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find the sum lend at c . i . at 5 p . c per annum will amount to rs . 650 in 2 years ? | "explanation : 650 = p ( 21 / 20 ) 2 p = 589.56 answer : d" | a ) 221 , b ) 287 , c ) 400 , d ) 589 , e ) 171 | d | divide(650, power(add(const_1, divide(5, const_100)), 2)) | divide(n0,const_100)|add(#0,const_1)|power(#1,n2)|divide(n1,#2)| | general | allenai/math_qa |
right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 21 more than eliot in his account . how much money does eliot have in his account right now ? | "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 21 + 1.2 e = = > 11 a = 210 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 210 + 12 e = = > e = 210 e" | a ) $ 110 , b ) $ 120 , c ) $ 180 , d ) $ 220 , e ) $ 210 | e | divide(multiply(21, const_100), subtract(multiply(add(12, 1), 10), add(const_100, 20))) | add(n0,n1)|add(n3,const_100)|multiply(n4,const_100)|multiply(#0,n2)|subtract(#3,#1)|divide(#2,#4)| | general | allenai/math_qa |
p and q invested in a shop . the profits were divided in the ratio of 5 : 2 respectively . if p invested rs . 5600 , the amount invested by q is : | suppose q invested rs . y . then , 5600 / y = 5 / 2 or y = [ 5600 x 2 / 5 ] = 2240 answer e | a ) 3500 , b ) 5600 , c ) 2200 , d ) 2400 , e ) none | e | multiply(divide(5600, 5), 2) | divide(n2,n0)|multiply(n1,#0) | gain | allenai/math_qa |
find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 5 as quotient and the 4 as remainder | "let the smaller number be x . then larger number = ( x + 1200 ) . x + 1200 = 5 x + 4 4 x = 1196 x = 299 large number = 299 + 1200 = 1499 e" | a ) 1234 , b ) 1345 , c ) 1456 , d ) 1567 , e ) 1499 | e | multiply(divide(subtract(1200, 4), subtract(5, const_1)), 5) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general | allenai/math_qa |
if there are 200 questions in a 3 hr examination . among these questions are 25 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ? | "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 175 x + 25 * 2 x = 180 x = 180 / 225 x = 0.8 time taken for type a problem = 25 * 2 * 0.8 = 40 min answer : a" | a ) 40 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 76 min | a | multiply(multiply(const_2, divide(multiply(3, const_60), add(subtract(200, 25), multiply(const_2, 25)))), 25) | multiply(n1,const_60)|multiply(n2,const_2)|subtract(n0,n2)|add(#1,#2)|divide(#0,#3)|multiply(#4,const_2)|multiply(n2,#5)| | general | allenai/math_qa |
how many positive integers between 100 and 500 are there such that they are multiples of 19 ? | multiples of 19 = 114 , 133,152 , - - - - - , 494 number of multiples of 19 = > 494 - 114 / 19 + 1 = 21 answer is c | a ) 10 , b ) 15 , c ) 21 , d ) 18 , e ) 19 | c | divide(subtract(500, 100), 19) | subtract(n1,n0)|divide(#0,n2) | general | allenai/math_qa |
rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 6 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ? | "for 100 - 40 - 10 = 50 pages only cost is 10 $ per page for the first time page is typed - 50 * 10 = 500 $ ; for 40 pages the cost is : first time 5 $ + 6 $ of the first revision - 40 * ( 5 + 6 ) = 440 $ ; for 10 pages the cost is : first time 5 $ + 6 $ of the first revision + 6 $ of the second revision - 10 ( 5 + 6 + 6 ) = 170 $ ; total : 500 + 440 + 170 = 1110 $ . answer : d ." | a ) $ 430 , b ) $ 1620 , c ) $ 1650 , d ) $ 1110 , e ) $ 1770 | d | add(add(multiply(100, 10), multiply(40, const_4.0)), multiply(multiply(10, 6), const_2)) | multiply(n0,n2)|multiply(const_4.0,n3)|multiply(n1,n4)|add(#0,#1)|multiply(#2,const_2)|add(#3,#4)| | general | allenai/math_qa |
the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1250 resolutions ? | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1250 resolutions . = 1250 * 2 * 22 / 7 * 22.4 = 176000 cm = 1760 m answer : b" | a ) 1277 m , b ) 1760 m , c ) 1278 m , d ) 1288 m , e ) 1378 v | b | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 1250), const_100) | add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)| | physics | allenai/math_qa |
the speed of boat in still water is 20 km / hr . if it travels 26 km downstream and 14 km upstream in same time , what is the speed of the stream ? | explanation : let x be speed of stream speed of boat downstream = ( 20 + x ) speed of boat upstream = ( 20 – x ) it is given that boat takes same time to travel 26 km downstream and 14 km upstream [ 26 / ( 20 + x ) ] = [ 14 / ( 20 – x ) ] 520 – 26 x = 280 + 14 x 40 x = 240 x = 6 km / hr answer : a | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2 | a | divide(subtract(multiply(20, 26), multiply(20, 14)), add(26, 14)) | add(n1,n2)|multiply(n0,n1)|multiply(n0,n2)|subtract(#1,#2)|divide(#3,#0) | physics | allenai/math_qa |
a pipe takes a hours to fill the tank . but because of a leakage it took 3 times of its original time . find the time taken by the leakage to empty the tank | "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 180 x = 90 min answer : c" | a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min | c | multiply(const_10, multiply(const_1, 3)) | multiply(n0,const_1)|multiply(#0,const_10)| | physics | allenai/math_qa |
what is the maximum number of pieces of birthday cake of size 4 ” by 4 ” that can be cut from a cake 16 ” by 16 ” ? | "the prompt is essentially asking for the maximum number of 4 x 4 squares that can be cut from a larger 16 by 16 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 4 ' pieces ' each , we have ( 4 ) ( 4 ) = 16 total smaller squares ( at maximum ) . c" | a ) 5 , b ) 4 , c ) 16 , d ) 20 , e ) 25 | c | divide(multiply(16, 16), multiply(4, 4)) | multiply(n2,n2)|multiply(n0,n0)|divide(#0,#1)| | physics | allenai/math_qa |
the speed of a car is 80 km in the first hour and 60 km in the second hour . what is the average speed of the car ? | "s = ( 80 + 60 ) / 2 = 70 kmph answer : b" | a ) 76 kmph , b ) 70 kmph , c ) 87 kmph , d ) 56 kmph , e ) 86 kmph | b | divide(add(80, 60), const_2) | add(n0,n1)|divide(#0,const_2)| | physics | allenai/math_qa |
how many different 3 - digit multiples of 5 can be composed of digits 1 , 2 , 3 , 4 , and 5 if none of the digits is repeated ? | can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 4 possible choices . x can be any of the 3 possible choices . 4 + 3 + 1 = 8 c | a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 18 | c | subtract(multiply(4, 3), 4) | multiply(n0,n5)|subtract(#0,n5) | general | allenai/math_qa |
