Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 164 | correct stringclasses 5
values | annotated_formula stringlengths 7 1.65k | linear_formula stringlengths 8 925 | category stringclasses 6
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find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 100 of money ? | "p = 100 ( 100 / 10 ) 2 = > p = 2000 answer : e" | a ) 1500 , b ) 6000 , c ) 2500 , d ) 1400 , e ) 2000 | e | multiply(multiply(divide(100, multiply(10, 2)), const_100), multiply(10, 2)) | multiply(n0,n1)|divide(n2,#0)|multiply(#1,const_100)|multiply(#2,#0)| | general | E |
what is the minimum value of | x - 4 | + | x + 7 | + | x - 5 | ? | "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 7 | > = 0 - - > minimum occurs at x = - 7 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 7 - - > result = 11 + 0 + 12 = 23 . also any negative value will pu... | a ) - 3 , b ) 3 , c ) 5 , d ) - 12 , e ) 12 | e | add(7, 5) | add(n1,n2)| | general | E |
45 x ? = 60 % of 900 | "answer let 45 x a = ( 60 x 900 ) / 100 ∴ a = ( 60 x 9 ) / 45 = 12 correct option : b" | a ) 16.2 , b ) 12 , c ) 5 , d ) 500 , e ) none | b | divide(multiply(divide(60, const_100), 900), 45) | divide(n1,const_100)|multiply(n2,#0)|divide(#1,n0)| | general | B |
the area of a square field is 900 km 2 . how long will it take for a horse to run around at the speed of 12 km / h ? | explanation area of field = 900 km 2 . then , each side of field = √ 900 = 30 km distance covered by the horse = perimeter of square field = 30 × 4 = 120 km ∴ time taken by horse = distances / peed = 120 / 12 = 10 h answer b | ['a ) 12 h', 'b ) 10 h', 'c ) 8 h', 'd ) 6 h', 'e ) none of these'] | b | divide(multiply(const_4, sqrt(900)), 12) | sqrt(n0)|multiply(#0,const_4)|divide(#1,n2) | geometry | B |
cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ? | "2 % is 2 % - points below 4 % and 11 % is 7 % - points above 4 % . the ratio of a : b should be 2 : 7 . the answer is c ." | a ) 2 : 5 , b ) 1 : 3 , c ) 2 : 7 , d ) 3 : 4 , e ) 1 : 5 | c | divide(subtract(4, 2), subtract(11, 4)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | general | C |
a vessel of capacity 45 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ? | "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 45 , y = 9 and n = 2 . hence , quantit... | a ) 28.8 , b ) 72.9 , c ) 38.3 , d ) 78.3 , e ) 79.3 | a | subtract(subtract(45, multiply(const_3, const_3)), multiply(divide(subtract(45, multiply(const_3, const_3)), 45), multiply(const_3, const_3))) | multiply(const_3,const_3)|subtract(n0,#0)|divide(#1,n0)|multiply(#2,#0)|subtract(#1,#3)| | physics | A |
the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 44 degrees . find the temperature on friday ? | "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 44 tu + w + th = 192 - 44 = 148 f = 184 – 148 = 36 answer : c" | a ) 65 degrees , b ) 73 degrees , c ) 36 degrees , d ) 34 degrees , e ) 74 degrees | c | subtract(44, subtract(multiply(48, const_4), multiply(46, const_4))) | multiply(n0,const_4)|multiply(n1,const_4)|subtract(#0,#1)|subtract(n2,#2)| | general | C |
in a mixed college 160 students are there in one class . out of this 160 students 5 / 8 students are girls . how many boys are there ? | "total number of students : 160 total girls : 160 * 5 / 8 = 100 total boys : 160 - 100 = 60 answer is b" | a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140 | b | multiply(divide(160, 8), const_3) | divide(n0,n3)|multiply(#0,const_3)| | general | B |
how many positive integers less than 7,000 are there in which the sum of the digits equals 5 ? | "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x... | a ) 52 , b ) 54 , c ) 56 , d ) 58 , e ) 60 | c | divide(factorial(subtract(add(const_4, 5), const_1)), multiply(factorial(5), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general | C |
triangle atriangle b are similar triangles with areas 1536 units square and 1734 units square respectively . the ratio of there corresponding height would be | "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 1536 / 1734 ( x ^ 2 / y ^ 2 ) = ( 16 * 16 * 6 ) / ( 17 * 17 * 7 ) ( x ^ 2 / y ^ 2 ) = 16 ^ 2 / 17 ^ 2 x / y = 16 / 17 ans = d" | a ) 9 : 10 , b ) 17 : 19 , c ) 23 : 27 , d ) 16 : 17 , e ) 15 : 23 | d | sqrt(divide(1536, 1734)) | divide(n0,n1)|sqrt(#0)| | geometry | D |
a train speeds past a pole in 23 seconds and a platform 125 m long in 33 seconds . its length is ? | "let the length of the train be x meters and its speed be y m / sec . they , x / y = 23 = > y = x / 23 x + 125 / 33 = x / 23 x = 287.5 m . answer : b" | a ) 275 , b ) 287.5 , c ) 288 , d ) 233.5 , e ) 245.6 | b | multiply(125, subtract(const_2, const_1)) | subtract(const_2,const_1)|multiply(n1,#0)| | physics | B |
in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number of employees who take the subway to work ? | "let part time emp = x let full time emp = y then , 48 = x + y . . . . . . . . . ( 1 ) ( 1 / 3 ) x + ( 1 / 4 ) y = no . of ppl taking the subway 4 x + 3 y / 12 = no . of ppl taking the subway using 1 x / 12 + 3 * 48 / 12 = no . of ppl taking the subway so , the minimum value of x has to be 12 . hence to maximize the no... | a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16 | d | add(divide(multiply(48, 3), multiply(3, 4)), divide(subtract(48, multiply(3, 4)), divide(multiply(48, 3), multiply(3, 4)))) | multiply(n0,n2)|multiply(n2,n4)|divide(#0,#1)|subtract(n0,#1)|divide(#3,#2)|add(#2,#4)| | general | D |
a part - time employee whose hourly wage was increased by 50 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ? | "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.5 x now we need to find number of hours worked so that x * y = 1.5 x * z i . e z = 1 / 1.5 y = 2 / 3 y % decrease = ( y - 2 / 3 y ) / y * 100 = 100 / 3 = 33.33 % . thus my answer is e .... | a ) 9 , b ) 13 , c ) 17 , d ) 20 , e ) 33.33 | e | multiply(divide(const_1, multiply(divide(add(50, const_100), const_100), 50)), const_100) | add(n0,const_100)|divide(#0,const_100)|multiply(#1,n0)|divide(const_1,#2)|multiply(#3,const_100)| | general | E |
