Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation .... | "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 1 . so , x = 65 / 4 ounces . water = ( 60 / 65 ) * ( 65 / 4 ) = 15 ounces . ans a" | a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90 | a | multiply(divide(multiply(divide(1, 12), const_3), divide(divide(1, 30), const_2)), 1) | divide(n0,n1)|divide(n0,n2)|divide(#1,const_2)|multiply(#0,const_3)|divide(#3,#2)|multiply(n3,#4)| | other |
in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 8 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ? | "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 8 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . al... | a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60 | c | multiply(divide(divide(multiply(7, 8), subtract(11, 7)), 7), 15) | multiply(n1,n2)|subtract(n4,n1)|divide(#0,#1)|divide(#2,n1)|multiply(n0,#3)| | other |
the number 523 fbc is divisible by 7 , 89 . then what is the value of f * b * c | lcm of 7 , 8 and 9 is 504 , thus 523 fbc must be divisible by 504 . 523 fbc = 523000 + fbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + fbc = k * 504 . k = 1 fbc = 152 - - > f * b * c = 10 k = 2 fbc = 656 - - > f * b * c = 180 as fbc is three digit number k can not be more than 2 . two answers ? well ... | a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280 | d | add(divide(add(divide(523, const_4), divide(523, const_4)), const_2), multiply(add(const_4, const_1), const_10)) | add(const_1,const_4)|divide(n0,const_4)|add(#1,#1)|multiply(#0,const_10)|divide(#2,const_2)|add(#4,#3) | general |
the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 0.50 ( x β 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 2 wheels on each of its other axles ? | "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 2 = 8 total number of axles = 9 t = 1.50 + 0.50 ( 9 β 2 ) = 1.50 + . 5 * 7 = 1.5 + 1.5 = 5 $ answer e" | a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00 | e | add(1.50, multiply(0.50, subtract(add(divide(subtract(18, 2), 2), const_1), 2))) | subtract(n3,n2)|divide(#0,n5)|add(#1,const_1)|subtract(#2,n2)|multiply(n1,#3)|add(n0,#4)| | general |
indu gave bindu rs . 5000 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ? | "5000 = d ( 100 / 4 ) 2 d = 8 answer : a" | a ) 8 , b ) 2 , c ) 9 , d ) 5 , e ) 1 | a | subtract(subtract(multiply(5000, power(add(const_1, divide(4, const_100)), 2)), 5000), multiply(multiply(5000, divide(4, const_100)), 2)) | divide(n2,const_100)|add(#0,const_1)|multiply(n0,#0)|multiply(n1,#2)|power(#1,n1)|multiply(n0,#4)|subtract(#5,n0)|subtract(#6,#3)| | gain |
a sum of money at simple interest amounts to $ 700 in 3 years and to $ 764 in 4 years . the sum is : | "a $ 508 s . i . for 1 year = $ ( 764 - 700 ) = $ 64 . s . i . for 3 years = $ ( 64 x 3 ) = $ 192 . principal = $ ( 700 - 192 ) = $ 508 ." | a ) $ 508 , b ) $ 698 , c ) $ 398 , d ) $ 549 , e ) $ 675 | a | subtract(700, divide(multiply(subtract(764, 700), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | gain |
how many factors does 34 ^ 2 have ? | "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 5 * 4 = 20 answer c ." | a ) 2 , b ) 8 , c ) 20 , d ) 25 , e ) 26 | c | divide(34, multiply(const_10, const_2)) | multiply(const_10,const_2)|divide(n0,#0)| | other |
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 |
a man walking at a rate of 10 km / hr crosses a bridge in 3 minutes . the length of the bridge is ? | "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 5 minutes = 50 / 18 * 5 * 60 = 500 m answer is a" | a ) 500 , b ) 650 , c ) 250 , d ) 111 , e ) 236 | a | multiply(divide(multiply(10, const_1000), const_60), 3) | multiply(n0,const_1000)|divide(#0,const_60)|multiply(n1,#1)| | gain |
how many paying stones , each measuring 3 * 2 m are required to pave a rectangular court yard 15 m long and 6 m board ? | "15 * 6 = 3 * 2 * x = > x = 15 answer : d" | a ) 99 , b ) 18 , c ) 26 , d ) 15 , e ) 12 | d | divide(rectangle_area(15, 6), rectangle_area(3, 2)) | rectangle_area(n2,n3)|rectangle_area(n0,n1)|divide(#0,#1)| | physics |
on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction w of the total distance did... | if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or... | a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7 | e | subtract(divide(lcm(const_2, const_3), 2.8), const_2) | lcm(const_2,const_3)|divide(#0,n1)|subtract(#1,const_2)| | general |
what number has a 15 : 1 ratio to the number 10 ? | "15 : 1 = x : 10 x = 10 * 15 x = 150 answer : d" | a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120 | d | multiply(10, 15) | multiply(n0,n2)| | other |
if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 7 , what is the value of 2 ^ a * 2 ^ b ? | "2 ^ ab = 2 ^ 7 therefore ab = 7 either a = 1 or 7 or b = 7 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 8 = 256 d" | a ) 16 , b ) 32 , c ) 64 , d ) 256 , e ) 128 | d | multiply(power(2, const_3.0), 2) | power(n0,n2)|multiply(n0,#0)| | general |
a man is 30 years older than his son . in four years , his age will be twice the age of his son . the present age of this son is | "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 4 ) = ( x + 30 + 4 ) = > 2 x + 8 = x + 34 = > x = 26 years answer : option e" | a ) 22 years , b ) 23 years , c ) 24 years , d ) 25 years , e ) 26 years | e | divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 17 terms of the arithmetic progression ? | "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 17 . . . we get 17 / 2 [ 2 a + 14 d ] = 17 [ a + 7 d ] = 17 * 10 = 170 . . . answer is d... | a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270 | d | divide(multiply(20, 17), const_2) | multiply(n0,n1)|divide(#0,const_2)| | general |