when 242 is divided by a certain divisor the remainder obtained is 11 . when 698 is divided by the same divisor the remainder obtained is 18 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 9 . what is the value of the divisor ? | "let that divisor be x since remainder is 11 or 18 it means divisor is greater than 18 . now 242 - 11 = 231 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 18 = 680 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 231 + 680 ) + 11 + 18 = x ( k + l ) + 29 when we divide this number by x then remainder will be equal to remainder of ( 29 divided by x ) = 9 hence x = 29 - 9 = 20 hence d" | a ) 11 , b ) 17 , c ) 13 , d ) 20 , e ) none of these | d | subtract(add(11, 18), 9) | add(n1,n3)|subtract(#0,n6)| | general | allenai/math_qa |
850 - ( 1500 ÷ ? ) × 8 / 15 = 770 | "explanation : = > 850 - ( 1500 ÷ ? ) × 8 / 15 = 770 = > 850 - 770 = ( 1500 ÷ ? ) × 8 / 15 = > 80 = ( 1500 ÷ ? ) × 8 / 15 = > 80 × 15 / 8 = ( 1500 ÷ ? ) = 150 = > 1 / ? = 150 / 1500 = 1 / 10 = > ? = 10 answer : option b" | a ) a ) 31 , b ) b ) 10 , c ) c ) 15 , d ) d ) 26 , e ) e ) 17 | b | subtract(850, divide(1500, 8)) | divide(n1,n2)|subtract(n0,#0)| | general | allenai/math_qa |
in the first 5 overs of a cricket game , the run rate was only 2.1 . what should be the rate in the remaining 30 overs to reach the target of 200 runs ? | "required run rate = [ 200 - ( 2.1 * 5 ) ] / 30 = 189.50 / 30 = 6.31 answer : c" | a ) 6.25 , b ) 6.28 , c ) 6.31 , d ) 6.19 , e ) 6.21 | c | divide(subtract(200, multiply(5, 2.1)), 30) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain | allenai/math_qa |
praveen starts business with rs . 3220 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ? | "let hari ’ s capital be rs . x . then , 3220 * 12 / 7 x = 2 / 3 = > 14 x = 115920 = > x = 8280 . answer : c" | a ) s . 7500 , b ) s . 8000 , c ) s . 8280 , d ) s . 9000 , e ) s . 6000 | c | divide(divide(3220, subtract(const_1, divide(5, const_12))), divide(2, 3)) | divide(n1,const_12)|divide(n2,n3)|subtract(const_1,#0)|divide(n0,#2)|divide(#3,#1)| | other | allenai/math_qa |
the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 50 per cent . the two reductions together are equal to a single reduction of | "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 50 percent is reduced which means the new price is merely 50 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 1 / 2 ) p = 3 / 8 p is the new price after both deduction which is 37.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 62.5 % of p . so answer is b = 62.5 %" | a ) 45 % , b ) 62.5 % , c ) 35 % , d ) 32.5 % , e ) 30 % | b | subtract(const_100, multiply(divide(subtract(const_100, 50), const_100), subtract(const_100, 25))) | subtract(const_100,n1)|subtract(const_100,n0)|divide(#0,const_100)|multiply(#2,#1)|subtract(const_100,#3)| | general | allenai/math_qa |
a contractor undertakes to do a piece of work in 40 days . he engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time . if he had not engaged the additional men , how many days behind schedule would it be finished ? | explanation : \ inline \ fn _ jvn [ ( 100 \ times 35 ) + ( 200 \ times 5 ) ] men can finish the work in 1 day \ inline \ fn _ jvn \ therefore 4500 men can finish the work in 1 day . 100 men can finish it in \ inline \ fn _ jvn \ frac { 4500 } { 100 } = 45 days . this is 5 days behind schedule answer : b | a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 2 | b | subtract(divide(add(multiply(100, 35), multiply(add(const_2, const_3), multiply(100, const_2))), const_100), 40) | add(const_2,const_3)|multiply(n1,n3)|multiply(n1,const_2)|multiply(#0,#2)|add(#1,#3)|divide(#4,const_100)|subtract(#5,n0) | general | allenai/math_qa |
it takes avery 4 hours to build a brick wall while tom can do it in 2 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ? | "avery takes 4 hours tom takes 2 hours efficiency of avery is 1 / 4 units / hr efficiency of tom is 1 / 2 units / hr combined efficiency of tom and avery is 1 / 4 + 1 / 2 = 3 / 4 units / hr since they worked for 1 hour they completed 3 / 4 units of work and 1 / 4 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 4 / 1 / 2 hours = > 1 / 2 * 60 = 30 minutes . . . answer will be ( c )" | a ) 20 , b ) 40 , c ) 30 , d ) 50 , e ) 60 | c | multiply(divide(subtract(const_1, add(divide(const_1, 4), divide(const_1, 2))), divide(const_1, 2)), const_60) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|subtract(const_1,#2)|divide(#3,#1)|multiply(#4,const_60)| | physics | allenai/math_qa |
what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 6 | "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 2 / 3 their difference is 5 / 6 - 2 / 3 = 1 / 6 option c" | a ) 2 / 5 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these | c | subtract(divide(4, 5), divide(2, 3)) | divide(n3,n5)|divide(n0,n1)|subtract(#0,#1)| | general | allenai/math_qa |
the ratio of length to width of a rectangular showroom window is 3.3 to 2 . if the width of the window is 8 feet , what is the approximate length of the display in feet ? | explanation : letting l be the length of the window , the proportion for the ratio of the length to the width can be expressed in the following equation : 3.3 / 2 = l / 8 26.4 = 2 l 13.2 = l answer : option c | ['a ) 7', 'b ) 11', 'c ) 13', 'd ) 16', 'e ) 26'] | c | multiply(3.3, divide(8, 2)) | divide(n2,n1)|multiply(n0,#0) | other | allenai/math_qa |
in the coordinate plane , points ( x , 1 ) and ( 12 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y = | "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 12 , y ) = ( 12,6 ) - - > x + y = 2 + 6 = 8 . answer : c ." | a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12 | c | multiply(multiply(12, 2), divide(1, 2)) | divide(n0,n3)|multiply(n1,n3)|multiply(#0,#1)| | general | allenai/math_qa |
lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is : | total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a | a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435 | a | multiply(divide(divide(480, divide(60, const_100)), subtract(subtract(subtract(add(add(add(add(add(44000, 44000), 44000), add(44000, 44000)), add(44000, 44000)), 44000), const_3600), const_3600), divide(480, divide(60, const_100)))), const_100) | add(n2,n2)|divide(n0,const_100)|add(n2,#0)|divide(n3,#1)|add(#2,#0)|add(#4,#0)|add(n2,#5)|subtract(#6,const_3600)|subtract(#7,const_3600)|subtract(#8,#3)|divide(#3,#9)|multiply(#10,const_100) | general | allenai/math_qa |
the line y = 5 x / 3 + b goes through the point ( 7 , – 1 ) . what is the value of b ? | “ finding the equation ” procedure . plug ( x , y ) = ( 7 , – 1 ) into this equation : { - 1 } = { { 5 ( 7 ) } / 3 } + b = { 35 / 3 } + b b = { - 35 / 3 } - 1 = { - 35 / 3 } - { 3 / 3 } = - { 38 / 3 } answer = e | a ) 3 , b ) – 5 / 3 , c ) – 7 / 5 , d ) 16 / 3 , e ) – 38 / 3 | e | subtract(negate(1), negate(divide(multiply(5, 7), 3))) | multiply(n0,n2)|negate(n3)|divide(#0,n1)|negate(#2)|subtract(#1,#3) | general | allenai/math_qa |
sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 6 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ? | "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 6 x = 5 / 6 x so if gold card balance is transferred then the rest unspent will be 5 / 6 x - x / 6 = 2 / 3 x so the ans is a" | a ) 2 / 3 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15 | a | subtract(1, add(multiply(inverse(3), inverse(const_2)), inverse(6))) | inverse(n3)|inverse(n1)|inverse(const_2)|multiply(#1,#2)|add(#0,#3)|subtract(n0,#4)| | general | allenai/math_qa |
what number has a 1 : 20 ratio to the number 10 ? | "1 : 20 = x : 10 20 x = 10 ; x = 10 / 20 x = 1 / 2 answer : b" | a ) 10 , b ) 1 / 2 , c ) 2 , d ) 1 / 4 , e ) 20 | b | multiply(10, 1) | multiply(n0,n2)| | other | allenai/math_qa |
in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 5 % . what is population of after 2 year . | "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 5 % so total man = 150 * . 95 = 142.5 women will be = 175 - 142.5 = 32.5 so population after two years = [ 135 ^ 2 + 32.5 ^ 2 ] ^ . 5 = 146.15 = 146 so population after two year = 146 answer : e" | a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 146 | e | power(add(power(multiply(subtract(1, divide(1, 5)), 150), 2), power(subtract(power(add(power(150, 2), power(90, 2)), divide(1, 2)), multiply(subtract(1, divide(1, 5)), 150)), 2)), divide(1, 2)) | divide(n4,n6)|divide(n4,n2)|power(n0,n2)|power(n1,n2)|add(#2,#3)|subtract(n4,#0)|multiply(n0,#5)|power(#4,#1)|power(#6,n2)|subtract(#7,#6)|power(#9,n2)|add(#8,#10)|power(#11,#1)| | general | allenai/math_qa |
10 years ago a was half of b in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages | explanation : let a ' s age 10 years ago = x years . then , b ' s age 10 years ago = 2 x years . ( x + 10 ) / ( 2 x + lo ) = 3 / 4 = > x = 5 . so , the total of their present ages = ( x + 10 + 2 x + 10 ) = ( 3 x + 20 ) = 35 years . answer : option b | a ) 30 , b ) 35 , c ) 37 , d ) 41 , e ) 43 | b | add(multiply(3, divide(subtract(10, divide(10, const_2)), subtract(3, divide(4, const_2)))), multiply(4, divide(subtract(10, divide(10, const_2)), subtract(3, divide(4, const_2))))) | divide(n0,const_2)|divide(n2,const_2)|subtract(n0,#0)|subtract(n1,#1)|divide(#2,#3)|multiply(n1,#4)|multiply(n2,#4)|add(#5,#6) | general | allenai/math_qa |
a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 146 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ? | "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 146 / 25 = 5 . . . . so the max is 5 146 / 20 = 7 . . . so the max is 7 146 - 145 = 1 ( 6 small box + 1 big box ) answer : d" | a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5 | d | subtract(25, 20) | subtract(n0,n1)| | general | allenai/math_qa |
the average of 10 numbers is 23 . if each number is increased by 5 , what will the new average be ? | "sum of the 10 numbers = 230 if each number is increased by 5 , the total increase = 5 * 10 = 50 the new sum = 230 + 50 = 280 the new average = 280 / 10 = 28 . answer : b" | a ) 36 , b ) 28 , c ) 72 , d ) 29 , e ) 22 | b | multiply(23, 5) | multiply(n1,n2)| | general | allenai/math_qa |
what is the sum of natural numbers between 20 and 100 | "a = first number l = last number sn = n / 2 [ a + l ] between 20 and 100 numbers = 81 = > 100 - 20 = 80 + 1 = 81 sn = 81 / 2 × 120 = 81 × 60 = 4860 b )" | a ) 4800 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 5550 | b | add(100, const_1) | add(n1,const_1)| | general | allenai/math_qa |
a shop owner sells 40 mtr of cloth and gains sp of 10 mtrs . find the gain % ? | "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 40 m cloth ) – ( c . p . of 40 m cloth ) selling price of 30 m cloth = selling price of 40 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 30 m cloth = rs . 3000 and s . p . of 30 m cloth = rs . rs . 4000 profit % = 10 / 30 × 100 = 33.33 % profit of 33.33 % was made by the merchant . a" | a ) 33.33 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 % | a | multiply(divide(10, subtract(40, 10)), const_100) | subtract(n0,n1)|divide(n1,#0)|multiply(#1,const_100)| | gain | allenai/math_qa |
if two integers x , y ( x > y ) are selected from - 4 to 4 ( inclusive ) , how many cases are there ? | "there are 9 integers from - 4 to 4 inclusive . 9 c 2 = 36 . the answer is d ." | a ) 27 , b ) 30 , c ) 33 , d ) 36 , e ) 39 | d | add(add(add(add(add(add(add(4, 4), add(4, const_2)), add(4, const_1)), 4), 4), const_2), const_1) | add(n0,n1)|add(n1,const_2)|add(n1,const_1)|add(#0,#1)|add(#3,#2)|add(#4,n1)|add(#5,n0)|add(#6,const_2)|add(#7,const_1)| | general | allenai/math_qa |
12 : 21 : : 31 : ? | "ans 13 reverse of 31 answer : a" | a ) 13 , b ) 14 , c ) 30 , d ) 31 , e ) 40 | a | multiply(31, divide(12, 21)) | divide(n0,n1)|multiply(n2,#0)| | general | allenai/math_qa |
if the cost price is 90 % of the selling price , then what is the profit percent ? | "let s . p . = $ 100 c . p . = $ 90 profit = $ 10 profit % = 10 / 90 * 100 = 25 / 6 = 11 % approximately answer is b" | a ) 5 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 19 % | b | multiply(divide(subtract(const_100, 90), 90), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain | allenai/math_qa |
the rhombus ( afce ) is inscribed in rectangle ( abcd ) . the length of bf = de . if the rectangle has a width of 20 yards and a length of 25 yards , what would be the total length ( the perimeter ) of a fence along the sides defined by afce ? | the definition of a rhombus states that every side is of equal length . this definition is the key to solving this question . 1 ) we state that the hypotenuse of either side triangle is x . for this solution , i will be working with the left triangle . 2 ) we state that the bottom and top sides of the rhombus are also x , due to the definition of a rhombus . 3 ) we will define the bottom of the left triangle as y . that is , for the rectangle bottom itself , we can define it as 25 = y + x , where x is a side for the rhombus and y is the bottom part of the left triangle . 4 ) from ( 1 ) , we know that x = 202 + y 2 − − − − − − − √ 202 + y 2 . 5 ) from ( 3 ) , we know x = 25 - y . 6 ) from ( 4 ) and ( 5 ) , we have the equation 202 + y 2 − − − − − − − √ = 25 − y 202 + y 2 = 25 − y 7 ) solving for y , we get 4.5 . 8 ) 25 - 4.5 = 20.5 = x 9 ) since all sides of the rhombus are the same , 20.5 * 4 = 41 * 2 = 82 . the answer is b , 82 | a ) 80 yards , b ) 82 yards , c ) 84 yards , d ) 85 yards , e ) 90 yards | b | multiply(subtract(25, divide(subtract(power(25, const_2), power(20, const_2)), multiply(25, const_2))), const_4) | multiply(n1,const_2)|power(n1,const_2)|power(n0,const_2)|subtract(#1,#2)|divide(#3,#0)|subtract(n1,#4)|multiply(#5,const_4) | geometry | allenai/math_qa |
