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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a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of pupils in the class is : | "let there be x pupils in the class . total increase in marks = x x 1 / 2 = x / 2 x / 2 = ( 83 - 63 ) x / 2 = 20 x = 40 . answer : c" | a ) 32 , b ) 50 , c ) 40 , d ) 20 , e ) 10 | c | multiply(subtract(83, 63), const_2) | subtract(n0,n1)|multiply(#0,const_2)| | general |
in how many ways can 21 books on english and 19 books on french be placed in a row on a shelf so that two books on french may not be together ? | "in order that two books on french are never together , we must place all books as under x e x e x e x e x e . . . . . x e x where e denotes the position of an english book and x that of a french book . since there are 21 books on english , the number of places marked x are therefore , 22 . now , 19 places out of 22 ca... | a ) 3990 , b ) 1540 , c ) 1995 , d ) 3672 , e ) none of these | b | add(add(choose(subtract(21, const_1), const_3), permutation(subtract(21, const_1), const_2)), choose(subtract(21, const_1), const_1)) | subtract(n0,const_1)|choose(#0,const_3)|choose(#0,const_1)|permutation(#0,const_2)|add(#1,#3)|add(#4,#2)| | probability |
120 is what percent of 40 ? | "40 * x = 120 - - > x = 3 - - > 3 expressed as percent is 300 % . answer : d ." | a ) 5 % , b ) 20 % , c ) 50 % , d ) 300 % , e ) 500 % | d | multiply(divide(120, 40), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
an alloy of copper and zinc contains copper and zinc in the ratio 9 : 6 . another alloy of copper and zinc contains copper and zinc in the ratio 6 : 9 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ? | "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 9 x / 15 , and fraction of zinc in alloy _ 1 = 6 x / 15 similarly , fraction of copper in alloy _ 2 = 6 y / 15 , and fraction of zinc in alloy _ 2 = 9 y / 15 . mixing them , we get copper = 9 x / 15 + 6 y / 15 ; zinc = 6 x... | a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2 | d | divide(subtract(divide(9, add(6, 9)), divide(6, 9)), subtract(divide(6, 9), divide(6, add(6, 9)))) | add(n2,n3)|divide(n2,n3)|divide(n0,#0)|divide(n2,#0)|subtract(#2,#1)|subtract(#1,#3)|divide(#4,#5)| | general |
a searchlight on top of the watchtower makes 4 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 12 seconds ? | "the searchlight completes one revolution every 15 seconds . the probability that the man ' s area will be lit up is 12 / 15 = 4 / 5 . the probability that he will stay in the dark is 1 - 4 / 5 = 1 / 5 the answer is e ." | a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5 | e | subtract(const_1, divide(12, multiply(12, const_3))) | multiply(n1,const_3)|divide(n1,#0)|subtract(const_1,#1)| | physics |
which is the smallest no which divides 2880 and gives a perfect square ? | 2880 = 20 * 144 ( because w . k . t 144 is perfect square ) = 2 * 10 * 144 = 2 * 2 * 5 * 144 = 4 * 5 * 144 ( here 4 and 144 are perfect square ) so the smallest number is 5 answer : d | ['a ) 4', 'b ) 9', 'c ) 3', 'd ) 5', 'e ) 7'] | d | divide(divide(divide(divide(divide(divide(2880, const_4), const_3), const_4), const_3), const_2), const_2) | divide(n0,const_4)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_3)|divide(#3,const_2)|divide(#4,const_2) | geometry |
4.036 divided by 0.02 gives : | "= 4.036 / 0.02 = 403.6 / 2 = 201.8 answer is d ." | a ) 10.09 , b ) 1.06 , c ) 10.06 , d ) 201.8 , e ) 100.9 | d | divide(4.036, 0.02) | divide(n0,n1)| | general |