a man invests rs . 4,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ? | "explanation : interest on rs . 4000 at 5 % per annum = ( 4000 Γ 5 Γ 1 ) / 100 = rs . 200 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x Γ 8 Γ 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 4000 + x ) Γ 6 Γ 1 / 100 . = > 200 + 2 x / 25 = ( 4000 + x ) Γ 6 Γ ... | a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 2000 , e ) none of these | d | multiply(multiply(8, const_1000), divide(subtract(6, 5), subtract(8, 6))) | multiply(n2,const_1000)|subtract(n3,n1)|subtract(n2,n3)|divide(#1,#2)|multiply(#3,#0)| | gain |
a cab driver 5 days income was $ 400 , $ 250 , $ 650 , $ 400 , $ 500 . then his average income is ? | "avg = sum of observations / number of observations avg income = ( 400 + 250 + 650 + 400 + 500 ) / 5 = 440 answer is c" | a ) $ 400 , b ) $ 420 , c ) $ 440 , d ) $ 460 , e ) $ 480 | c | divide(add(add(add(add(400, 250), 650), 400), 500), 5) | add(n1,n2)|add(n3,#0)|add(n4,#1)|add(n5,#2)|divide(#3,n0)| | general |
calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length , if the speed of the train is 40 km / hour ? | speed = 40 km / hr = 40 * ( 5 / 18 ) m / sec = 11.1111 m / sec total distance = 120 + 160 = 280 meter time = distance / speed = 280 * ( 1 / 11.1111 ) = 25.2 seconds answer : b | a ) 21.2 seconds , b ) 25.2 seconds , c ) 29.2 seconds , d ) 35.2 seconds , e ) 11.2 seconds | b | divide(add(120, 160), divide(40, const_3_6)) | add(n0,n1)|divide(n2,const_3_6)|divide(#0,#1) | physics |
the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 540 . what is the banker ' s discount ? | "explanation : td = ( bg Γ 100 ) / tr = ( 540 Γ 100 ) / ( 6 Γ 12 ) = ( 90 Γ 100 ) / 12 = ( 15 Γ 100 ) 2 / = rs . 750 bg = bd β td = > 540 = bd - 750 = > bd = 540 + 750 = 1290 answer : option d" | a ) 1240 , b ) 1120 , c ) 1190 , d ) 1290 , e ) none of these | d | add(540, divide(multiply(540, const_100), multiply(12, 6))) | multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|add(n2,#2)| | gain |
if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 246 m , what is its area ? | "length = breadth + 23 . therefore , 4 Γ breadth + 2 Γ 23 = 246 m β breadth = 50 m length = 50 + 23 = 73 m area = 73 Γ 50 = 3650 m 2 answer is b ." | a ) 2510 , b ) 3650 , c ) 2530 , d ) 2515 , e ) 2520 | b | rectangle_area(add(divide(subtract(246, multiply(const_2, 23)), const_4), 23), divide(subtract(246, multiply(const_2, 23)), const_4)) | multiply(n0,const_2)|subtract(n1,#0)|divide(#1,const_4)|add(n0,#2)|rectangle_area(#3,#2)| | geometry |
a and b can together finish a work in 30 days . they worked together for 20 days and then b left . after another 20 days , a finished the remaining work . in how many days a alone can finish the job ? | "( a + b ) ' s 20 days work = ( 1 / 30 * 20 ) = 2 / 3 . remaining work = ( 1 - 2 / 3 ) = 1 / 3 . now , 1 / 3 work is done by a in 20 days . whole work will be done by a in ( 20 * 3 ) = 60 days . correct option : d" | a ) 40 , b ) 50 , c ) 54 , d ) 60 , e ) none of these | d | divide(multiply(20, 30), subtract(30, 20)) | multiply(n0,n2)|subtract(n0,n1)|divide(#0,#1)| | physics |
how many numbers between 190 and 580 are divisible by 4,5 and 6 ? | every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | a | subtract(floor(divide(580, lcm(lcm(const_4, add(const_4, const_1)), 6))), floor(divide(190, lcm(lcm(const_4, add(const_4, const_1)), 6)))) | add(const_1,const_4)|lcm(#0,const_4)|lcm(n3,#1)|divide(n1,#2)|divide(n0,#2)|floor(#3)|floor(#4)|subtract(#5,#6) | general |
a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec . what is the length of the platform ? | "speed = 300 / 24 = 25 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 2 = > x = 187.5 m . answer : c" | a ) 389 m , b ) 350 m , c ) 187.5 m , d ) 299 m , e ) 219.5 m | c | subtract(multiply(speed(300, 24), 39), 300) | speed(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | physics |
what percent is 3 % of 5 % ? | "required percentage = 3 % / 5 % * 100 = 3 / 5 * 100 = 60 % answer is a" | a ) 60 % , b ) 50 % , c ) 75 % , d ) 45 % , e ) 30 % | a | multiply(divide(3, 5), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum t of all possible 2 - digit remainders for x / y ? | "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . t = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b" | a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784 | b | divide(59.32, subtract(2, floor(2))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | general |
perimeter of an equilateral and isosceles is 45 and 40 respectively . at least one of the sides of isosceles is equal to the equilateral . what ' s the base of isosceles triangle ? | 10 units as other 2 sides will be 15,15 units . answer : d | ['a ) 7', 'b ) 8', 'c ) 9', 'd ) 10', 'e ) 11'] | d | subtract(40, multiply(divide(45, const_3), const_2)) | divide(n0,const_3)|multiply(#0,const_2)|subtract(n1,#1) | geometry |
kamal obtained 76 , 60 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ? | "sol . average = 76 + 60 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 74 . answer c" | a ) 65 , b ) 69 , c ) 74 , d ) 75 , e ) none | c | divide(add(add(add(add(76, 60), 82), 67), 85), add(const_1, const_4)) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | general |
a train covers a distance of 12 km in 10 min . if it takes 16 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 16 = 320 m . answer : a" | a ) 320 m , b ) 188 m , c ) 120 m , d ) 178 m , e ) 189 m | a | divide(12, subtract(divide(12, 10), 16)) | divide(n0,n1)|subtract(#0,n2)|divide(n0,#1)| | physics |