if log 1087.5 = 5.9421 , then the number of digits in ( 875 ) 10 is ? | "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 5.9421 + 1 ) = 10 ( 6.9421 ) = 69.421 x = antilog ( 69.421 ) therefore , number of digits in x = 70 . answer : b" | a ) 30 , b ) 70 , c ) 27 , d ) 26 , e ) 25 | b | add(multiply(const_4, 5.9421), divide(log(const_100), log(const_10))) | log(const_100)|log(const_10)|multiply(n1,const_4)|divide(#0,#1)|add(#3,#2)| | other | allenai/math_qa |
two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.25 km and 1.00 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 = 1.25 + 1.0 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : e" | a ) 48 , b ) 9 , c ) 7 , d ) 67 , e ) 54 | e | subtract(divide(multiply(1.25, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(1.00, 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 | allenai/math_qa |
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 | allenai/math_qa |
find the simple interest on $ 10000 at 8 % per annum for 12 months ? | "p = $ 10000 r = 8 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 8 * 1 / 100 = $ 800 answer is d" | a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 800 , e ) $ 1000 | d | multiply(10000, divide(8, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain | allenai/math_qa |
for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers v are there between # 6 + 2 and # 6 + 6 , inclusive ? | "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a" | a ) none , b ) one , c ) two , d ) three , e ) four | a | add(1, 1) | add(n0,n0)| | general | allenai/math_qa |
a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 2.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters ) | "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 2.5 gms in 400,000 cm ^ 3 , x = 2.5 * 400,000 = 1 , 000,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 000,000 + 1 , 800,000 = 2 , 800,000 answer : b" | a ) 5 , 500,000 , b ) 2 , 800,000 , c ) 55,000 , d ) 28,000 , e ) 280 | b | subtract(add(multiply(multiply(divide(volume_cube(100), const_10), 2.5), 2.5), multiply(multiply(divide(volume_cube(100), const_10), multiply(const_2, 3)), 3)), volume_cube(100)) | multiply(const_2,n3)|volume_cube(n5)|divide(#1,const_10)|multiply(#2,n2)|multiply(#2,#0)|multiply(#3,n2)|multiply(#4,n3)|add(#5,#6)|subtract(#7,#1)| | geometry | allenai/math_qa |
in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ? | 40 students total 10 did not opt for math 15 did not opt for science 2 did not opt for either total of 30 students in math and 13 did not opt for sci but did for math 30 - 13 = 7 7 students of the class opted for both math and science answer : c . 7 | a ) 13 , b ) 15 , c ) 7 , d ) 17 , e ) 18 | c | subtract(subtract(40, 10), subtract(subtract(40, 15), 2)) | subtract(n0,n1)|subtract(n0,n2)|subtract(#1,n3)|subtract(#0,#2) | other | allenai/math_qa |
s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits q are in s ( 99 ) ? | focus on the points where the number of digits q in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b | a ) q = 350 , b ) q = 353 , c ) q = 354 , d ) q = 356 , e ) 357 | b | add(add(add(add(const_60, const_4), 4), multiply(add(add(const_60, const_4), 4), 4)), add(multiply(3, 1), multiply(multiply(3, 2), 2))) | add(const_4,const_60)|multiply(n0,n4)|multiply(n2,n4)|add(n6,#0)|multiply(n2,#2)|add(#1,#4)|multiply(n6,#3)|add(#3,#6)|add(#7,#5) | general | allenai/math_qa |
if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 370 will be : | z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 740 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 37 3.7 z = 370 , z = 100 answer : . c | a ) rs . 300 , b ) rs . 200 , c ) rs . 100 , d ) rs . 350 , e ) none of these | c | divide(370, add(add(multiply(add(const_1, divide(25, const_100)), add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))), const_1)) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#3,#2)|add(#2,#4)|add(#5,const_1)|divide(n2,#6) | general | allenai/math_qa |
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 | allenai/math_qa |
angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 6,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ? | "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 6,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 6,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 480 = 0.10 x combine terms and subtract 0.08 x from both sides : 70 = 0.02 x divide both sides by 0.02 : 3,500 = x your answer is a ." | a ) 3,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500 | a | floor(divide(divide(subtract(550, multiply(6,000, divide(8, const_100))), subtract(divide(10, const_100), divide(8, const_100))), 6,000)) | divide(n1,const_100)|divide(n3,const_100)|multiply(#0,n2)|subtract(#1,#0)|subtract(n0,#2)|divide(#4,#3)|divide(#5,n2)|floor(#6)| | general | allenai/math_qa |
a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1340 in total compensation , how many total hours did he work that week ? | "for 40 hrs = 40 * 16 = 640 excess = 1340 - 640 = 700 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 700 / 28 = 25 total hrs = 40 + 25 = 65 answer c 65" | a ) 76 , b ) 60 , c ) 65 , d ) 48 , e ) 52 | c | add(40, divide(subtract(1340, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100))) | add(n3,const_100)|multiply(n0,n1)|multiply(n0,#0)|subtract(n4,#1)|divide(#2,const_100)|divide(#3,#4)|add(n1,#5)| | general | allenai/math_qa |
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 | allenai/math_qa |
p , q and r have rs . 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ? | "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 . answer : c" | a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2000 , d ) rs . 4000 , e ) none of these | c | multiply(divide(5000, add(const_1, divide(const_2, const_3))), divide(const_2, const_3)) | divide(const_2,const_3)|add(#0,const_1)|divide(n0,#1)|multiply(#2,#0)| | general | allenai/math_qa |
mike earns $ 12 per hour and phil earns $ 6 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ? | "what % less of 12 is 6 let it be x % less , then = 12 ( 1 - x / 100 ) = 6 1 - x / 100 = 6 / 12 x = 100 / 2 x = 50 % ans a" | a ) 50 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 % | a | multiply(divide(6, 12), const_100) | divide(n1,n0)|multiply(#0,const_100)| | general | allenai/math_qa |