a 300 m long train crosses a platform in 33 sec while it crosses a signal pole in 18 sec . what is the length of the platform ? | "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 33 = 50 / 3 = > x = 250 m . answer : b" | a ) 286 m , b ) 250 m , c ) 277 m , d ) 278 m , e ) 267 m | b | subtract(multiply(speed(300, 18), 33), 300) | speed(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | physics | B |
the area of a rectangular plot is 23 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ? | "l × b = 23 × b ∴ l = 23 m and l – b = 10 ∴ b = 23 – 10 = 13 m answer a" | a ) 13 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these | a | subtract(23, 10) | subtract(n0,n1)| | geometry | A |
a , band c can do a piece of work in 11 days , 5 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ? | ( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 5 = 16 / 55 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 16 / 55 + 6 / 55 = 2 / 5 2 / 5 th work done in 2 days work done = 5 / 2 * 2 = 5 days answer : a | a ) 5 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days | a | divide(55, divide(add(add(divide(55, 11), divide(55, 5)), add(divide(55, 11), divide(55, 55))), const_2)) | divide(n2,n0)|divide(n2,n1)|divide(n2,n2)|add(#0,#1)|add(#0,#2)|add(#3,#4)|divide(#5,const_2)|divide(n2,#6) | physics | A |
if a is the smallest positive integer such that 5880 multiplied by a is the square of an integer , then ya must be | 5880 = 2 * 2 * 7 * 7 * 5 * 6 , so we need one 5 and one 6 to make it a square of a number . so 5 * 6 = 30 ans : a | a ) 30 , b ) 15 , c ) 12 , d ) 23 , e ) 17 | a | divide(5880, multiply(power(add(const_3, const_4), const_2), power(const_2, const_2))) | add(const_3,const_4)|power(const_2,const_2)|power(#0,const_2)|multiply(#2,#1)|divide(n0,#3) | geometry | A |
a present value of a machine is $ 900 . its value depletion rate is 10 % per annum then find the machine value after 2 years ? | "p = $ 900 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 900 * 9 / 10 * 9 / 10 = $ 729 answer is e" | a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 729 | e | multiply(900, power(subtract(const_1, divide(10, const_100)), 2)) | divide(n1,const_100)|subtract(const_1,#0)|power(#1,n2)|multiply(n0,#2)| | gain | E |
in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 100 ? | "c 25 x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 40 = 25 * 3 = 75 . in x game of 100 points , y gives ( 100 - 75 ) = 25 points to c ." | a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50 | c | subtract(multiply(subtract(60, 20), const_3), multiply(subtract(60, 30), const_3)) | subtract(n1,n0)|subtract(n1,n2)|multiply(#0,const_3)|multiply(#1,const_3)|subtract(#2,#3)| | general | C |
a can complete the job in 3 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete | 1 / 6 = a | a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9 | a | divide(subtract(subtract(3, 1), 3), multiply(3, 3)) | multiply(n0,n1)|subtract(n0,n2)|subtract(#1,n1)|divide(#2,#0)| | physics | A |
find the area of trapezium whose parallel sides are 18 cm and 12 cm long , and the distance between them is 14 cm ? | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 18 + 12 ) * ( 14 ) = 224 cm 2 answer : c" | a ) 288 cm 2 , b ) 277 cm 2 , c ) 224 cm 2 , d ) 226 cm 2 , e ) 227 cm 2 | c | quadrilateral_area(14, 12, 18) | quadrilateral_area(n2,n1,n0)| | physics | C |
one men and three women working 7 hours a day finish a work in 5 days . four men and four women working 3 hours a day complete the work in 7 days . the number of days in which only 7 men working 4 hours a day will finish the work is ? | "1 m + 3 w - - - - - 35 h 4 m + 4 w - - - - - - - 21 h 7 m - - - - - - - ? d 35 m + 105 w = 84 m + 84 m 21 w = 49 m 4 * 35 = 7 * x = > x = 20 hours 20 / 4 = 5 days answer : b" | a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days | b | divide(const_1, multiply(multiply(4, 7), divide(subtract(divide(3, multiply(3, 7)), divide(4, multiply(5, 7))), 4))) | multiply(n0,n2)|multiply(n0,n1)|multiply(n0,n5)|divide(n2,#0)|divide(n5,#1)|subtract(#3,#4)|divide(#5,n5)|multiply(#6,#2)|divide(const_1,#7)| | physics | B |
what is the least common multiple of 152 and 190 ? | "yes there is a shorter way 152 = 2 * 2 * 2 * 19 190 = 2 * 5 * 19 i think everyone knows how to do this . then choose 2 * 2 * 2 and choose 5 and choose 19 2 * 2 * 2 * 5 * 19 = 760 answer is c" | a ) 304 , b ) 14440 , c ) 760 , d ) 28880 , e ) 1520 | c | multiply(add(152, const_1), const_2) | add(n0,const_1)|multiply(#0,const_2)| | general | C |
a rectangular tiled patio is composed of 160 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 160 tiles , and it will still be rectangular . how many rows are in the tile patio before ... | "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 160 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , ... | a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28 | c | divide(160, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(160, 2))))), 2)) | multiply(n0,n1)|negate(n2)|power(n2,n1)|multiply(n2,#0)|add(#3,#2)|sqrt(#4)|add(#1,#5)|divide(#6,n1)|divide(n0,#7)| | geometry | C |
find the 12 th term of an arithmetic progression whose first term is 2 and the common difference is 8 . | "n th term of a . p = a + ( n - 1 ) * d = 2 + ( 12 - 1 ) * 8 , = 2 + 88 = 90 . answer : d" | a ) 45 , b ) 38 , c ) 44 , d ) 90 , e ) 96 | d | add(multiply(subtract(12, const_1), 8), 2) | subtract(n0,const_1)|multiply(n2,#0)|add(n1,#1)| | general | D |
how many multiples of 2 are there between 1 and 54 , exclusive ? | "26 multiples of 2 between 1 and 54 exclusive . from 2 * 1 upto 2 * 26 , ( 1,2 , 3,4 , . . . , 26 ) . hence , 26 multiples ! correct option is d" | a ) 21 , b ) 22 , c ) 24 , d ) 26 , e ) 28 | d | add(divide(subtract(54, 1), 2), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | general | D |