if 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy . | "12 m + 16 b - - - - - 5 days 13 m + 24 b - - - - - - - 4 days 60 m + 80 b = 52 m + 96 b 8 m = 16 b = > 1 m = 2 b m : b = 2 : 1 answer : b" | a ) 2 : 9 , b ) 2 : 1 , c ) 2 : 7 , d ) 2 : 5 , e ) 2 : 2 | b | divide(subtract(multiply(4, 24), multiply(5, 16)), subtract(multiply(5, 12), multiply(4, 13))) | multiply(n4,n5)|multiply(n1,n2)|multiply(n0,n2)|multiply(n3,n5)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)| | physics |
what least value should be replaced by * in 223 * 431 so the number become divisible by 9 | "explanation : trick : number is divisible by 9 , if sum of all digits is divisible by 9 , so ( 2 + 2 + 3 + * + 4 + 3 + 1 ) = 15 + * should be divisible by 9 , 15 + 3 will be divisible by 9 , so that least number is 3 . answer : option a" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | a | subtract(431, subtract(431, 431)) | subtract(n1,n1)|subtract(n1,#0)| | general |
the cost price of a radio is rs . 1340 and it was sold for rs . 1210 , find the loss % ? | "1340 - - - - 130 100 - - - - ? = > 9 % answer : b" | a ) 18 % , b ) 9 % , c ) 22 % , d ) 24 % , e ) 21 | b | multiply(divide(subtract(1340, 1210), 1340), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain |
the probability that a number selected at random from the first 50 natural numbers is a composite number is ? | "the number of exhaustive events = β΅ β° c β = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . answer : b" | a ) 17 / 65 , b ) 17 / 25 , c ) 17 / 28 , d ) 17 / 65 , e ) 17 / 39 | b | divide(multiply(subtract(multiply(const_6, const_3), const_1), const_2), 50) | multiply(const_3,const_6)|subtract(#0,const_1)|multiply(#1,const_2)|divide(#2,n0)| | probability |
if x : y = 4 : 7 , find the value of ( 6 x + 2 y ) : ( 5 x β y ) | explanation : given : x / y = 4 / 7 ( 6 x + 2 y ) : ( 5 x β y ) = ( 6 * 4 + 2 * 7 ) : ( 5 * 4 β 7 ) 38 : 13 answer : e | a ) 7 : 13 , b ) 38 : 7 , c ) 3 : 13 , d ) 2 : 3 , e ) 38 : 13 | e | divide(add(power(6, 2), 2), add(add(4, 7), 2)) | add(n0,n1)|power(n2,n3)|add(n3,#1)|add(n3,#0)|divide(#2,#3) | general |
ritesh and co . generated revenue of rs . 2,500 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ? | "explanation : given , ritesh and co . generated revenue of rs . 2,500 in 2006 and that this was 12.5 % of the gross revenue . hence , if 2500 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) Γ 2500 . = > 20,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue... | a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these | a | multiply(divide(add(multiply(const_2, multiply(multiply(const_2, add(const_1, const_4)), const_100)), multiply(add(const_1, const_4), const_100)), divide(add(multiply(multiply(const_2, add(const_1, const_4)), const_100), multiply(add(const_2, const_4), const_100)), divide(12.5, const_100))), const_100) | add(const_1,const_4)|add(const_2,const_4)|divide(n2,const_100)|multiply(#0,const_2)|multiply(#0,const_100)|multiply(#1,const_100)|multiply(#3,const_100)|add(#6,#5)|multiply(#6,const_2)|add(#8,#4)|divide(#7,#2)|divide(#9,#10)|multiply(#11,const_100)| | gain |
according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 15 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ? | "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 15 oz can = 300 oz / 15 oz = 20 answer d , 20 cans" | a ) 25 , b ) 34 , c ) 50 , d ) 20 , e ) 100 | d | divide(multiply(6, 200), divide(200, const_10)) | divide(n2,const_10)|multiply(n2,n3)|divide(#1,#0)| | general |
the difference between compound interest and simple interest on an amount of $ 15,000 for 2 years is $ 96 . what is the rate of interest per annum ? | "[ 15000 x ( 1 + r / 100 ) ^ 2 - 15000 ] - [ ( 15000 x r x 2 ) / 100 ] = 96 = = > 15000 [ ( 1 + r / 100 ) ^ 2 - 1 - 2 r / 100 ] = 96 = = > 15000 [ ( ( 100 + r ) ^ 2 - 10000 - ( 200 x r ) ) / 10000 ] = 96 = = > r ^ 2 = ( 96 x 2 ) / 3 = 64 = = > r = 8 . rate = 8 % answer d ) 8 %" | a ) 6 % , b ) 7 % , c ) 9 % , d ) 8 % , e ) 5 % | d | divide(96, subtract(power(add(const_1, divide(15,000, const_100)), 2), add(const_1, multiply(2, divide(15,000, const_100))))) | divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|add(#2,const_1)|power(#1,n1)|subtract(#4,#3)|divide(n2,#5)| | gain |
if x + y = 14 , x - y = 60 , for integers of x and y , x = ? | "x + y = 14 x - y = 60 2 x = 74 x = 37 answer is a" | a ) 37 , b ) 35 , c ) 25 , d ) 20 , e ) 42 | a | divide(add(14, 60), const_2) | add(n0,n1)|divide(#0,const_2)| | general |
if in a race of 100 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by : | "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 100 * 5 ) / 25 = 20 m hence , a beats b by 20 m . answer a" | a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 15 m | a | multiply(divide(subtract(25, 20), 25), 100) | subtract(n2,n1)|divide(#0,n2)|multiply(n0,#1)| | physics |
the speed of a car is 90 km in the first hour and 30 km in the second hour . what is the average speed of the car ? | "explanation : s = ( 90 + 30 ) / 2 = 60 kmph b )" | a ) 50 kmph , b ) 60 kmph , c ) 75 kmph , d ) 85 kmph , e ) 90 kmph | b | divide(add(90, 30), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
suzie β s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 580 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 800 . how much more do pairs of boots cost than pairs of shoes... | "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 580 . . . eq 1 8 x + 32 y = 800 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1160 8 x = 800 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 800 . . . then we get 32 y = 720 then y = 22.50 differenece between x and y is 12.5... | a ) $ 10.50 , b ) $ 12.50 , c ) $ 11.50 , d ) $ 16.50 , e ) $ 9.50 | b | divide(subtract(580, multiply(22, divide(subtract(multiply(580, const_2), 800), subtract(multiply(22, const_2), 8)))), 16) | multiply(n2,const_2)|multiply(n0,const_2)|subtract(#0,n5)|subtract(#1,n3)|divide(#2,#3)|multiply(n0,#4)|subtract(n2,#5)|divide(#6,n1)| | general |