stacy and heather are 5 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two... | "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 5 - 2.4 = 2.6 time taken = distance / speed = 2.6 / 11 = 0.23 hrs heather will... | a ) 2.5 mile , b ) 1.9 mile , c ) 1.7 mile , d ) 1.5 mile , e ) 1.18 mile | e | multiply(divide(subtract(5, multiply(24, divide(add(1, 5), const_60))), add(5, add(1, 5))), 5) | add(n1,n2)|add(n2,#0)|divide(#0,const_60)|multiply(n3,#2)|subtract(n0,#3)|divide(#4,#1)|multiply(n2,#5)| | physics |
a train travels from albany to syracuse , a distance of 120 miles , at the average rate of 50 miles per hour . the train then travels back to albany from syracuse . the total travelling time of the train is 5 hours and 30 minutes . what was the average rate of speed of the train on the return trip to albany ? | 50 * t = 120 therefore t = 120 / 50 = 2.4 on return speed * ( 5.5 - 2.4 ) = 120 therefore t = 120 / 3.1 = 38.70 b | a ) 31 , b ) 38.7 , c ) 35 , d ) 36 , e ) 39 | b | speed(120, subtract(add(5, divide(30, const_60)), divide(120, 50))) | divide(n3,const_60)|divide(n0,n1)|add(n2,#0)|subtract(#2,#1)|speed(n0,#3) | physics |
a train crosses a platform of 180 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ? | "length of the train be β x β x + 180 / 15 = x + 250 / 20 20 x + 3600 = 15 x + 3750 5 x = 150 x = 30 m answer : a" | a ) 30 , b ) 887 , c ) 167 , d ) 197 , e ) 161 | a | subtract(multiply(250, divide(15, divide(15, const_3))), multiply(180, divide(20, divide(15, const_3)))) | divide(n1,const_3)|divide(n1,#0)|divide(n3,#0)|multiply(n2,#1)|multiply(n0,#2)|subtract(#3,#4)| | physics |
2 + 2 + 2 Β² + 2 Β³ . . . + 2 ^ 7 | "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 7 + 2 ^ 7 , which will give you 2 ^ 8 answer e" | a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 35 , e ) 2 ^ 8 | e | divide(multiply(2, add(2, 2)), 2) | add(n0,n3)|multiply(n3,#0)|divide(#1,n1)| | general |
what will be the difference between simple interest and compound interest @ 10 % per annum on a sum of rs . 1000 after 4 years ? | solution s . i . = rs ( 1000 x 10 x 4 / 100 ) = rs . 400 . c . i . = rs . [ 1000 x ( 1 x 10 / 100 ) 4 - 1000 ] = rs . 464.10 β΄ difference = rs . ( 464.10 - 400 ) = rs . 64.10 answer d | a ) rs . 31 , b ) rs . 32.10 , c ) rs . 40.40 , d ) rs . 64.10 , e ) none | d | subtract(subtract(multiply(power(add(divide(10, const_100), const_1), const_4), 1000), 1000), divide(multiply(4, multiply(10, 1000)), const_100)) | divide(n0,const_100)|multiply(n0,n1)|add(#0,const_1)|multiply(n2,#1)|divide(#3,const_100)|power(#2,const_4)|multiply(n1,#5)|subtract(#6,n1)|subtract(#7,#4) | gain |
two men start together to walk a certain distance , one at 4 kmph and another at 3 kmph . the former arrives half an hour before the latter . find the distance . | let the distance be x km . then , x / 3 - x / 4 = 1 / 2 ( 4 x - 3 x ) / 12 = 1 / 2 x = 6 km answer : a | a ) 6 km , b ) 7 km , c ) 8 km , d ) 9 km , e ) none of these | a | divide(multiply(3, 4), const_2) | multiply(n0,n1)|divide(#0,const_2) | physics |
cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 25 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ? | "use the options . the options which after getting added to 25 shows a cube of a number could be right . here 64 + 25 = 89 72 + 25 = 97 86 + 25 = 111 98 + 25 = 123 100 + 25 = 125 - - - ( 5 * 5 * 5 ) so we have 100 as the answer ! e" | a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 100 | e | subtract(power(add(const_1, add(const_1, const_3)), const_3), 25) | add(const_1,const_3)|add(#0,const_1)|power(#1,const_3)|subtract(#2,n0)| | geometry |