a man can swim in still water at 9 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ? | "m = 9 s = x ds = 9 + x us = 9 - x 9 + x = ( 9 - x ) 2 9 + x = 18 - 2 x 3 x = 9 x = 3 answer : c" | a ) 1.7 , b ) 1.9 , c ) 3 , d ) 1.5 , e ) 1.2 | c | divide(9, const_3) | divide(n0,const_3)| | general | C |
a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ? | "d 20 hours | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 50 40 d = 20 rs = 50 – 40 = 10 t = 20 / 10 = 2 hours" | a ) 22 hours , b ) 21 hours , c ) 23 hours , d ) 20 hours , e ) 28 hours | d | subtract(divide(multiply(divide(const_1, const_2), 40), subtract(50, 40)), divide(const_1, const_2)) | divide(const_1,const_2)|subtract(n1,n0)|multiply(n0,#0)|divide(#2,#1)|subtract(#3,#0)| | physics | D |
in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 72 per kg ? | "( 96 - 72 ) / ( 72 - 68 ) = 24 / 4 = 6 / 1 answer : a" | a ) 6 : 1 , b ) 4 : 7 , c ) 3 : 7 , d ) 9 : 5 , e ) 9 : 8 | a | divide(divide(subtract(96, 72), subtract(96, 68)), subtract(const_1, divide(subtract(96, 72), subtract(96, 68)))) | subtract(n1,n2)|subtract(n1,n0)|divide(#0,#1)|subtract(const_1,#2)|divide(#2,#3)| | other | A |
the h . c . f . of two numbers is 59 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is : | : explanation : clearly , the numbers are ( 59 x 13 ) and ( 59 x 16 ) . { \ color { blue } \ therefore } larger number = ( 59 x 16 ) = 944 . answer : b ) 944 | a ) 678 , b ) 944 , c ) 456 , d ) 323 , e ) 899 | b | multiply(59, 16) | multiply(n0,n2) | other | B |
how many bricks each measuring 21 cm x 10 cm x 8 cm , will be needed to build a wall 9 m x 5 m x 18.5 m | "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 900 x 500 x 18.5 ) / ( 21 x 10 x 8 ) = 4955 answer : a" | a ) 4955 , b ) 4899 , c ) 4650 , d ) 7200 , e ) none of these | a | divide(multiply(multiply(9, 5), 18.5), divide(divide(multiply(multiply(21, 10), 8), const_100), const_100)) | multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#3,const_100)|divide(#4,const_100)|divide(#2,#5)| | physics | A |
a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 240 . find the sum ? | "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 240 = > 36 x / 100 - 24 x / 100 = 240 = > 12 x / 100 = 240 = > x = 2000 . answer : e" | a ) 7000 , b ) 7029 , c ) 2778 , d ) 2800 , e ) 2000 | e | divide(240, divide(multiply(subtract(18, 12), const_2), const_100)) | subtract(n0,n1)|multiply(#0,const_2)|divide(#1,const_100)|divide(n2,#2)| | gain | E |
a machine , working at a constant rate , manufactures 72 staplers in 28 minutes . how many staplers does it make in 1 hr 52 min ? | "change 1 hr 52 min to 112 min . for this , we need to set up a simple proportion of staplers per time 72 / 28 = s / 112 . the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 28 in the two denominat... | a ) 268 , b ) 262 , c ) 300 , d ) 288 , e ) 250 | d | multiply(divide(add(multiply(1, const_60), 52), 28), 72) | multiply(n2,const_60)|add(n3,#0)|divide(#1,n1)|multiply(n0,#2)| | physics | D |
the length of rectangle is thrice its breadth and its perimeter is 96 m , find the area of the rectangle ? | "2 ( 3 x + x ) = 96 l = 36 b = 12 lb = 36 * 12 = 432 answer : a" | a ) 432 , b ) 288 , c ) 376 , d ) 397 , e ) 592 | a | multiply(multiply(divide(96, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(96, add(multiply(const_3, const_2), multiply(const_1, const_2)))) | multiply(const_2,const_3)|multiply(const_1,const_2)|add(#0,#1)|divide(n0,#2)|multiply(#3,const_3)|multiply(#3,#4)| | geometry | A |
mrs . evans gave a test to her freshmen economics class , which has 25 students enrolled and 22 of them answered question 1 correctly . if 20 answered question 2 correctly and 3 did not take the test then how many answered both questions correctly ? | "total number of enrolled students = 25 number of students who did not take test = 3 hence , number of students who took test = 25 - 3 = 22 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answe... | a ) 30 , b ) 20 , c ) 23 , d ) 17 , e ) 19 | b | subtract(add(add(22, 20), 3), 25) | add(n1,n3)|add(n5,#0)|subtract(#1,n0)| | other | B |
7 does not occur in 1000 . so we have to count the number of times it appears between 1 and 999 . any number between 1 and 999 can be expressed in the form of xyz where 0 < x , y , z < 9 . | 1 . the numbers in which 7 occurs only once . e . g 7 , 17 , 78 , 217 , 743 etc this means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits ( i . e 0 to 9 with the exception of 7 ) you have 1 * 9 * 9 = 81 such numbers . however , 7 could appear as the first or the second or the... | a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 470 | b | add(add(multiply(const_3, multiply(9, 9)), multiply(multiply(const_3, 9), const_2)), const_3) | multiply(n7,n7)|multiply(n7,const_3)|multiply(#0,const_3)|multiply(#1,const_2)|add(#2,#3)|add(#4,const_3) | general | B |
a library branch originally contained 18365 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 3 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ? | "fiction novels = 5,509 transferred to another location = 6,121 transferred fiction novels = 2,040 non transferred fiction novels = 3,469 percent of the remaining collection was fiction novels = 3469 / ( 18365 - 6121 ) * 100 = > 28.332 . . . % hence answer will be ( c )" | a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 45.2 % , e ) 73.6 % | c | multiply(divide(multiply(divide(30, const_100), subtract(1, divide(1, 3))), subtract(1, divide(1, 3))), const_100) | divide(n1,const_100)|divide(n2,n5)|divide(n2,n3)|subtract(n2,#1)|subtract(n2,#2)|multiply(#0,#3)|divide(#5,#4)|multiply(#6,const_100)| | gain | C |