the speed of a boat in still water in 65 km / hr and the rate of current is 15 km / hr . the distance travelled downstream in 25 minutes is : | "explanation : speed downstream = ( 65 + 15 ) = 80 kmph time = 25 minutes = 25 / 60 hour = 5 / 12 hour distance travelled = time Γ speed = ( 2 / 5 ) Γ 80 = 33.33 km answer : option c" | a ) 55.55 km , b ) 44.44 km , c ) 33.33 km , d ) 22.22 km , e ) 11.11 km | c | multiply(add(65, 15), divide(25, const_60)) | add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)| | physics |
( β 27 + β 243 ) / β 48 = ? | "( β 27 + β 243 ) / β 48 = ( 3 β 3 + 9 β 3 ) / 4 β 3 = 12 β 3 / 4 β 3 = 3 . hence , the correct answer is e ." | a ) 2 β 2 , b ) 2 β 3 , c ) 3 β 2 , d ) 3 β 3 , e ) 3 | e | divide(add(sqrt(27), sqrt(243)), sqrt(48)) | sqrt(n0)|sqrt(n1)|sqrt(n2)|add(#0,#1)|divide(#3,#2)| | general |
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ? | "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 answer : b" | a ) 2887 , b ) 444 , c ) 877 , d ) 278 , e ) 178 | b | add(multiply(divide(60, subtract(21, 16)), 16), multiply(divide(60, subtract(21, 16)), 21)) | subtract(n1,n0)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(#2,#3)| | physics |
the volume of a cube is 1728 cc . find its surface ? | a 3 = 1728 = > a = 12 6 a 2 = 6 * 12 * 12 = 864 answer : a | ['a ) 864', 'b ) 209', 'c ) 278', 'd ) 276', 'e ) 280'] | a | surface_cube(cube_edge_by_volume(1728)) | cube_edge_by_volume(n0)|surface_cube(#0) | geometry |
you hold some gold in a vault as an investment . over the past year the price of gold increases by 50 % . in order to keep your gold in the vault , you must pay 8 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year . | "( 100 % + 50 % ) * ( 100 % - 8 % ) = 150 * 0.92 = 138 % an increase of 38 % your gold holdings have increased in value by 38 % . the answer is d" | a ) 35 % , b ) 36 % , c ) 37 % , d ) 38 % , e ) 40 % | d | subtract(50, divide(50, 8)) | divide(n0,n1)|subtract(n0,#0)| | gain |
18 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ? | "alcohol in the 18 litres of mix . = 20 % of 18 litres = ( 20 * 18 / 100 ) = 3.6 litres water in it = 18 - 3.6 = 14.4 litres new quantity of mix . = 18 + 3 = 21 litres quantity of alcohol in it = 3.6 litres percentage of alcohol in new mix . = 3.6 * 100 / 21 = 17.14 % answer is b" | a ) 16.67 % , b ) 17.14 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 % | b | multiply(divide(subtract(add(18, 3), add(multiply(divide(subtract(const_100, 20), const_100), 18), 3)), add(18, 3)), const_100) | add(n0,n2)|subtract(const_100,n1)|divide(#1,const_100)|multiply(n0,#2)|add(n2,#3)|subtract(#0,#4)|divide(#5,#0)|multiply(#6,const_100)| | gain |
two isosceles triangles have equal vertical angles and their areas are in the ratio 4 : 9 . find the ratio of their corresponding heights . | we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 4 / 9 - - > height / height = 2 / 3 . answer : e . | ['a ) 4 / 5', 'b ) 5 / 4', 'c ) 3 / 2', 'd ) 5 / 7', 'e ) 2 / 3'] | e | divide(sqrt(const_4), sqrt(9)) | sqrt(const_4)|sqrt(n1)|divide(#0,#1) | geometry |
in a certain company , the ratio of male to female employees is 7 : 8 . if 3 more men were hired , this ratio would increase to 8 : 9 . how many male employees are there in the company ? | another approach is to use two variables . let m = present number of males let f = present number of females the ratio of male to female employees is 7 : 8 so , m / f = 7 / 8 cross multiply to get 7 f = 8 m if 3 more men were hired , this ratio would increase to 8 : 9 so , ( m + 3 ) / f = 8 / 9 cross multiply to get 9 ... | a ) 6 , b ) 21 , c ) 27 , d ) 189 , e ) 192 | d | divide(multiply(divide(3, subtract(divide(8, 9), divide(7, 8))), 7), 8) | divide(n1,n4)|divide(n0,n1)|subtract(#0,#1)|divide(n2,#2)|multiply(n0,#3)|divide(#4,n1) | general |
a guy was asked to specify his age in years . he said , β take my age 5 years hence , multiply it by 5 and subtract 5 times of my age 5 years ago and you will know my age . β what was the age of that guy ? | current age of the guy = a years . then , 5 ( a + 5 ) β 5 ( a β 5 ) = a ( 5 a + 25 ) β ( 5 a β 25 ) = a a = 50 e | a ) 18 , b ) 15 , c ) 33 , d ) 39 , e ) 50 | e | add(multiply(5, 5), multiply(5, 5)) | multiply(n0,n0)|add(#0,#0) | general |
of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 17 boys and 43 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ? | "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you ... | a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | a | subtract(subtract(17, subtract(10, 4)), 6) | subtract(n2,n7)|subtract(n4,#0)|subtract(#1,n6)| | other |
ram , who is half as efficient as krish , will take 27 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ? | number of days taken by ram to complete task = 27 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 27 days is 27 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work d... | a ) 16 days , b ) 12 days , c ) 9 days , d ) 6 days , e ) 18 days | c | inverse(add(divide(const_1, 27), divide(const_1, divide(27, const_2)))) | divide(const_1,n0)|divide(n0,const_2)|divide(const_1,#1)|add(#0,#2)|inverse(#3) | physics |
what is the compound interest on rs : 60,000 for 4 months at the rate of 5 % per annum | "it is monthly compound rate = 5 / 12 % per month 60000 * ( 1 + 5 / 1200 ) ^ 4 - 60000 = 1006.13 answer : c" | a ) 1058.24 , b ) 2006.24 , c ) 1006.13 , d ) 1015.24 , e ) 1014.24 | c | divide(multiply(multiply(multiply(const_3, const_100), const_100), multiply(5, divide(4, multiply(4, const_3)))), const_100) | multiply(const_100,const_3)|multiply(const_3,n1)|divide(n1,#1)|multiply(#0,const_100)|multiply(n2,#2)|multiply(#3,#4)|divide(#5,const_100)| | gain |