how many positive integers h less than 10000 are such that the product of their digits is 210 ? | 210 is the answer when 2 , 3 , 5 and 7 are multiplied . 210 can also be arrive using 56 and 7 and 1 , 5 , 6 and 7 . so sum of arrangements of 2357 , 567 and 1567 . this translates to 4 ! + 3 ! + 4 ! , this equals to 24 + 6 + 24 = 54 , d is the answer . | a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 72 | d | add(add(factorial(subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), const_3)), factorial(subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), const_3))), factorial(subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), subtract(divide(divide(divide(210, add(const_4, const_1)), const_3), const_2), const_3)))) | add(const_1,const_4)|divide(n1,#0)|divide(#1,const_3)|divide(#2,const_2)|subtract(#3,const_3)|factorial(#4)|subtract(#3,#4)|add(#5,#5)|factorial(#6)|add(#7,#8) | general | allenai/math_qa |
a man can do a piece of work in 6 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ? | "son ' s 1 day work = 1 / 3 - 1 / 6 = 1 / 6 son alone can do the work in 6 days = 6 days answer is d" | a ) 5 , b ) 5 1 / 2 , c ) 7 1 / 2 , d ) 6 , e ) 9 1 / 2 | d | divide(multiply(6, 3), subtract(6, 3)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | physics | allenai/math_qa |
16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 4 girls will take to construct ? | "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 4 girls = 8 ã — 6 / 4 + 12 = 12 + 4 = 16 girls 9 days to complete the work answer : option e" | a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days | e | divide(const_1, add(multiply(4, divide(divide(const_1, 6), 24)), multiply(8, divide(divide(const_1, 6), 16)))) | divide(const_1,n2)|divide(#0,n1)|divide(#0,n0)|multiply(n4,#1)|multiply(n3,#2)|add(#3,#4)|divide(const_1,#5)| | physics | allenai/math_qa |
p is 60 % more efficient than q . p can complete a work in 26 days . if p and q work together , how many days will it take to complete the same work ? | the work done by p in 1 day = 1 / 26 let work done by q in 1 day = q q × ( 160 / 100 ) = 1 / 26 q = 100 / ( 26 × 160 ) = 10 / ( 26 × 16 ) the work done by p and q in 1 day = 1 / 26 + 10 / ( 26 × 16 ) = 26 / ( 26 × 16 ) = 1 / 16 p and q together can do the work in 16 days . the answer is c . | a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20 | c | divide(multiply(add(divide(60, const_100), const_1), 26), add(add(divide(60, const_100), const_1), const_1)) | divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(n1,#1)|divide(#3,#2) | physics | allenai/math_qa |
if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units z digit of ( a + 2 ) ^ 2 ? | "i also got a . by punching in numers : z . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a" | a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14 | a | power(add(multiply(9, 2), 2), 2) | multiply(n0,n1)|add(n0,#0)|power(#1,n0)| | general | allenai/math_qa |
the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.10 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ? | "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.1 = 732.6 answer : c" | a ) 399 , b ) 272 , c ) 732.6 , d ) 277 , e ) 311 | c | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 1.10), 3) | multiply(n3,const_2)|sqrt(n0)|multiply(#1,const_4)|subtract(#2,#0)|multiply(n2,#3)|multiply(#4,n1)| | physics | allenai/math_qa |
sachin is younger than rahul by 6 years . if the ratio of their ages is 7 : 9 , find the age of sachin | "if rahul age is x , then sachin age is x - 6 , so ( x - 6 ) / x = 7 / 9 = > 9 x - 42 = 7 x = > 2 x = 42 = > x = 21 so sachin age is 21 - 6 = 15 answer : c" | a ) 24.58 , b ) 14 , c ) 15 , d ) 24.9 , e ) 24.1 | c | multiply(divide(6, subtract(9, 7)), 7) | subtract(n2,n1)|divide(n0,#0)|multiply(n1,#1)| | other | allenai/math_qa |
two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 200 m , in what time will they cross other travelling in opposite direction ? | "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 200 + 200 ) / 20 = 20 sec . answer : e" | a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 20 sec | e | divide(multiply(200, const_2), add(speed(200, 15), speed(200, 10))) | multiply(n2,const_2)|speed(n2,n1)|speed(n2,n0)|add(#1,#2)|divide(#0,#3)| | physics | allenai/math_qa |
the length of the bridge is 200 m , which a 100 m long train cross in 60 sec . then what is the speed of train ? | speed = length / time length = ( 200 + 100 ) = 300 m time = 60 sec speed = 300 / 60 = 5 m / sec answer b | a ) 6 , b ) 5 , c ) 4 , d ) 10 , e ) 8 | b | divide(add(200, 100), 60) | add(n0,n1)|divide(#0,n2) | physics | allenai/math_qa |
a train 160 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ? | "c 340 c = ( 72 * 5 / 18 ) * 25 - 160 = 340" | a ) 443 m , b ) 354 m , c ) 340 m , d ) 350 m , e ) 250 m | c | subtract(multiply(25, multiply(72, const_0_2778)), 160) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics | allenai/math_qa |
in a certain company , a third of the workers do not have a retirement plan . 50 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ? | "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,5 * 1 / 3 * x 120 = 13 / 30 x x = 276 276 - 120 = 156 answer d" | a ) 80 , b ) 95 , c ) 105 , d ) 156 , e ) 210 | d | multiply(divide(120, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(50, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(50, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100))))) | divide(const_1,const_3)|divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|subtract(#0,#3)|add(#5,#6)|subtract(#4,#5)|add(#3,#8)|divide(n2,#7)|multiply(#9,#10)| | gain | allenai/math_qa |
by investing in 1623 % stock at 64 , one earns rs . 1900 . the investment made is | explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1500 , investment needed = 64 × 3 × 1500 / 50 = 5760 answer : option d | a ) s . 9600 , b ) s . 7500 , c ) s . 5640 , d ) s . 5760 , e ) - 7296 | d | multiply(divide(multiply(multiply(multiply(const_4, const_2), multiply(const_4, const_2)), const_3), divide(const_100, const_2)), subtract(1900, multiply(const_4, const_100))) | divide(const_100,const_2)|multiply(const_2,const_4)|multiply(const_100,const_4)|multiply(#1,#1)|subtract(n2,#2)|multiply(#3,const_3)|divide(#5,#0)|multiply(#6,#4) | gain | allenai/math_qa |