the interest on a certain deposit at 4.5 % p . a . is rs . 202.50 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a . ? | "solution s . i . = rs . 202.50 , r = 4.5 % , t = 1 year . principal = rs . ( 100 x 202.50 / 4.5 x 1 ) = rs . 4500 . now , p = rs . 4500 , r = 5 % , t = 1 year . s . i . = rs . ( 4500 x 5 x 1 / 1000 = rs . 225 . ∴ difference in interest = rs . ( 225 - 202.50 ) = rs . 22.50 . answer b" | a ) rs . 20.25 , b ) rs . 22.50 , c ) rs . 25 , d ) rs . 42.75 , e ) none | b | subtract(divide(multiply(divide(202.50, divide(4.5, const_100)), 5), const_100), 202.50) | divide(n0,const_100)|divide(n1,#0)|multiply(n2,#1)|divide(#2,const_100)|subtract(#3,n1)| | gain | B |
a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in ? | "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : e" | a ) 25 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 24 days | e | multiply(divide(multiply(8, add(const_2, const_1)), const_2), const_2) | add(const_1,const_2)|multiply(n0,#0)|divide(#1,const_2)|multiply(#2,const_2)| | physics | E |
a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn | let total salary be x a / q = > x = ( x / 3 ) + ( x / 4 ) + ( x / 5 ) + 1760 = > x - 47 x / 60 = 1760 = > 13 x / 60 = 1760 = > x = 1760 * 60 / 13 = > x = 8123 ( approax ) answer : b | a ) 8223 , b ) 8123 , c ) 8323 , d ) 8423 , e ) 8523 | b | divide(1760, subtract(const_1, add(add(divide(1, 3), divide(1, 4)), divide(1, 5)))) | divide(n0,n1)|divide(n0,n3)|divide(n0,n5)|add(#0,#1)|add(#3,#2)|subtract(const_1,#4)|divide(n6,#5) | general | B |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , the how old is b ? | "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 ⇒ 5 x = 40 ⇒ x = 8 . hence , b ' s age = 2 x = 16 years . answer : a" | a ) 16 , b ) 9 , c ) 8 , d ) 11 , e ) 10 | a | divide(multiply(subtract(42, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general | A |
huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 8 inches on a side and costs $ 10 , and a large pizza that measures 12 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if t... | "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 8 * 8 = 64 ) for the small pizza and ( 12 * 12 = 144 ) for the large pizza . in total sq inches that would be ( 64 + 144 ) * 2 = 416 sq inches . in the second case if they pool their money together they can buy 3 ... | a ) 5 square inches , b ) 10 square inches , c ) 16 square inches , d ) 25 square inches , e ) 350 square inches | c | subtract(multiply(power(12, const_2), const_3), add(add(power(8, const_2), power(12, const_2)), add(power(8, const_2), power(12, const_2)))) | power(n2,const_2)|power(n0,const_2)|add(#1,#0)|multiply(#0,const_3)|add(#2,#2)|subtract(#3,#4)| | geometry | C |
if 1 = 6 , 2 = 12 , 3 = 18 , 4 = 24 , 5 = 30 , then 6 = ? | solution : 1 as stated 1 = 6 = > 6 = 1 answer c | a ) 5 , b ) 3 , c ) 1 , d ) 7 , e ) 9 | c | subtract(2, 1) | subtract(n2,n0) | general | C |
if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 39 | "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 39 = 19008 / 39 = 487 , remainder = 15 c" | a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19 | c | reminder(multiply(432, 44), 39) | multiply(n0,n1)|reminder(#0,n3)| | general | C |
at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 162.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ? | "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 162.5 subtracting the first equation from the second gives us b + 3 s = 42.5 now if we subtract the new equation two times from first or 3 times fro... | a ) $ 21 , b ) $ 35 , c ) $ 31 , d ) $ 41 , e ) it can not be determined | b | subtract(add(120, subtract(162.50, 120)), multiply(subtract(162.50, 120), 3)) | subtract(n3,n2)|add(n2,#0)|multiply(#0,n0)|subtract(#1,#2)| | general | B |
if y > 0 , ( 8 y ) / 20 + ( 3 y ) / 10 is what percent of y ? | "can be reduced to 4 y / 10 + 3 y / 10 = 7 y / 10 = 70 % answer d" | a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 % | d | multiply(const_100, add(divide(8, 20), divide(3, 10))) | divide(n1,n2)|divide(n3,n4)|add(#0,#1)|multiply(#2,const_100)| | general | D |
a rectangular tiled patio is composed of 30 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 30 tiles , and it will still be rectangular . how many rows are in the tile patio before th... | "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 30 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , n... | a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28 | a | divide(30, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(30, 2))))), 2)) | multiply(n0,n1)|negate(n2)|power(n2,n1)|multiply(n2,#0)|add(#3,#2)|sqrt(#4)|add(#1,#5)|divide(#6,n1)|divide(n0,#7)| | geometry | A |
a group of 4 investment bankers and 5 clients recently frequented the bonbon ribs restaurant . the total bill for the meal , including 20 % gratuity , came to $ 756 . on average , how much did the meal of each individual cost before gratuity ? | 4 ibs and 5 clients - so total 9 people the bill $ 756 includes 20 % gratuity . . . so the actual cost of dinner was $ 630 now , the cost per person will be $ 630 / 9 which is $ 70 option b | a ) $ 160 , b ) $ 70 , c ) $ 90 , d ) $ 80 , e ) $ 55 | b | divide(divide(756, divide(add(20, const_100), const_100)), add(4, 5)) | add(n2,const_100)|add(n0,n1)|divide(#0,const_100)|divide(n3,#2)|divide(#3,#1) | general | B |
if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 58 ? | "four wheeler = 14 * 4 = 56 ( max ) 2 wheel = 1 so no of 4 wheeler = 14 answer : d" | a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | d | divide(subtract(58, 2), 4) | subtract(n3,n0)|divide(#0,n1)| | general | D |
20 machines can do a work in 5 days . how many machines are needed to complete the work in 10 days ? | "required number of machines = 20 * 5 / 10 = 10 answer is a" | a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20 | a | divide(multiply(20, 5), 10) | multiply(n0,n1)|divide(#0,n2)| | physics | A |