two persons a and b can complete a piece of work in 40 days and 60 days respectively . if they work together , what part of the work will be completed in 6 days ? | "a ' s one day ' s work = 1 / 40 b ' s one day ' s work = 1 / 60 ( a + b ) ' s one day ' s work = 1 / 40 + 1 / 60 = 1 / 24 the part of the work completed in 6 days = 6 ( 1 / 24 ) = 1 / 4 . answer : e" | a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 4 | e | multiply(6, add(divide(const_1, 40), divide(const_1, 60))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)| | physics |
at what price must an article costing rs . 95 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ? | "cp = 95 sp = 47.50 * ( 125 / 100 ) = 118.125 mp * ( 95 / 100 ) = 118.125 mp = 125 answer : b" | a ) 130 , b ) 125 , c ) 145 , d ) 135 , e ) 144 | b | divide(multiply(add(95, divide(multiply(95, 25), const_100)), const_100), subtract(const_100, 5)) | multiply(n0,n2)|subtract(const_100,n1)|divide(#0,const_100)|add(n0,#2)|multiply(#3,const_100)|divide(#4,#1)| | gain |
a β sophie germain β prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 9 is | "in that case , the sophie prime numbers greater than 9 are 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be d" | a ) 3 , b ) 7 , c ) 21 , d ) 189 , e ) 267 | d | multiply(multiply(multiply(subtract(add(add(subtract(9, 1), add(2, 1)), add(2, 1)), const_10), subtract(add(multiply(2, add(subtract(9, 1), add(2, 1))), 1), const_10)), add(2, 1)), subtract(add(multiply(2, add(add(add(subtract(9, 1), add(2, 1)), add(2, 1)), add(2, 1))), 1), multiply(2, const_10))) | add(n0,n1)|multiply(n0,const_10)|subtract(n2,n1)|add(#0,#2)|add(#3,#0)|multiply(n0,#3)|add(n1,#5)|add(#4,#0)|subtract(#4,const_10)|multiply(n0,#7)|subtract(#6,const_10)|add(n1,#9)|multiply(#8,#10)|multiply(#0,#12)|subtract(#11,#1)|multiply(#13,#14)| | general |
a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 3 km on foot . his total journey is | "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 3 = x 5 x + 18 = 6 x x = 18 km answer : option a" | a ) 18 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km | a | multiply(3, 3) | multiply(n3,n4)| | general |
the sum of all consecutive odd integers from β 27 to 37 , inclusive , is | "the sum of the odd numbers from - 27 to + 27 is 0 . let ' s add the remaining numbers . 29 + 31 + 33 + 35 + 37 = 5 ( 33 ) = 165 the answer is d ." | a ) 110 , b ) 135 , c ) 150 , d ) 165 , e ) 235 | d | add(add(add(add(27, const_2), add(add(27, const_2), const_2)), add(add(add(27, const_2), const_2), const_2)), 37) | add(n0,const_2)|add(#0,const_2)|add(#0,#1)|add(#1,const_2)|add(#2,#3)|add(n1,#4)| | physics |
if 20 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ? | "let 20 % of a = 1 / 3 b then 20 a / 100 = 1 b / 3 a / 5 = b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is c" | a ) 2 : 5 , b ) 1 : 4 , c ) 5 : 3 , d ) 6 : 11 , e ) 2 : 3 | c | divide(divide(const_1, const_4), divide(20, const_100)) | divide(const_1,const_4)|divide(n0,const_100)|divide(#0,#1)| | general |
a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ? | speed on return trip = 150 % of 60 = 90 km / hr . average speed of trip = 60 + 90 / 2 = 150 / 2 = 75 km / hr answer : b | a ) 33 , b ) 75 , c ) 48 , d ) 99 , e ) 21 | b | divide(add(multiply(60, add(const_1, divide(50, const_100))), 60), const_2) | divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)|add(n0,#2)|divide(#3,const_2) | general |
( 1.1 + 1.1 + 1.1 + 1.1 ) x 1.1 x 1.1 = ? = ? x 0.121 | "explanation : ? = ( 1.1 + 1.1 + 1.1 + 1.1 ) x 1.1 x 1.1 / 0.121 = ( 4.4 x 1.1 x 1.1 ) / 0.121 = 44 answer : option c" | a ) 54 , b ) 33 , c ) 44 , d ) 22 , e ) 26 | c | subtract(divide(multiply(1.1, add(1.1, const_1)), const_2), divide(multiply(subtract(1.1, const_1), 1.1), const_2)) | add(n3,const_1)|subtract(n0,const_1)|multiply(n3,#0)|multiply(n0,#1)|divide(#2,const_2)|divide(#3,const_2)|subtract(#4,#5)| | general |
how much is 85 % of 40 is greater than 4 / 5 of 25 ? | "( 85 / 100 ) * 40 β ( 4 / 5 ) * 25 = 14 answer : b" | a ) 22 , b ) 14 , c ) 88 , d ) 12 , e ) 66 | b | subtract(multiply(40, divide(85, const_100)), multiply(divide(4, 5), 25)) | divide(n0,const_100)|divide(n2,n3)|multiply(n1,#0)|multiply(n4,#1)|subtract(#2,#3)| | general |
( 23341379 x 72 ) = ? | "explanation : 23341379 x 72 = 23341379 ( 70 + 2 ) = ( 23341379 x 70 ) + ( 23341379 x 2 ) = 1633896530 + 46682758 = 1680579288 . answer : option a" | a ) 1680579288 , b ) 1223441288 , c ) 2142579288 , d ) 2142339288 , e ) none of these | a | multiply(23341379, power(add(const_4, const_1), const_4)) | add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)| | general |
in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ? | the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 10.50 = $ 347.20 the answer is d . | a ) $ 338.50 , b ) $ 341.40 , c ) $ 344.30 , d ) $ 347.20 , e ) $ 350.10 | d | add(add(multiply(multiply(add(divide(multiply(120, 65), const_100), 65), 2), 0.7), multiply(multiply(3, 65), 0.7)), multiply(2.1, add(3, 2))) | add(n2,n3)|multiply(n4,n5)|multiply(n2,n4)|divide(#1,const_100)|multiply(n1,#2)|multiply(n0,#0)|add(n4,#3)|multiply(n3,#6)|multiply(n1,#7)|add(#8,#4)|add(#9,#5) | general |
following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 15 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ? | price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 15 / 1.5 = 10 total price = 8 + 10 = 18 d is the answer | a ) 11 . , b ) 12 . , c ) 13 . , d ) 18 . , e ) 14.5 | d | add(divide(multiply(10, const_100), add(const_100, 25)), divide(multiply(15, const_100), add(const_100, 50))) | add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|multiply(n1,const_100)|divide(#2,#0)|divide(#3,#1)|add(#4,#5) | general |
