of 10 % . he incurred an overall loss of rs . 500 . find the total worth of the stock ? | "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 6 / 5 = 6 x / 25 the sp of 80 % of the stock = 4 / 5 * x * 0.9 = 24 x / 25 total sp = 6 x / 25 + 18 x / 25 = 49 x / 50 overall loss = x - 24 x / 50 = x / 25 x / 25 = 500 = > x = 12500 answer : c" | a ) 13500 , b ) 12000 , c ) 12500 , d ) 15000 , e ) 15500 | c | divide(500, subtract(multiply(divide(10, const_100), divide(subtract(const_100, 20), const_100)), multiply(divide(20, const_100), divide(20, const_100)))) | divide(n2,const_100)|divide(n1,const_100)|divide(n0,const_100)|subtract(const_100,n0)|divide(#3,const_100)|multiply(#1,#2)|multiply(#0,#4)|subtract(#6,#5)|divide(n3,#7)| | gain |
triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ? | "ans a . . 10 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 25 or yz = 5 * \ sqrt { 2 } . . therefore hyp = xy = 10" | a ) 10 , b ) 4 β 2 , c ) 8 , d ) 8 β 2 , e ) can not be determined from the information provided | a | sqrt(add(power(multiply(sqrt(25), sqrt(const_2)), const_2), power(multiply(sqrt(25), sqrt(const_2)), const_2))) | sqrt(n0)|sqrt(const_2)|multiply(#0,#1)|power(#2,const_2)|add(#3,#3)|sqrt(#4)| | geometry |
a pharmaceutical company received $ 2 million in royalties on the first $ 12 ; million in sales of generic equivalent of one of its products and then $ 4 million in royalties on the next $ 48 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 12 million in sal... | change in ratio of royalties to sales = 2 / 12 - 4 / 48 = 1 / 12 % decrease = ( 1 / 12 ) / ( 2 / 12 ) * 100 = 50 % ( approx ) answer : d ) | a ) 20 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 55 % | d | multiply(divide(subtract(divide(2, 12), divide(4, 48)), divide(2, 12)), const_100) | divide(n0,n1)|divide(n2,n3)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100) | general |
an ore contains 25 % of an alloy that has 90 % iron . other than this , in remaining 75 % of the ore , there is no iron . how many kgs of the ore are needed to obtain 60 kg . of pure iron . ? | "explanation : let us take 100 x kgs of ore . now it contains 25 x kgs of alloy and it contains 90 % ( 25 x ) kgs of iron . 90 % ( 25 x ) = 60 kg β x = 60 Γ 10090 Γ 12560 Γ 10090 Γ 125 = 8383 so iron ore required = 100 Γ 8383 = 266.66 answer : d" | a ) 266.69 , b ) 266.67 , c ) 266.66 , d ) 263.66 , e ) 266.61 | d | divide(multiply(const_100, 60), divide(multiply(25, 90), const_100)) | multiply(n3,const_100)|multiply(n0,n1)|divide(#1,const_100)|divide(#0,#2)| | gain |
what is 15 % of 2 / 3 of 0.4 ? | "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 4 / 10 ) = 120 / 3000 = 0.04 option a" | a ) 0.09 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above | a | divide(multiply(15, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)| | gain |
the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 43 degrees . find the temperature on friday ? | m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 43 tu + w + th = 192 - 43 = 149 f = 184 β 149 = 35 answer : d | a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 35 degrees , e ) 74 degrees | d | subtract(43, subtract(multiply(48, const_4), multiply(46, const_4))) | multiply(n0,const_4)|multiply(n1,const_4)|subtract(#0,#1)|subtract(n2,#2) | general |
what is the probability that the sum of two dice will yield a 4 , and then when both are thrown again , their sum will again yield a 4 ? assume that each die has 3 sides with faces numbered 1 to 3 . | "solution - rolling dices is an independent event . the combinations to get 4 are ( 1,3 ) , ( 3,1 ) , ( 2,2 ) , and total combinations of both dices is 9 . the probability of getting 4 in first attempt is 3 / 9 = 1 / 3 . probability of getting 4 again in second attempt = ( 1 / 3 ) * ( 1 / 3 ) = 1 / 9 . ans c" | a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3 | c | multiply(divide(3, power(3, const_2)), divide(3, power(3, const_2))) | power(n2,const_2)|divide(n2,#0)|multiply(#1,#1)| | probability |
in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ? | "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 232 = 31 greatest - smallest is 144 - 31 = 113 so answer must... | a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31 | c | subtract(119, subtract(add(144, 119), 232)) | add(n1,n2)|subtract(#0,n0)|subtract(n2,#1)| | other |
albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born . what is the difference between the ages of her parents ? | mother ' s age when albert ' s brother was born = 46 years father ' s age when albert ' s brother was born = 48 + 2 = 50 years required difference = 50 - 46 = 4 years answer is b | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | b | subtract(add(add(const_2, const_3), const_4), add(const_2, const_3)) | add(const_2,const_3)|add(#0,const_4)|subtract(#1,#0) | general |