john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 45 miles per hour , what is v in miles per hour ? | "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 40 = > v = 40... | a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70 | b | multiply(subtract(const_100, 80), subtract(divide(const_100, 45), divide(80, 80))) | divide(const_100,n2)|divide(n0,n0)|subtract(const_100,n0)|subtract(#0,#1)|multiply(#2,#3)| | physics | B |
a sum of 25 was paid for a work which a can do in 32 days , b in 20 days , b and c in 12 days and d in 24 days . how much did c receive if all the 4 work together ? | a ' s one day ' s work = 1 ⁄ 32 b ' s one day ' s work = 1 ⁄ 20 ( b + c ) ' s one day ' s work = 1 ⁄ 12 ∴ c ' s one day ' s work = 1 ⁄ 12 - 1 ⁄ 20 = 1 ⁄ 30 d ' s one day ' s work = 1 ⁄ 24 ∴ ( a + b + c + d ) ' s one day ' s work 1 / 32 + 1 / 20 + 1 / 30 + 1 / 24 = 75 + 120 + 80 + 100 / 2400 = 375 ⁄ 2400 = 15 ⁄ 96 = 5 ⁄... | a ) 14 ⁄ 3 , b ) 16 ⁄ 3 , c ) 15 ⁄ 3 , d ) 17 ⁄ 3 , e ) none of these | b | multiply(divide(lcm(lcm(32, 20), 24), divide(const_1, subtract(divide(const_1, 12), divide(const_1, 20)))), divide(25, add(add(add(divide(lcm(lcm(32, 20), 24), 32), divide(lcm(lcm(32, 20), 24), 20)), divide(lcm(lcm(32, 20), 24), divide(const_1, subtract(divide(const_1, 12), divide(const_1, 20))))), divide(lcm(lcm(32, 2... | divide(const_1,n3)|divide(const_1,n2)|lcm(n1,n2)|lcm(n4,#2)|subtract(#0,#1)|divide(const_1,#4)|divide(#3,n1)|divide(#3,n2)|divide(#3,n4)|add(#6,#7)|divide(#3,#5)|add(#9,#10)|add(#11,#8)|divide(n0,#12)|multiply(#10,#13) | physics | B |
a semicircle has a radius of 11 . what is the approximate perimeter of the semicircle ? | the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 11 + 2 * 11 which is about 57 . the answer is c . | ['a ) 45', 'b ) 51', 'c ) 57', 'd ) 63', 'e ) 69'] | c | add(divide(circumface(11), const_2), multiply(const_2, 11)) | circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1) | geometry | C |
zoey won the lottery and got $ 7 , 348340 . she wants to split it among herself and 5 friends evenly . how much money must she add if she wants to split it evenly ? | zoey and her 5 friends is 6 people in all . $ 7 , 348340 must be divisible by 6 if she wants to split it evenly . the money is divisible by 6 if it ' s divisible by 2 and 3 . 7 + 3 + 4 + 8 + 3 + 4 + 0 = 29 . 2 and 3 cant go into 29 . adding 1 dollar makes it 30 . 2 and 3 can go into 30 so 6 can also . the answer is d . | a ) $ 3 , b ) $ 2 , c ) $ 9 , d ) $ 1 , e ) $ 4 | d | subtract(reminder(add(multiply(7, multiply(const_1000, const_1000)), 348340), add(5, const_1)), const_1) | add(n2,const_1)|multiply(const_1000,const_1000)|multiply(n0,#1)|add(n1,#2)|reminder(#3,#0)|subtract(#4,const_1) | general | D |
if the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is ? | "2 * 22 / 7 * 14 * x = 1056 = > x = 12 answer : d" | a ) 17 , b ) 19 , c ) 17 , d ) 12 , e ) 91 | d | divide(1056, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14)) | multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)| | physics | D |
a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 50 to incur a loss 20 % ? | production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 50 * ( 100 % + 20 % ) = $ 60 number of articles to be sold for $ 60 to incur a 20 % loss : $ 60 / $ 2.40 = 25 thus , solution a is correct . | a ) 25 , b ) 36 , c ) 40 , d ) 50 , e ) 48 | a | divide(original_price_before_loss(20, 50), divide(original_price_before_gain(20, 60), 20)) | original_price_before_gain(n0,n1)|original_price_before_loss(n0,n3)|divide(#0,n0)|divide(#1,#2) | gain | A |
find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ? | "1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 c )" | a ) 13 / 89 , b ) 15 / 87 , c ) 27 / 89 , d ) 27 / 87 , e ) 89 / 27 | c | divide(1, add(3, divide(1, add(3, divide(1, subtract(3, divide(1, 3))))))) | divide(n0,n1)|subtract(n1,#0)|divide(n0,#1)|add(n1,#2)|divide(n0,#3)|add(n1,#4)|divide(n0,#5)| | general | C |
a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 30 as remainder . find the no . is ? | "( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 e" | a ) 122443 , b ) 154546 , c ) 165454 , d ) 186545 , e ) 220030 | e | add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 30) | add(n0,n1)|subtract(n0,n1)|multiply(n2,#0)|multiply(#2,#1)|add(n3,#3)| | general | E |
steve traveled the first 2 hours of his journey at 50 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ? | "distance traveled in 2 hours = 2 * 50 = 100 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 100 = 340 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 340 / 5 = 68 mph answer : a" | a ) 68 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph | a | add(divide(add(multiply(80, 3), multiply(50, 2)), add(3, 2)), subtract(divide(const_100, 3), const_0_33)) | add(n0,n2)|divide(const_100,n2)|multiply(n2,n3)|multiply(n0,n1)|add(#2,#3)|subtract(#1,const_0_33)|divide(#4,#0)|add(#6,#5)| | physics | A |
if a fraction is multiplied by itself and then divided by the reciprocal of the same fraction , the result is 18 26 / 27 . find the fraction . | answer if the required fraction be p according to the question ( p x p ) / ( 1 / p ) = 1826 / 27 ⇒ p 3 = 512 / 27 ∴ p = 8 / 3 = 2 2 / 3 correct option : c | a ) 8 / 27 , b ) 1 1 / 3 , c ) 2 2 / 3 , d ) 3 / 3 , e ) none of these | c | add(subtract(multiply(power(add(divide(26, 27), 18), divide(const_1, const_3)), const_3), power(add(divide(26, 27), 18), divide(const_1, const_3))), const_2) | divide(n1,n2)|divide(const_1,const_3)|add(n0,#0)|power(#2,#1)|multiply(#3,const_3)|subtract(#4,#3)|add(#5,const_2) | general | C |
how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 70 m long and 16 1 / 2 m board ? | "70 * 33 / 2 = 5 / 2 * 2 * x = > x = 231 answer : e" | a ) 99 , b ) 18 , c ) 16 , d ) 10 , e ) 231 | e | divide(multiply(70, add(16, divide(1, 2))), multiply(add(2, divide(1, 2)), 2)) | divide(n1,n0)|add(n5,#0)|add(n0,#0)|multiply(n4,#1)|multiply(n0,#2)|divide(#3,#4)| | general | E |