the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 11 days , how large is the colony today ? | "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 ans : e" | a ) 512 , b ) 768 , c ) 4096 , d ) 2048 , e ) 1024 | e | subtract(power(2, add(9, const_1)), const_1) | add(n0,const_1)|power(n1,#0)|subtract(#1,const_1)| | physics |
in how many ways can an answer key for a quiz be written if the quiz contains 4 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ? | "there are 2 ^ 4 = 16 possibilities for the true - false answers . however we need to remove two cases for tttt and ffff . there are 4 * 4 = 16 possibilities for the multiple choice questions . the total number of possibilities is 14 * 16 = 224 . the answer is c ." | a ) 120 , b ) 190 , c ) 224 , d ) 298 , e ) 256 | c | multiply(subtract(power(2, 4), 2), multiply(4, 4)) | multiply(n2,n2)|power(n1,n0)|subtract(#1,n1)|multiply(#0,#2)| | general |
in what time will a train 135 m long cross an electric pole , it its speed be 140 km / hr ? | "speed = 140 * 5 / 18 = 38.8 m / sec time taken = 135 / 38.8 = 3.5 sec . answer : a" | a ) 3.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1 | a | divide(135, multiply(140, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
a man buys a cycle for rs . 1200 and sells it at a loss of 10 % . what is the selling price of the cycle ? | "s . p . = 90 % of rs . 1200 = rs . 90 x 1200 / 100 = rs . 1080 answer : option a" | a ) s . 1080 , b ) s . 1140 , c ) s . 1090 , d ) s . 1202 , e ) s . 1092 | a | divide(multiply(subtract(const_100, 10), 1200), const_100) | subtract(const_100,n1)|multiply(n0,#0)|divide(#1,const_100)| | gain |
the average age of 30 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher . | explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 30 ) = 45 years answer : c | a ) 43 , b ) 44 , c ) 45 , d ) 47 , e ) 48 | c | subtract(add(add(multiply(30, 14), 15), 30), multiply(30, 14)) | multiply(n0,n1)|add(n2,#0)|add(n0,#1)|subtract(#2,#0) | general |
john and lewis leave city a for city b simultaneously at 6 a . m in the morning driving in two cars at speeds of 40 mph and 60 mph respectively . as soon as lewis reaches city b , he returns back to city a along the same route and meets john on the way back . if the distance between the two cities is 240 miles , how fa... | time taken by lewis to reach city b = 240 / 60 = 4 hours in 4 hours , john travels 40 * 4 = 160 miles so distance at which they meet should be greater than 160 miles . only b satisfies . answer is b . | a ) 150 miles , b ) 160 miles , c ) 140 miles , d ) 170 miles , e ) 200 miles | b | multiply(40, divide(240, 60)) | divide(n3,n2)|multiply(n1,#0) | physics |
a salesman Γ’ β¬ β’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 700 more than that by the previous schema , his sales were worth ? | [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 700 x = 8000 answer a | a ) s . 8,000 , b ) s . 9,000 , c ) s . 20,000 , d ) s . 10,000 , e ) s . 50,000 | a | divide(divide(subtract(subtract(1000, multiply(4000, divide(2.5, const_100))), 700), subtract(divide(5, const_100), divide(2.5, const_100))), 1000) | divide(n2,const_100)|divide(n0,const_100)|multiply(n3,#0)|subtract(#1,#0)|subtract(n1,#2)|subtract(#4,n4)|divide(#5,#3)|divide(#6,n1) | general |
the average weight of 8 persons increases by 3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 65 + 24 ) kg = 89 kg . answer : d | a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 89 kg , e ) 25 kg | d | add(65, multiply(8, 3)) | multiply(n0,n1)|add(n2,#0) | general |
in a village of 100 households , 85 have at least one dvd player , 90 have at least one cell phone , and 55 have at least one mp 3 player . if x and y are respectively the greatest and lowest possible number of households that have all 3 of these devices , x β y is : | am i missing something here ? ? ? it seems straightforward . . . . . . the obvious maximum that have all 3 is 55 , because you are limited by the smallest number . the minimum is simply the sum of the max of each people who dont have the product , so : 100 - 90 = 10 do n ' t have cell 100 - 85 = 15 do n ' t have dvd an... | a ) 65 , b ) 55 , c ) 45 , d ) 35 , e ) 25 | e | subtract(55, subtract(100, add(subtract(100, 55), add(subtract(100, 85), subtract(100, 90))))) | subtract(n0,n1)|subtract(n0,n2)|subtract(n0,n3)|add(#0,#1)|add(#3,#2)|subtract(n0,#4)|subtract(n3,#5) | general |
of the diplomats attending a summit conference , 14 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ? | { total } = { french } + { russian } - { both } + { neither } { total } = 14 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 180 . answer : e . | a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 180 | e | divide(subtract(32, 14), subtract(divide(20, const_100), divide(10, const_100))) | divide(n2,const_100)|divide(n3,const_100)|subtract(n1,n0)|subtract(#0,#1)|divide(#2,#3) | other |
in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 80 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the ... | "the percent of tagged fish in the second catch is 2 / 80 * 100 = 2.5 % . we are told that 2.5 % approximates the percent of tagged fish in the pond . since there are 80 tagged fish , then we have 0.025 x = 80 - - > x = 3,200 . answer : d ." | a ) 400 , b ) 625 , c ) 1250 , d ) 3200 , e ) 10 000 | d | divide(80, divide(2, 80)) | divide(n2,n1)|divide(n0,#0)| | gain |