what was the principal , if at 12 % per annum the interest after 3 years amounted to rs . 5888 less than the sum lent ? | p - 2336 = ( p * 12 * 3 ) / 100 p = 9200 answer : e | a ) 9000 , b ) 3000 , c ) 5000 , d ) 1300 , e ) 9200 | e | divide(5888, subtract(const_1, divide(multiply(12, 3), const_100))) | multiply(n0,n1)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2) | gain |
what is the 14 th digit to the right of the decimal point in the decimal equivalent of 82 / 11 ? | "82 / 11 = 7.4545 . . . . 45 is non - repeating terminating decimal . the 14 th digit to the right of decimal point will be 5 . answer d" | a ) 4 , b ) 3 , c ) 1 , d ) 5 , e ) 7 | d | divide(82, 11) | divide(n1,n2)| | general |
on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 14 more transactions than cal . how much transactions did jade handled ? | "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 Γ 10 % = 90 + 90 Γ 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 Γ 99 = 66 jade handled 14 more transactions than cal . jade = 66 + 14 = 80 jade handled = 80 tran... | a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84 | a | add(divide(multiply(multiply(divide(90, const_100), add(10, const_100)), 2), 3), 14) | add(n1,const_100)|divide(n0,const_100)|multiply(#0,#1)|multiply(n2,#2)|divide(#3,n3)|add(n4,#4)| | general |
two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 12 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ? | "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 15 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 2 + 7 / 2 = 11 litres as 16 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 11 : 5 answer : d" | a ) 19 : 2 , b ) 18 : 3 , c ) 11 : 1 , d ) 11 : 5 , e ) 11 : 4 | d | divide(add(divide(multiply(62.5, 12), const_100), divide(multiply(87.5, 4), const_100)), add(subtract(12, divide(multiply(62.5, 12), const_100)), subtract(4, divide(multiply(87.5, 4), const_100)))) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,const_100)|divide(#1,const_100)|add(#2,#3)|subtract(n2,#2)|subtract(n3,#3)|add(#5,#6)|divide(#4,#7)| | other |
two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.9 km and 2.1 km respectively . the time taken by the slower train to cross the faster train in seconds is ? | "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.9 + 2.1 = 4 km = 4000 m . required time = 4000 * 3 / 125 = 96 sec . answer : d" | a ) 99 , b ) 277 , c ) 48 , d ) 96 , e ) 22 | d | subtract(divide(multiply(1.9, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(2.1, const_1000), divide(multiply(90, const_1000), const_3600))) | multiply(n2,const_1000)|multiply(n0,const_1000)|multiply(n3,const_1000)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#3,const_3600)|divide(#0,#4)|divide(#2,#5)|subtract(#6,#7)| | physics |
on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orang... | "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is ... | a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45 | d | divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2)) | add(const_1,const_1)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)| | general |
two numbers are in the ratio of 2 : 3 . if 4 is added in both numbers the ratio becomes 5 : 7 . find the difference between numbers . | we ' re told that two numbers are in the ratio of 2 : 3 . thus , the two numbers could be . . . 2 and 3 4 and 6 6 and 9 8 and 12 10 and 15 etc . we ' re told that adding 4 to each number changes the ratio of the numbers to 5 : 7 . we ' re asked for the difference between the original numbers . since adding 4 makes the ... | a ) 8 , b ) 6 , c ) 4 , d ) 2 , e ) 10 | a | subtract(multiply(multiply(subtract(multiply(7, 4), multiply(5, 4)), 2), divide(3, 2)), multiply(subtract(multiply(7, 4), multiply(5, 4)), 2)) | divide(n1,n0)|multiply(n2,n4)|multiply(n2,n3)|subtract(#1,#2)|multiply(n0,#3)|multiply(#0,#4)|subtract(#5,#4) | other |
after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6600 . find the actual price of the good . | "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6600 1 = 6600 / 68.4 100 = ( 6600 * 100 ) / 68.4 = rs . 9649 . answer : option d" | a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9649 , e ) s . 9980 | d | divide(multiply(6600, const_100), subtract(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), divide(multiply(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), 5), const_100))) | multiply(n3,const_100)|subtract(const_100,n0)|multiply(n1,#1)|divide(#2,const_100)|subtract(#1,#3)|multiply(n2,#4)|divide(#5,const_100)|subtract(#4,#6)|divide(#0,#7)| | gain |
in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 55 % , and the students on the make - up date had an average score of 95 % , what wa... | "70 % of the class scored 55 % and 30 % of the class scored 95 % . the difference between 55 % and 95 % is 40 % . the average will be 55 % + 0.3 ( 40 % ) = 67 % . the answer is c ." | a ) 60 % , b ) 65 % , c ) 67 % , d ) 70 % , e ) 75 % | c | divide(add(multiply(70, 55), multiply(95, subtract(100, 70))), 100) | multiply(n1,n2)|subtract(n0,n1)|multiply(n3,#1)|add(#0,#2)|divide(#3,n0)| | general |
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