how many positive integers between 1 and 100 are there such that they are multiples of 15 ? | "multiples of 15 = 15 , 30,45 , - - - - - 90 number of multiples of 15 = > 90 - 15 / 15 + 1 = 6 answer is e" | a ) 5 , b ) 4 , c ) 7 , d ) 1 , e ) 6 | e | divide(subtract(100, 1), 15) | subtract(n1,n0)|divide(#0,n2)| | general | allenai/math_qa |
joe invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 500 at the end of another 5 years . what was the rate of interest in which he invested his sum ? | in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 400 - $ 60 = 340 . the interest rate is $ 20 / $ 340 = 1 / 17 which is about 5.88 % the answer is b . | a ) 4.76 % , b ) 5.88 % , c ) 6.33 % , d ) 7.75 % , e ) 8.33 % | b | multiply(divide(divide(subtract(500, 400), 5), subtract(400, multiply(divide(subtract(500, 400), 5), 3))), const_100) | subtract(n2,n0)|divide(#0,n3)|multiply(n1,#1)|subtract(n0,#2)|divide(#1,#3)|multiply(#4,const_100) | gain | allenai/math_qa |
if x is a positive integer with fewer than 3 digits , what is the probability w that x * ( x + 1 ) is a multiple of either 4 or 5 ? | "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability w that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ." | a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99 | e | divide(subtract(add(multiply(divide(const_100, 4), const_2), multiply(divide(const_100, 5), const_2)), 4), subtract(const_100, 1)) | divide(const_100,n2)|divide(const_100,n3)|subtract(const_100,n1)|multiply(#0,const_2)|multiply(#1,const_2)|add(#3,#4)|subtract(#5,n2)|divide(#6,#2)| | general | allenai/math_qa |
the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 1 year ? | "explanation : 40,000 * ( 3 / 4 ) ^ 1 answer : c" | a ) 3277 , b ) 2977 , c ) 30000 , d ) 6077 , e ) 17112 | c | multiply(multiply(4, multiply(const_100, const_100)), power(divide(3, 4), 1)) | divide(n0,n1)|multiply(const_100,const_100)|multiply(n1,#1)|power(#0,n3)|multiply(#2,#3)| | general | allenai/math_qa |
the banker â € ™ s discount of a certain sum of money is rs . 80 and the true discount on the same sum for the same time is rs . 70 . the sum due is | "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 80 * 70 / 80 - 70 ] = rs . [ 80 * 70 / 10 ] = rs . 560 answer c" | a ) 210 , b ) 280 , c ) 560 , d ) 450 , e ) none | c | divide(multiply(80, 70), subtract(80, 70)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | gain | allenai/math_qa |
the weight of a glass of jar is 20 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ? | "let weight of jar filled with beans = 100 g weight of jar = 20 g weight of coffee beans = 80 g weight of jar and remaining beans = 60 g weight of remaining beans = 40 g fraction remaining = 40 / 80 = 1 / 2 answer is d ." | a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 2 / 3 | d | divide(subtract(60, 20), subtract(const_100, 20)) | subtract(n1,n0)|subtract(const_100,n0)|divide(#0,#1)| | gain | allenai/math_qa |
there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 16 other amateurs , what is the total number of chess games possible to be played in the tournament ? | "each person is one participant of 4 games . so there are in all 16 * 5 = 80 instances of one participant games . but each game has 2 participants so total number of games = 80 / 2 = 40 c" | a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120 | c | divide(multiply(5, 16), const_2) | multiply(n0,n1)|divide(#0,const_2)| | general | allenai/math_qa |
john and david work at a hospital with 10 other workers . for an internal review , 2 of the 10 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ? | "probability that john and david will both be chosen out of 8 workers = ( 2 / 10 ) * ( 1 / 9 ) = 1 / 45 answer a" | a ) 1 / 45 , b ) 1 / 35 , c ) 1 / 25 , d ) 1 / 15 , e ) 1 / 10 | a | multiply(2, multiply(divide(const_1, subtract(10, const_1)), divide(const_1, 10))) | divide(const_1,n0)|subtract(n0,const_1)|divide(const_1,#1)|multiply(#2,#0)|multiply(n1,#3)| | physics | allenai/math_qa |
if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? | "if we are to select 4 people from 7 couples without any restriction , how many ways can we make the selection ? 14 ! / 4 ! 10 ! = 1001 if we are to select 4 people from 7 couples with restriction that no married couple can both make it to the group , only a representative ? 7 ! / 4 ! 3 ! = 35 but we know that to select a person from each couple , take 2 possibilities 35 * 2 * 2 * 2 * 2 = 560 probability = desired / all possibilities = 560 / 1001 = 47 / 84 answer : e" | a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84 | e | multiply(multiply(multiply(divide(multiply(7, const_2), multiply(7, const_2)), divide(multiply(4, 4), subtract(multiply(7, const_2), const_1))), divide(subtract(multiply(4, 4), const_2), multiply(4, 4))), divide(subtract(subtract(multiply(4, 4), const_2), const_2), subtract(multiply(4, 4), const_1))) | multiply(n0,n0)|multiply(n1,const_2)|divide(#1,#1)|subtract(#0,const_2)|subtract(#0,const_1)|subtract(#1,const_1)|divide(#3,#0)|divide(#0,#5)|subtract(#3,const_2)|divide(#8,#4)|multiply(#2,#7)|multiply(#6,#10)|multiply(#9,#11)| | probability | allenai/math_qa |
how many integers from 20 to 150 , inclusive , are divisible by 3 but not divisible by 7 ? | "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 20 to 150 , inclusive is ( 147 - 21 ) / 21 + 1 = 7 ; 44 - 7 = 37 . answer : a ." | a ) 37 , b ) 40 , c ) 42 , d ) 45 , e ) 55 | a | divide(150, const_10) | divide(n1,const_10)| | general | allenai/math_qa |
a taxi owner buys diesel at rs . 8.50 , rs . 9 and rs . 9.50 per litre for 3 successive years . what approximately is the average cost per litre of diesel if he spends rs . 5000 each year ? | total cost = 5000 × 3 = 15000 total diesel used = 5000 / 8.50 + 5000 / 9 + 5000 / 9.50 = 588 + 555 + 527 = 1670 average cost per litre of diesel = 15000 / 1670 = 8.98 answer : b | a ) 7.98 , b ) 8.98 , c ) 9.98 , d ) 6.98 , e ) 8.12 | b | divide(multiply(5000, 3), add(add(divide(5000, 8.5), divide(5000, 9)), divide(5000, 9.5))) | divide(n4,n0)|divide(n4,n1)|divide(n4,n2)|multiply(n3,n4)|add(#0,#1)|add(#4,#2)|divide(#3,#5) | general | allenai/math_qa |
david and andrew can finish the work 12 days if they work together . they worked together for 8 days and then andrew left . david finished the remaining work in another 8 days . in how many days david alone can finish the work ? | amount of work done by david and andrew in 1 day = 1 / 12 amount of work done by david and andrew in 8 days = 8 ã — ( 1 / 12 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 david completes 1 / 3 work in 8 days amount of work david can do in 1 day = ( 1 / 3 ) / 8 = 1 / 24 = > david can complete the work in 24 days answer : e | a ) 30 days , b ) 60 days , c ) 70 days , d ) 80 days , e ) 24 days | e | multiply(divide(8, subtract(12, 8)), 12) | subtract(n0,n1)|divide(n1,#0)|multiply(n0,#1) | physics | allenai/math_qa |