the cost price of an article is 25 % of the marked price . calculate the gain percent after allowing a discount of 50 % . | "sol . let marked price = rs . 100 . then , c . p . = rs . 25 . s . p = rs . 50 . Γ’ Λ Β΄ gain % = [ 25 / 25 * 100 ] % = 100.0 % . answer c" | a ) 25 % , b ) 50 % , c ) 100 % , d ) 150 % , e ) none | c | multiply(subtract(divide(subtract(const_100, 50), 25), const_1), const_100) | subtract(const_100,n1)|divide(#0,n0)|subtract(#1,const_1)|multiply(#2,const_100)| | gain |
the total marks obtained by a student in mathematics and physics is 40 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . | "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 40 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 40 + 20 ) / 2 = 30 . answer : e" | a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 30 | e | divide(add(40, 20), const_2) | add(n0,n1)|divide(#0,const_2)| | general |
anup manages to draw 7 circles of equal radii with their centres on the diagonal of a square such that two extreme circles touch two sides of the square and each middle circle touches two circles on either side . find the ratio of radius of the circles to the side of the square . | diagonal of square = ( 2 * r ) * 7 + ( 2 ^ ( 1 / 2 ) * r - r ) * 2 diagonal has 7 squares diameters length + little distance between extreme squares to the end point [ form a square of side r from center of extreme circle to the extreme end to find distance ] distance = 2 ^ ( 1 / 2 ) * r - r d = a * 2 ^ ( 1 / 2 ) a = 2... | ['a ) 1 : ( 2 + 6 ^ ( 1 / 2 ) )', 'b ) 1 : ( 4 + 7 ^ ( 1 / 3 ) )', 'c ) ( 2 + 7 ^ ( 1 / 2 ) ) : 1', 'd ) ( 2 + 7 ^ ( 1 / 2 ) ) : 2', 'e ) none of these'] | e | divide(sqrt(const_2), multiply(const_2, add(7, sqrt(const_2)))) | sqrt(const_2)|add(n0,#0)|multiply(#1,const_2)|divide(#0,#2) | geometry |
a light flashes every 20 seconds , how many times will it flash in ? of an hour ? | "1 flash = 20 sec for 1 min = 3 flashes so for 1 hour = 3 * 60 = 180 flashes . answer : d" | a ) 550 , b ) 600 , c ) 650 , d ) 180 , e ) 750 | d | divide(const_3600, 20) | divide(const_3600,n0)| | physics |
the cost of 3 pens and 5 pencils is rs . 240 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ? | "explanation : let the cost of one pen is β 5 x β and pencil is β x β 3 x 5 x + 5 x = rs . 240 15 x + 5 x = rs . 240 x = 240 / 20 = 12 : . cost of 1 pen = 5 x = 5 x 12 = 60 : . cost of 12 pens , i . e . ( one dozen ) = 60 x 12 = rs . 720 answer : option b" | a ) rs . 200 , b ) rs . 720 , c ) rs . 300 , d ) rs . 150 , e ) none of these | b | multiply(multiply(3, const_4), divide(240, add(3, 1))) | add(n0,n4)|multiply(n0,const_4)|divide(n2,#0)|multiply(#2,#1)| | other |
the regular price per can of a certain brand of soda is $ 0.55 . if the regular price per can is discounted 25 percent when the soda is purchased in 24 - can cases , what is the price of 70 cans of this brand of soda purchased in 24 - can cases ? | "the discounted price of one can of soda is ( 0.75 ) ( $ 0.55 ) , or $ 0.4125 therefore , the price of 70 cans of soda at the discounted price would be ( 70 ) ( $ 0.4125 ) = 28.875 answer : e" | a ) $ 16.32 , b ) $ 18.00 , c ) $ 21.60 , d ) $ 24.48 , e ) $ 28.87 | e | multiply(divide(subtract(const_100, 25), const_100), multiply(0.55, 70)) | multiply(n0,n3)|subtract(const_100,n1)|divide(#1,const_100)|multiply(#2,#0)| | gain |
the ratio between the number of sheep and the number of horses at the stewart farm is 2 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ? | "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 2 x = 2 * 8 = 16 . hence b" | a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 60 | b | multiply(divide(divide(add(add(multiply(multiply(const_4, const_2), const_10), multiply(multiply(const_4, const_2), const_100)), multiply(const_12, const_1000)), 230), 7), 2) | multiply(const_2,const_4)|multiply(const_1000,const_12)|multiply(#0,const_10)|multiply(#0,const_100)|add(#2,#3)|add(#4,#1)|divide(#5,n2)|divide(#6,n1)|multiply(n0,#7)| | other |
the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ? | "manager ' s monthly salary rs . ( 1600 * 21 - 1500 * 20 ) = rs . 3600 . answer : a" | a ) 3600 , b ) 2988 , c ) 2789 , d ) 2887 , e ) 1297 | a | subtract(multiply(add(1500, 100), add(20, const_1)), multiply(1500, 20)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
a call center has two teams . each member of team a was able to process 6 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ? | "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 6 calls , so total calls for team a = 30 fraction for team b = 40 / ( 40 + 30 ) = 4 / 7 = answer = c" | a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 7 , d ) 1 / 2 , e ) 1 / 5 | c | divide(multiply(8, 5), add(multiply(8, 5), multiply(5, 6))) | multiply(n1,n3)|multiply(n0,n1)|add(#0,#1)|divide(#0,#2)| | general |
after decreasing 24 % in the price of an article costs rs . 1064 . find the actual cost of an article ? | "cp * ( 76 / 100 ) = 1064 cp = 14 * 100 = > cp = 1400 answer : e" | a ) 1667 , b ) 6789 , c ) 1200 , d ) 6151 , e ) 1400 | e | divide(1064, subtract(const_1, divide(24, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | gain |
a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is : | "explanation clearly , l = ( 48 β 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer b" | a ) 4830 , b ) 5120 , c ) 6420 , d ) 8960 , e ) none | b | volume_rectangular_prism(subtract(48, multiply(8, const_2)), subtract(36, multiply(8, const_2)), 8) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|volume_rectangular_prism(n2,#1,#2)| | geometry |
300 Γ ? + ( 12 + 4 ) Γ 1 / 8 = 602 | explanation : = > 300 Γ ? + ( 12 + 4 ) Γ 1 / 8 = 602 = > 300 Γ ? = 602 - ( 12 + 4 ) Γ 1 / 8 = > 300 Γ ? = 602 - 2 = 600 = > ? = 600 / 300 = 2 answer : option d | a ) a ) 4 , b ) b ) 3 , c ) c ) 5 , d ) d ) 2 , e ) e ) 8 | d | divide(subtract(602, multiply(add(12, 4), divide(1, 8))), 300) | add(n1,n2)|divide(n3,n4)|multiply(#0,#1)|subtract(n5,#2)|divide(#3,n0) | general |