a train 825 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 90 seconds . the speed of the train is : | "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = = > x = 50 km / hr . answer : d" | a ) 33 , b ) 27 , c ) 27 , d ) 50 , e ) 81 | d | divide(divide(subtract(825, multiply(multiply(5, const_0_2778), 5)), 5), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)| | physics | D |
the sale price sarees listed for rs . 350 after successive discount is 20 % and 5 % is ? | "350 * ( 80 / 100 ) * ( 95 / 100 ) = 266 answer : a" | a ) 266 , b ) 278 , c ) 342 , d ) 787 , e ) 191 | a | subtract(subtract(350, divide(multiply(350, 20), const_100)), divide(multiply(subtract(350, divide(multiply(350, 20), const_100)), 5), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain | A |
find the product of the local value and absolute value of 6 in 564823 | "explanation : place value = local value face value = absolute value the place value of 6 in 564823 is 6 x 10000 = 60000 the face value of 6 in 564823 is nothing but 6 . = > 60000 x 6 = 360,000 answer : option e" | a ) 8000 , b ) 16000 , c ) 12000 , d ) 18000 , e ) 360000 | e | multiply(multiply(6, const_1000), 6) | multiply(n0,const_1000)|multiply(n0,#0)| | general | E |
when a train travels at a speed of 60 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ? | "let x be the time reached with the speed 60 km / h 50 km / h - - - - > x + 15 distance is equal so 60 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 60 x = 50 x + 750 so the would be in km and x = 75 so 75 km answer : a" | a ) 75 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km | a | multiply(const_60, divide(multiply(divide(15, const_60), 50), 50)) | divide(n2,const_60)|multiply(n1,#0)|divide(#1,n1)|multiply(#2,const_60)| | physics | A |
in a company the manager wants to give some gifts to all of the workers . in each block there are about 200 workers are there . the total amount for giving the gifts for all the workers is $ 6000 . the worth of the gift is 2 $ . how many blocks are there in the company ? | "each employee will get a gift worth of = $ 2 total employees = 6000 / 2 = 3000 total blocks = 3000 / 200 = 15 correct option is e" | a ) 10 , b ) 12 , c ) 18 , d ) 20 , e ) 15 | e | divide(divide(6000, 2), 200) | divide(n1,n2)|divide(#0,n0)| | general | E |
a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of each . | c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is c | a ) 25 , b ) 50 , c ) 75 , d ) 80 , e ) none of them | c | multiply(divide(const_1, add(add(const_4, const_3), const_1)), 600) | add(const_3,const_4)|add(#0,const_1)|divide(const_1,#1)|multiply(n0,#2) | physics | C |
a boat running up stram takes 6 hours to cover a certain distance , while it takes 7 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ? | "explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 7 ( x - y ) 6 x + 6 y = 7 x - 7 y 13 y = x 13 y = x x / y = 13 / 1 13 : 1 answer : option d" | a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 13 : 1 , e ) 8 : 1 | d | subtract(7, 6) | subtract(n1,n0)| | physics | D |
the cash difference between the selling prices of an article at a profit of 10 % and 6 % is rs . 3 . the ratio of the two selling prices is ? | "let c . p . of the article be rs . x . then , required ratio = 110 % of x / 106 % of x = 110 / 106 = 55 / 53 = 55 : 53 answer : b" | a ) 52 : 56 , b ) 55 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51 | b | divide(add(const_100, 10), add(const_100, 6)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)| | gain | B |
n and m are each 3 - digit integers . each of the numbers 2 , 3,4 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ? | you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as smal... | a ) 39 , b ) 49 , c ) 58 , d ) 113 , e ) 131 | a | subtract(subtract(const_100, multiply(subtract(8, 2), const_10)), const_1) | subtract(n5,n1)|multiply(#0,const_10)|subtract(const_100,#1)|subtract(#2,const_1) | general | A |
a train passes a station platform in 46 sec and a man standing on the platform in 16 sec . if the speed of the train is 54 km / hr . what is the length of the platform ? | "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 16 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 46 = 15 = > x = 450 m . answer : d" | a ) 227 , b ) 240 , c ) 460 , d ) 450 , e ) 455 | d | multiply(16, multiply(54, const_0_2778)) | multiply(n2,const_0_2778)|multiply(n1,#0)| | physics | D |
in what time will a train 95 m long cross an electric pole , it its speed be 214 km / hr ? | "speed = 214 * 5 / 18 = 59 m / sec time taken = 95 / 59 = 1.6 sec . answer : a" | a ) 1.6 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec | a | divide(95, multiply(214, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics | A |
find the value of ( 28 + 48 / 69 ) × 69 | "= ( 28 + 48 / 69 ) × 69 = ( 1932 + 48 ) / 69 × 69 = 1980 / 69 × 69 = 1980 answer is a ." | a ) 1980 , b ) 1982 , c ) 1930 , d ) 1988 , e ) 1680 | a | multiply(add(divide(48, 69), 28), 69) | divide(n1,n2)|add(n0,#0)|multiply(#1,n2)| | general | A |
express 15 mps in kmph ? | "15 * 18 / 5 = 54 kmph answer : e" | a ) 22 , b ) 88 , c ) 90 , d ) 21 , e ) 54 | e | multiply(divide(15, const_1000), const_3600) | divide(n0,const_1000)|multiply(#0,const_3600)| | physics | E |
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 21.6 % . what would have been the percentage of profit earned if no discount was offered ? | "let c . p . be rs . 100 . then , s . p . = rs . 121.60 let marked price be rs . x . then , 95 / 100 x = 121.60 x = 12160 / 95 = rs . 128 now , s . p . = rs . 128 , c . p . = rs . 100 profit % = 28 % . answer : b" | a ) 60 % , b ) 28 % , c ) 30 % , d ) 56 % , e ) 73 % | b | subtract(divide(multiply(add(const_100, 21.6), const_100), subtract(const_100, 5)), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)| | gain | B |
cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 4 hours , how many minutes did it take cole to drive to work ? | first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 4 hrs therefore , 4 = d / 75 + d / 105 lcm of 75 and 105 = 525 4 = d / 75 + d / 105 = > 4 = 7 d / 525 + 5 d / 5... | a ) 66 , b ) 70 , c ) 95 , d ) 112 , e ) 140 | e | multiply(divide(multiply(105, 4), add(75, 105)), const_60) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0)|multiply(#2,const_60) | physics | E |
which no . need to add to 859622 to get a no . exactly divisible by 456 ? | dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e | a ) 546577 , b ) 674645 , c ) 566578 , d ) 465766 , e ) 859622 | e | subtract(859622, reminder(859622, 456)) | reminder(n0,n1)|subtract(n0,#0) | general | E |
what is the unit ’ s digit of 7 ^ 7 | "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 7 = 3 answer c" | a ) 9 , b ) 5 , c ) 3 , d ) 7 , e ) 1 | c | reminder(power(7, const_2), const_10) | power(n0,const_2)|reminder(#0,const_10)| | general | C |
what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ? | "required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e" | a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters | e | subtract(18, divide(multiply(18, 40), 60)) | multiply(n0,n1)|divide(#0,n2)|subtract(n0,#1)| | gain | E |
15 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 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 3 = 18 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 18 = 50 / 3 = 16.67 % answer is a" | a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 % | a | multiply(divide(subtract(add(15, 3), add(multiply(divide(subtract(const_100, 20), const_100), 15), 3)), add(15, 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 | A |
if 20 men can build a water fountain 56 metres long in 42 days , what length of a similar water fountain can be built by 35 men in 3 days ? | "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 42 : 3 : : 56 : x therefore ( 20 x 42 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 840 = 7 hence , the required length is 7 m . answer : c" | a ) 3 m , b ) 4 m , c ) 7 m , d ) 9 m , e ) 10 m | c | multiply(divide(56, multiply(20, 42)), multiply(35, 3)) | multiply(n0,n2)|multiply(n3,n4)|divide(n1,#0)|multiply(#2,#1)| | physics | C |
a certain lab experiments with white and brown mice only . in one experiment , 4 / 9 of the mice are brown . if there are 20 brown mice in the experiment , how many mice in total are in the experiment ? | "let total number of mice = m number of brown mice = 4 / 9 m number of white mice = 5 / 9 m = 20 = > m = 36 answer c" | a ) 32 , b ) 26 , c ) 36 , d ) 28 , e ) 24 | c | subtract(divide(20, divide(4, 9)), 20) | divide(n0,n1)|divide(n2,#0)|subtract(#1,n2)| | general | C |
the length of a rectangle is reduced by 15 % . by what % would the width have to be increased to maintain the original area ? | sol . required change = ( 15 * 100 ) / ( 100 - 15 ) = 17.6 % c | ['a ) 10 %', 'b ) 20 %', 'c ) 17.6 %', 'd ) 30 %', 'e ) 35 %'] | c | multiply(divide(subtract(const_1, divide(subtract(const_100, 15), const_100)), divide(subtract(const_100, 15), const_100)), const_100) | subtract(const_100,n0)|divide(#0,const_100)|subtract(const_1,#1)|divide(#2,#1)|multiply(#3,const_100) | geometry | C |
mike earns $ 17.5 per hour and phil earns $ 10.5 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ? | "what % less of 17.5 is 10.5 let it be x % less , then = 17.5 ( 1 - x / 100 ) = 10.5 1 - x / 100 = 10.5 / 17.5 x = 200 / 5 x = 40 % ans e" | a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 % | e | multiply(divide(10.5, 17.5), const_100) | divide(n1,n0)|multiply(#0,const_100)| | general | E |
when n is divided by 24 , the remainder is 6 . what is the remainder when 3 n is divided by 8 ? | "let n = 6 ( leaves a remainder of 6 when divided by 24 ) 3 n = 3 ( 6 ) = 18 , which leaves a remainder of 2 when divided by 8 . answer e" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2 | e | subtract(6, reminder(3, 8)) | reminder(n2,n3)|subtract(n1,#0)| | general | E |
let f ( x ) = x ^ 2 + bx + c . if f ( 5 ) = 0 and f ( - 3 ) = 0 , then b + c = | "f ( x ) = x ^ 2 + bx + c . if f ( 5 ) = 0 and f ( - 3 ) = 0 , then b + c = f ( 5 ) = 0 = 25 + 5 b + c - - - taking 25 to the other side - > 5 b + c = - 25 f ( - 3 ) = 0 = 9 - 3 b + c - - - taking - 3 b + c to the other side - > 3 b - c = 9 when we add these 2 equations , we get 8 b = - 16 - - - > b = - 2 and while sub... | a ) 18 , b ) - 17 , c ) - 15 , d ) - 21 , e ) - 24 | b | negate(divide(subtract(power(3, 2), 5), add(3, 5))) | add(n3,n1)|power(n3,n0)|subtract(#1,n1)|divide(#2,#0)|negate(#3)| | general | B |
susan made a block with small cubes of 8 cubic cm volume to make a block , 3 small cubes long , 9 small cubes wide and 5 small cubes deep . she realizes that she has used more small cubes than she really needed . she realized that she could have glued a fewer number of cubes together to lock like a block with same dime... | the total volume ( in terms of number of cubes ) of the solid = 3 * 9 * 5 = 135 the total volume ( in terms of number of cubes ) of the hollow = ( 3 - 2 ) * ( 9 - 2 ) * ( 5 - 2 ) = 21 so number of cubes required = 135 - 21 = 114 answer : b | ['a ) 113', 'b ) 114', 'c ) 115', 'd ) 116', 'e ) 117'] | b | add(multiply(multiply(const_1, 9), 5), add(subtract(multiply(multiply(const_1, 9), 5), multiply(add(const_4, const_3), const_3)), multiply(multiply(const_1, 9), 5))) | add(const_3,const_4)|multiply(n2,const_1)|multiply(n3,#1)|multiply(#0,const_3)|subtract(#2,#3)|add(#2,#4)|add(#5,#2) | geometry | B |
during a sale , the price of a pair of shoes is marked down 12 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ? | "assume the price = 100 price during sale = 88 price after sale = 100 percent increase = 12 / 88 * 100 = 14 % approx . correct option : d" | a ) 9 % , b ) 10 % , c ) 11 % , d ) 14 % , e ) 90 % | d | divide(multiply(12, const_100), subtract(const_100, 12)) | multiply(n0,const_100)|subtract(const_100,n0)|divide(#0,#1)| | gain | D |