there is a point p on the circle . a and b started running in two constant different speeds . a in clockwise and b in anti - clockwise . first time 500 m in clockwise from p then 400 anti - clockwise . if b is yet to complete one round , what is the circumference of the circle ? | let the speeds of a & b be u and v resp . and let circumference be c . let their first meeting be after time t then ut + vt = c and ut = 500 ∴ vt = c − 500 and u / v = 500 / ( c − 500 ) for their second meeting after time t , ut + vt = 2 c and vt = 400 ∴ ut = 2 c − 400 and u / v = ( 2 c − 400 ) / 400 hence 500 / ( c − 500 ) = ( 2 c − 400 ) / 400 simplifying , 100000 = ( c − 200 ) ( c − 500 ) = c ² − 700 c + 100000 → c = 700 answer : a | a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100 | a | divide(add(multiply(multiply(const_1, const_2), 500), 400), const_2) | multiply(const_1,const_2)|multiply(n0,#0)|add(n1,#1)|divide(#2,const_2) | physics | allenai/math_qa |
what is 2 / 5 of 5 / 9 of 1 / 2 ? | "2 / 5 * 5 / 9 * 1 / 2 = 1 / 9 answer : b" | a ) 1 / 4 , b ) 1 / 9 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9 | b | multiply(divide(2, 5), multiply(divide(5, 9), divide(1, 2))) | divide(n0,n1)|divide(n1,n3)|divide(n4,n0)|multiply(#1,#2)|multiply(#0,#3)| | general | allenai/math_qa |
a contractor undertook to make 15 km of roadway in 40 weeks . in 10 weeks , 3 km was complete by 180 men working 8 hours a day . the men then agreed to work 1 hour a day overtime , and some boys were engaged to assist them , the work was finished in the stipulated time ( 40 weeks ) . how many boys were employed , if the work of 3 boys is equal to that of 2 men ? | explanation : let the capacity of man = 3 units , and boy = 2 units per hour . now total work = 3 × 180 × 8 × 7 × 10 = 3 km . - - - - - - - ( 1 ) let k boys were recruited . now total work = ( 3 × 180 + 2 × k ) × 9 × 7 × 30 = 12 km . - - - - - - ( 2 ) by dividing 2 nd equation by 1 st , ⇒ ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ( 540 + 2 k ) × 9 × 7 × 303 × 180 × 8 × 7 × 10 = 4 ⇒ k = 50 answer : b | a ) 48 , b ) 50 , c ) 22 , d ) 27 , e ) 221 | b | divide(subtract(15, add(3, multiply(180, multiply(multiply(divide(divide(divide(3, 10), 180), 8), add(8, 1)), subtract(40, 10))))), multiply(subtract(40, 10), multiply(divide(2, 3), multiply(divide(divide(divide(3, 10), 180), 8), add(8, 1))))) | add(n5,n6)|divide(n3,n2)|divide(n9,n3)|subtract(n1,n2)|divide(#1,n4)|divide(#4,n5)|multiply(#0,#5)|multiply(#6,#3)|multiply(#2,#6)|multiply(n4,#7)|multiply(#8,#3)|add(n3,#9)|subtract(n0,#11)|divide(#12,#10) | physics | allenai/math_qa |
what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 4 | "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 4 = 1.25 so biggest is 5 / 4 and smallest is 2 / 3 their difference is 5 / 4 - 2 / 3 = 7 / 12 option c" | a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 12 , d ) 1 / 7 , e ) none of these | c | subtract(divide(4, 5), divide(2, 3)) | divide(n3,n5)|divide(n0,n1)|subtract(#0,#1)| | general | allenai/math_qa |
what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 4 , and 5 if each digit can be used only once in each number ? | "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 444 ) + 2 ( 555 ) = 2442 the answer is a ." | a ) 2442 , b ) 2552 , c ) 2662 , d ) 2772 , e ) 2882 | a | multiply(add(add(multiply(add(add(5, 4), 2), const_100), multiply(add(add(const_4.0, 4), 2), const_10)), add(add(5, 4), 2)), 4) | add(n2,n3)|add(n1,#0)|multiply(#1,const_100)|multiply(#1,const_10)|add(#2,#3)|add(#4,#1)|multiply(#5,const_2)| | general | allenai/math_qa |
kanul spent $ 500 in buying raw materials , $ 400 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ? | "let the total amount be x then , ( 100 - 10 ) % of x = 500 + 400 90 % of x = 900 90 x / 100 = 9000 / 9 x = $ 1000 answer is e" | a ) $ 1010 , b ) $ 1025 , c ) $ 1125 , d ) $ 1100 , e ) $ 1000 | e | divide(add(500, 400), subtract(const_1, divide(10, const_100))) | add(n0,n1)|divide(n2,const_100)|subtract(const_1,#1)|divide(#0,#2)| | gain | allenai/math_qa |
if renee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ? | 5 % is 5 / 100 = 1 / 20 10 % is 10 / 100 = 1 / 10 the increase must be greater than 1 / 20 and less than 1 / 10 . 1 / 4 , 1 / 5 , and 1 / 10 are not less than 1 / 10 . 1 / 20 is not greater than 1 / 20 . the only option left is 2 / 25 , which is in the specified range . answer : d | a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 2 / 25 , e ) 1 / 20 | d | divide(subtract(5, const_1), multiply(5, const_10)) | multiply(n0,const_10)|subtract(n0,const_1)|divide(#1,#0) | general | allenai/math_qa |
stock / number of shares v - - - - - - - - - - - - 68 w - - - - - - - - - - 112 x - - - - - - - - - - - - 56 y - - - - - - - - - - - - 94 z - - - - - - - - - - - - 45 the table shows the number of shares of each of the 5 stocks owned by mr sami . if mr . sami was to sell 20 shares of stock x and buy 23 shares of stock y , what would be the increase in the range of the numbers of shares of the 5 stocks owned by mr . sami ? | based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewrange to theoldrange : 81 - 67 = 14 d | a ) 4 , b ) 6 , c ) 9 , d ) 14 , e ) 20 | d | subtract(subtract(add(94, 23), subtract(56, 20)), subtract(112, 45)) | add(n3,n7)|subtract(n2,n6)|subtract(n1,n4)|subtract(#0,#1)|subtract(#3,#2) | general | allenai/math_qa |
a jar contains only red , yellow , and orange marbles . if there are 3 red , 3 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? | "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 45 ) * ( 2 ) , which indeed is 2 / 45 . c" | a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22 | c | divide(multiply(choose(3, 2), choose(3, 1)), choose(add(add(3, 4), 3), 3)) | add(n1,n2)|choose(n1,n4)|choose(n0,n5)|add(n0,#0)|multiply(#1,#2)|choose(#3,n0)|divide(#4,#5)| | probability | allenai/math_qa |
on a certain road 14 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ? | "answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 14 % + 0,2 x id est x = 17,5 %" | a ) 10.5 % , b ) 12.5 % , c ) 17.5 % , d ) 22 % , e ) 30 % | c | divide(const_100, multiply(multiply(divide(14, const_100), divide(20, const_100)), const_100)) | divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|multiply(#2,const_100)|divide(const_100,#3)| | gain | allenai/math_qa |