if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 36 ) which of these integers could be the value of z ? | "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( β which of these integers β¦ β ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 36 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 37 incorrect c . 2 / 2 = 2 / 3 + 2 / 38 incorrect d . 2 / 3 ... | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 6 | e | divide(36, add(add(2, 2), 1)) | add(n0,n0)|add(n2,#0)|divide(n4,#1)| | general |
girl and boy together can complete a piece of work in 35 days while girl alone can complete the same work in 60 days . boy alone will be able to complete the same working in : | subtraction of fraction ab β cd = ad β cbbd girl and boy finish one work with company = 35 days ( girl + boy ) β² s one day β s work = 135 girl alone finish the same work = 60 days girl β² s one day β s work = 160 b β² s one day β s work = ( a + b ) β² s one day β s work - a β² s one day β s work 135 β 160 = 184 hence b alo... | a ) 72 , b ) 75 , c ) 84 , d ) 88 , e ) 90 | b | subtract(inverse(subtract(inverse(35), inverse(60))), const_10) | inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)|subtract(#3,const_10) | physics |
what is 15 percent of 34 | "explanation : it will be 15 % of 34 = ( 15 / 100 ) * 34 = 5.10 answer : option a" | a ) 5.1 , b ) 4.1 , c ) 3.1 , d ) 2.1 , e ) none of these | 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 |
rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ? | "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 140 x = 1000 answer : d" | a ) 2288 , b ) 27669 , c ) 1766 , d ) 1000 , e ) 2871 | d | divide(subtract(140, divide(multiply(6, 2500), const_100)), subtract(divide(5, const_100), divide(6, const_100))) | divide(n1,const_100)|divide(n2,const_100)|multiply(n0,n2)|divide(#2,const_100)|subtract(#0,#1)|subtract(n3,#3)|divide(#5,#4)| | gain |
the difference between the local value and the face value of 7 in the numeral 32675149 is ? | "( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 d )" | a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of these | d | subtract(multiply(7, const_1000), 7) | multiply(n0,const_1000)|subtract(#0,n0)| | general |
the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 42 , what is the greatest possible value of the median of the 5 integers ? | we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 42 , it is 26 more than 16 . we need r to be max... | a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22 | a | subtract(divide(subtract(multiply(16, 5), 42), const_2), const_2) | multiply(n0,n1)|subtract(#0,n2)|divide(#1,const_2)|subtract(#2,const_2) | general |
a rectangular field has a length 10 meters more than it is width . if the area of the field is 231 , what is the length ( in meters ) of the rectangular field ? | "area = l * w = ( l ) * ( l - 10 ) = 231 trial and error : 20 * 10 = 200 ( too low ) 21 * 11 = 231 the length is 21 meters . the answer is a ." | a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29 | a | add(10, add(const_0_25, add(const_0_33, divide(divide(231, 10), const_2)))) | divide(n1,n0)|divide(#0,const_2)|add(#1,const_0_33)|add(#2,const_0_25)|add(n0,#3)| | geometry |
a cycle is bought for rs . 600 and sold for rs . 1080 , find the gain percent ? | "600 - - - - 180 100 - - - - ? = > 80 % answer : d" | a ) 22 , b ) 20 , c ) 90 , d ) 80 , e ) 11 | d | multiply(divide(subtract(1080, 600), 600), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
how many integers are between 3 and 86 / 7 , inclusive ? | "86 / 7 = 12 . xx we are not concerned about the exact value of 86 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 3 and 86 / 7 would be 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 total number of integers = 10 option c if we need to find the ... | a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | c | add(subtract(divide(86, 7), 3), const_1) | divide(n1,n2)|subtract(#0,n0)|add(#1,const_1)| | general |
a man goes downstream at 15 kmph , and upstream 8 kmph . the speed of the stream is | "speed of the stream = 1 / 2 ( 15 - 8 ) kmph = 3.5 kmph . correct option : b" | a ) 0 kmph , b ) 3.5 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph | b | divide(subtract(15, 8), const_2) | subtract(n0,n1)|divide(#0,const_2)| | physics |
if 12 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is | d for me 11 people with 1 $ each - > maximum = 9 | a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 9.00 , e ) $ 20.00 | d | subtract(20, multiply(subtract(12, const_1), 1)) | subtract(n0,const_1)|multiply(n2,#0)|subtract(n1,#1) | general |
the diagonals of a rhombus are 12 cm and 20 cm . find its area ? | "1 / 2 * 12 * 20 = 120 answer : c" | a ) 329 , b ) 288 , c ) 120 , d ) 238 , e ) 31 | c | rhombus_area(12, 20) | rhombus_area(n0,n1)| | geometry |
the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 76,875 , how much profit did the business make ? | "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 76,875 p = $ 123,000 the answer is e ." | a ) $ 98,000 , b ) $ 106,000 , c ) $ 112,000 , d ) $ 118,000 , e ) $ 123,000 | e | divide(multiply(const_100, multiply(const_100, add(const_1, 4))), add(divide(25, const_100), multiply(multiply(divide(25, const_100), subtract(const_1, divide(25, const_100))), const_2))) | add(const_1,n1)|divide(n0,const_100)|multiply(#0,const_100)|subtract(const_1,#1)|multiply(#2,const_100)|multiply(#1,#3)|multiply(#5,const_2)|add(#1,#6)|divide(#4,#7)| | gain |
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