in a division , divident is 690 , divisior is 36 and quotient is 19 . find the remainder . | "explanation : 690 = 36 x 19 + r 690 = 684 + r r = 690 - 684 = 6 answer : option e" | a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6 | e | reminder(690, 36) | reminder(n0,n1)| | general | E |
if ( t - 8 ) is a factor of t ^ 2 - kt - 40 , then k = | "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 1 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ... | a ) 16 , b ) 1 , c ) 2 , d ) 6 , e ) 14 | b | add(const_10, 2) | add(n1,const_10)| | general | B |
what is the sum of the numbers between 1 and 10 , inclusive ? | "sol . add all the numbers between 1 and 10 . final answer = e , 55 ." | a ) 85 , b ) 95 , c ) 100 , d ) 105 , e ) 55 | e | divide(multiply(1, 10), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general | E |
a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter m of liquid a was contained by the can initially ? | "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 simil... | a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27 | c | multiply(7, divide(multiply(add(7, 9), subtract(9, multiply(divide(5, add(7, 5)), 9))), subtract(multiply(9, 7), multiply(7, 5)))) | add(n0,n2)|add(n0,n1)|multiply(n0,n2)|multiply(n0,n1)|divide(n1,#1)|subtract(#2,#3)|multiply(n2,#4)|subtract(n2,#6)|multiply(#0,#7)|divide(#8,#5)|multiply(n0,#9)| | physics | C |
mixture contains alcohol and water in the ratio 4 : 3 . if 7 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture . | "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 28 x = 4 ( 3 x + 5 ) 16 x = 20 x = 1.25 quantity of alcohol = ( 4 x 1.25 ) litres = 5 litres . answer : c" | a ) 10 , b ) 99 , c ) 5 , d ) 22 , e ) 29 | c | multiply(divide(multiply(4, 5), subtract(multiply(7, 4), multiply(3, 4))), 4) | multiply(n0,n4)|multiply(n0,n2)|multiply(n0,n1)|subtract(#1,#2)|divide(#0,#3)|multiply(n0,#4)| | general | C |
calculate the time it will take for a full tank of water to become completely empty due to a leak given that the tank could be filled in 10 hours , but due to the leak in its bottom it takes 11 hours to be filled ? | part filled without leak in 1 hour = 1 / 10 part filled with leak in 1 hour = 1 / 11 work done by leak in 1 hour = 1 / 10 â ˆ ’ 1 / 11 = 110 hours answer : e | a ) 90 hours , b ) 80 hours , c ) 50 hours , d ) 120 hours , e ) 110 hours | e | divide(multiply(10, 11), subtract(divide(multiply(10, 11), 10), divide(multiply(10, 11), 11))) | multiply(n0,n1)|divide(#0,n0)|divide(#0,n1)|subtract(#1,#2)|divide(#0,#3) | physics | E |
the average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results ? | "answer sum of 50 result = sum of 30 result + sum of 20 result . = 30 x 20 + 20 x 30 = 1200 correct option : a" | a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none | a | divide(add(multiply(30, 20), multiply(20, 30)), add(30, 20)) | add(n0,n1)|multiply(n0,n1)|add(#1,#1)|divide(#2,#0)| | general | A |
a and b go around a circular track of length 400 m on a cycle at speeds of 36 kmph and 36 kmph . after how much time will they meet for the first time at the starting point ? | "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 400 / ( 36 * 5 / 18 ) , 400 / ( 36 * 5 / 18 ) } = lcm ( 40 , 40 ) = 40 sec . answer : a" | a ) 40 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 276 sec | a | divide(400, subtract(multiply(36, const_0_2778), multiply(36, const_0_2778))) | multiply(n2,const_0_2778)|multiply(n1,const_0_2778)|subtract(#0,#1)|divide(n0,#2)| | physics | A |
a picnic attracts 240 persons . there are 80 more men than women , and 80 more adults than children . how many men are at this picnic ? | "adult + children = 240 let , children = y then , adult = y + 80 i . e . y + ( y + 80 ) = 240 i . e . y = 80 i . e . adult = 80 + 80 = 160 adults include only men and women i . e . men + women = 160 let women , w = x then men , m = x + 80 i . e . x + ( x + 20 ) = 2 x + 80 = 160 i . e . x = 40 i . e . men , m = 40 + 80 ... | a ) 240 , b ) 75 , c ) 110 , d ) 120 , e ) 200 | d | add(divide(subtract(add(divide(subtract(240, 80), const_2), 80), 80), const_2), 80) | subtract(n0,n1)|divide(#0,const_2)|add(n1,#1)|subtract(#2,n1)|divide(#3,const_2)|add(n1,#4)| | general | D |
two same glasses are respectively 1 / 4 th 1 / 5 th full of milk . they are then filled with water and the contents mixed in a tumbler . the ratio of milk and water in the tumbler is ? | 1 / 4 : 3 / 4 = ( 1 : 3 ) 5 = 5 : 15 1 / 5 : 4 / 5 = ( 1 : 4 ) 4 = 4 : 16 - - - - - - 9 : 31 answer : b | a ) 9 : 39 , b ) 9 : 31 , c ) 9 : 36 , d ) 9 : 32 , e ) 9 : 34 | b | divide(add(5, 4), add(multiply(const_3, const_10), 1)) | add(n1,n3)|multiply(const_10,const_3)|add(n0,#1)|divide(#0,#2) | general | B |
a bag contains 3 white marbles and 3 black marbles . if each of 3 girls and 3 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? | first , total ways to select for all boys and girls , i . e 6 ! / ( 3 ! * 3 ! ) = 6 * 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 3 * 2 * 1 = 20 then there are one two way girls can have all same colors , either white or black . the number of ways in which 3 girls can select 3 white balls = 3 c 3 = 1 the number of ways in which 3 ... | a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 15 , d ) 1 / 20 , e ) 1 / 25 | b | divide(const_2, choose(add(3, 3), 3)) | add(n0,n0)|choose(#0,n0)|divide(const_2,#1) | probability | B |
convert the 11 / 36 m / s into kilometers per hour ? | "11 / 36 m / s = 11 / 36 * 18 / 5 = 11 / 10 = 1.1 kmph . answer : b" | a ) 2.9 kmph , b ) 1.1 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph | b | multiply(const_3_6, divide(11, 36)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics | B |
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