how many ounces of a 60 % salt solution must be added to 40 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ? | "let x = ounces of 60 % salt solution to be added . 2 * 40 + . 6 x = . 4 ( 40 + x ) x = 40 amswer b" | a ) 16.67 , b ) 40 , c ) 50 , d ) 60.33 , e ) 70 | b | divide(subtract(multiply(divide(40, const_100), 40), multiply(divide(20, const_100), 40)), subtract(divide(40, const_100), divide(20, const_100))) | divide(n3,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n1,#1)|subtract(#0,#1)|subtract(#2,#3)|divide(#5,#4)| | gain | allenai/math_qa |
what least no . must be subtracted from 427398 so that remaining no . is divisible by 15 ? | "explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted option b" | a ) 344545629 , b ) 723437481 , c ) 354595321 , d ) 964564944 , e ) 458449909 | b | subtract(427398, multiply(floor(divide(427398, 15)), 15)) | divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)| | general | allenai/math_qa |
the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 828 . what is the banker ' s discount ? | "explanation : td = ( bg × 100 ) / tr = ( 828 × 100 ) / ( 6 × 12 ) = rs . 1150 bg = bd – td = > 828 = bd - 1150 = > bd = 1978 answer : option d" | a ) 1240 , b ) 1120 , c ) 1190 , d ) 1978 , e ) none of these | d | add(828, divide(multiply(828, const_100), multiply(12, 6))) | multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|add(n2,#2)| | gain | allenai/math_qa |
there are 172 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ? | "editing my solution : number of switches = 172 number of switches turned on by a : 3 , 6 , . . . 171 = 57 number of switches turned on by b : 5 , 10 , . . . . 170 = 34 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 57 - 6 ) + ( 34 - 6 ) = 79 answer : d" | a ) 83 , b ) 85 , c ) 87 , d ) 79 , e ) 89 | d | subtract(add(floor(divide(172, const_3)), floor(divide(172, add(const_1, const_4)))), multiply(floor(divide(172, multiply(const_3, add(const_1, const_4)))), const_2)) | add(const_1,const_4)|divide(n0,const_3)|divide(n0,#0)|floor(#1)|multiply(#0,const_3)|divide(n0,#4)|floor(#2)|add(#3,#6)|floor(#5)|multiply(#8,const_2)|subtract(#7,#9)| | other | allenai/math_qa |
a certain company reported that the revenue on sales increased 20 % from 2000 to 2003 , and increased 40 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ? | "assume the revenue in 2000 to be 100 . then in 2003 it would be 120 and and in 2005 140 , so from 2003 to 2005 it increased by ( 140 - 120 ) / 120 = 20 / 120 = 17 % answer : e ." | a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 17 % | e | multiply(divide(subtract(add(const_1, divide(40, const_100)), add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))), const_100) | divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(#2,#3)|divide(#4,#3)|multiply(#5,const_100)| | gain | allenai/math_qa |
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 ) ’ 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 | allenai/math_qa |
a train 100 m long crosses a platform 125 m long in 40 sec ; find the speed of the train ? | "d = 100 + 125 = 225 t = 40 s = 225 / 40 * 18 / 5 = 20.25 kmph answer : e" | a ) 36.21 , b ) 77.11 , c ) 54.12 , d ) 33.0 , e ) 20.25 | e | subtract(multiply(40, multiply(const_60.0, const_0_2778)), 100) | multiply(const_60.0,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics | allenai/math_qa |
what will be the ci on a sum of rs . 25000 after 3 years at the rate of 12 per year ? | amount = rs . 25000 x 1 + 12 3 100 = rs . 25000 x 28 x 28 x 28 25 25 25 = rs . 35123.20 c . i . = rs . ( 35123.20 - 25000 ) = rs . 10123.20 c | a ) rs . 10100 , b ) rs . 10110 , c ) rs . 10123.20 , d ) rs . 10135.50 , e ) rs . 10167.20 | c | subtract(multiply(power(add(divide(12, const_100), const_1), 3), 25000), 25000) | divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|subtract(#3,n0) | gain | allenai/math_qa |
the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 6500 , brokerage being 1 / 4 % , is : | "face value = rs . 6500 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 6500 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 90.27 . = market value of rs . 100 stock = rs . 90.27 - re . 0.25 . = market value of rs . 100 stock = rs . 90.03 . answer : a" | a ) 90.03 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75 | a | subtract(multiply(divide(6500, 756), 10.5), divide(1, 4)) | divide(n2,n1)|divide(n3,n4)|multiply(n0,#0)|subtract(#2,#1)| | gain | allenai/math_qa |
what will be the vulgar fraction of 0.70 | "explanation : 0.70 = 70 / 100 = 7 / 10 option b" | a ) 3 / 5 , b ) 7 / 10 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8 | b | divide(circle_area(divide(0.70, const_2)), const_2) | divide(n0,const_2)|circle_area(#0)|divide(#1,const_2)| | general | allenai/math_qa |
the balance of a trader weighs 20 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ? | the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 80 gms because it weighs 20 % less . say , the cost price is $ 80 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 80 + ( 30 / 100 ) * 80 = $ 104 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 104 , the mark up is simply 4 % . ans : a | a ) 4 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 9 % | a | subtract(add(multiply(multiply(const_4, 20), divide(30, const_100)), multiply(const_4, 20)), const_100) | divide(n1,const_100)|multiply(n0,const_4)|multiply(#0,#1)|add(#2,#1)|subtract(#3,const_100) | gain | allenai/math_qa |
9 log 9 ( 6 ) = ? | "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 6 ) = 6 correct answer b" | a ) 1 , b ) 6 , c ) 3 , d ) 4 , e ) 5 | b | divide(log(multiply(9, 9)), log(const_10)) | log(const_10)|multiply(n0,n0)|log(#1)|divide(#2,#0)| | other | allenai/math_qa |
when a random experiment is conducted , the probability that event a occurs is 1 / 5 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ? | "one case is : 1 / 5 * 1 / 5 * 4 / 5 * 4 / 5 * 4 / 5 = 64 / 3125 the total number of possible cases is 5 c 2 = 10 p ( event a occurs exactly twice ) = 10 * ( 64 / 3125 ) = 128 / 625 the answer is e ." | a ) 36 / 625 , b ) 48 / 625 , c ) 64 / 625 , d ) 98 / 625 , e ) 128 / 625 | e | subtract(1, divide(const_2, 5)) | divide(const_2,n1)|subtract(n0,#0)| | general | allenai/math_qa |
49 x 49 x 49 x 49 = 7 ? | "solution 49 * 49 * 49 * 49 = ( 72 * 72 * 72 * 72 ) = 7 ( 2 + 2 + 2 + 2 ) = 78 so , the correct answer is 8 answer c" | a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) 20 | c | divide(subtract(multiply(49, 49), multiply(49, 49)), 7) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)| | general | allenai/math_qa |
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