there are 35 kids in a play school . 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls . how many kids use yellow color balls ? | explanation : n ( aub ) = n ( a ) + n ( b ) - n ( anb ) . . . . ( 1 ) n ( a ) = number of kids playing with white color balls = 26 n ( aub ) = total number of kids in the play school = 35 n ( anb ) = number of kids playing with both white and yellow color balls = 19 we have to find , n ( b ) = number of kids playing wi... | a ) 12 , b ) 32 , c ) 5 , d ) 28 , e ) 35 | d | subtract(35, subtract(26, 19)) | subtract(n1,n2)|subtract(n0,#0) | other |
in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( β 8 , β 6 ) ? | "slope = rise / run = 9 / 18 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ." | a ) 4 , b ) 2 , c ) 0 , d ) β 2 , e ) β 4 | a | divide(subtract(multiply(divide(subtract(negate(6), 3), subtract(negate(8), 10)), 10), 3), divide(subtract(negate(6), 3), subtract(negate(8), 10))) | negate(n3)|negate(n2)|subtract(#0,n1)|subtract(#1,n0)|divide(#2,#3)|multiply(n0,#4)|subtract(#5,n1)|divide(#6,#4)| | general |
in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 21 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ? | "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 21 , s... | a ) 70 , b ) 245 , c ) 150 , d ) 35 , e ) 350 | c | divide(21, multiply(divide(subtract(const_100, 30), const_100), divide(20, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|divide(#1,const_100)|multiply(#2,#0)|divide(n2,#3)| | gain |
a train 110 m long is running with a speed of 80 km / hr . in what time will it pass a man who is running at 8 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 80 + 8 = 88 km / hr . = 88 * 5 / 18 = 220 / 9 m / sec . time taken to pass the men = 110 * 9 / 220 = 4.5 sec . answer : option c" | a ) 5 , b ) 6 , c ) 4.5 , d ) 8 , e ) 9 | c | divide(110, multiply(add(80, 8), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
tickets numbered 1 to 10 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 2 ? | "here , s = { 1 , 2,3 , . . . . . . , 9,10 } e = event getting a multiple of 3 = { 2 , 4,6 , 8,10 } probability = 5 / 10 = 1 / 2 correct option is c" | a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 1 / 4 | c | divide(2, const_10) | divide(n2,const_10)| | general |
set a contains all the even numbers between 6 and 50 inclusive . set b contains all the even numbers between 106 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ? | "set a contains 6 , 8 , . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 23 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 23 = 2300 answer a" | a ) 2300 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325 | a | multiply(subtract(106, 6), add(divide(subtract(50, 6), const_2), const_1)) | subtract(n1,n0)|subtract(n2,n0)|divide(#0,const_2)|add(#2,const_1)|multiply(#3,#1)| | general |
david completes a piece of work in 5 days , john completes the same work in 9 days . if both of them work together , then the number of days required to complete the work is ? | ifa can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 5 Γ 9 / 14 = 3.2 days answer : a | a ) 3.2 days , b ) 8 days , c ) 10 days , d ) 12 days , e ) 14 days | a | inverse(add(inverse(9), inverse(5))) | inverse(n1)|inverse(n0)|add(#0,#1)|inverse(#2) | physics |
what is the unit digit in 8 ^ 100 ? | unit digit in 8 ^ 100 = unit digit in [ ( 8 ^ 4 ) ^ 25 ] but unit digit in 8 ^ 4 = 6 unit digit 8 ^ 100 = 6 answer is c | a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 5 | c | reminder(power(8, const_2), const_10) | power(n0,const_2)|reminder(#0,const_10)| | general |
the citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8 . a certain street in nigiet contains 1000 buildings numbered 1 to 1000 in base 8 . how many 3 s are used in numbering these buildings ? express your answer in base 10 | "explanation : number 3 in 1 - 100 comes 20 times . 101 - 200 - > 20 times 201 - 300 - > 20 times 301 - 400 - > 120 times 401 - 500 - > 20 times 501 - 600 - > 20 times 601 - 700 - > 20 times 701 - 800 - > 20 times 801 - 900 - > 20 times 901 - 1000 - > 20 times total times : 300 times ( any no . from 1 to 9 except 0 wil... | a ) 192 , b ) 200 , c ) 196 , d ) 198 , e ) none | a | multiply(3, power(8, const_2)) | power(n0,const_2)|multiply(#0,n6)| | physics |
mixture a is 30 percent alcohol , and mixture b is 60 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 40 percent alcohol , approximately how many gallons of mixture a are in the mixture ? | "( 60 - 50 ) / ( 50 - 30 ) = qa / qb 10 / 20 = qa / qb 1 / 2 = qa / qb qa = ( 1 / 6 ) * 4 = 4 / 6 = 1 / 2 = 0.50 answer : d" | a ) 0.8 , b ) 0.7 , c ) 0.6 , d ) 0.5 , e ) 0.4 | d | divide(divide(multiply(30, 60), 60), const_2) | multiply(n0,n1)|divide(#0,n1)|divide(#1,const_2)| | general |
12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 4 days , working 15 hours a day , the number of men required ? | that is , 1 work done = 12 Γ 8 Γ 10 then , 12 8 Γ 10 = ? Γ 15 Γ 6 ? ( i . e . no . of men required ) = 12 Γ 8 Γ 10 / 15 Γ 6 = 16 days c ) | a ) 15 days , b ) 12 days , c ) 16 days , d ) 18 days , e ) 20 days | c | divide(multiply(multiply(12, 10), 8), multiply(4, 15)) | multiply(n0,n2)|multiply(n3,n4)|multiply(n1,#0)|divide(#2,#1) | physics |
due to construction , the speed limit along an 4 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | "4 / 35 - 4 / 55 = 4 / 5 * ( 11 - 7 ) / 77 = 4 / 5 * 4 / 77 * 60 min = 4 * 12 * 4 / 77 = 192 / 77 ~ 2.4 answer - e" | a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 2 | e | max(multiply(subtract(add(55, 4), const_1), subtract(divide(4, 35), divide(4, 55))), const_4) | add(n0,n1)|divide(n0,n2)|divide(n0,n1)|subtract(#0,const_1)|subtract(#1,#2)|multiply(#3,#4)|max(#5,const_4)| | physics |
if k ^ 3 is divisible by 162 , what is the least possible value of integer k ? | "k ^ 3 = 162 * x = 2 * 3 ^ 4 * x the factors of k must at minimum include 2 * 3 ^ 2 = 18 . the answer is c ." | a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 36 | c | divide(divide(162, const_2), const_2) | divide(n1,const_2)|divide(#0,const_2)| | general |
when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 3 . what is the value of 13 y β x ? | "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 3 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 1 = x 13 y - x = 1 the answer is a ." | a ) 1 , b ) 0 , c ) - 1 , d ) - 2 , e ) - 4 | a | subtract(multiply(13, divide(subtract(multiply(2, 4), 3), subtract(multiply(8, 3), multiply(2, 11)))), add(multiply(11, divide(subtract(multiply(2, 4), 3), subtract(multiply(8, 3), multiply(2, 11)))), 4)) | multiply(n1,n2)|multiply(n3,n4)|multiply(n0,n2)|subtract(#0,n5)|subtract(#1,#2)|divide(#3,#4)|multiply(n6,#5)|multiply(n0,#5)|add(n1,#7)|subtract(#6,#8)| | general |
a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 12 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ? | "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 12 hours . if the company used t... | a ) 3 , b ) 4 , c ) 6 , d ) 9 / 2 , e ) 12 | d | divide(const_1, multiply(12, add(divide(const_1, 36), divide(const_1, const_2.0)))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(const_2.0,#2)|divide(const_1,#3)| | gain |
a can do a piece of work in 20 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ? | "10 / 20 + 10 / 30 + 10 / x = 1 x = 60 days answer : b" | a ) 24 days , b ) 60 days , c ) 86 days , d ) 45 days , e ) 17 days | b | divide(10, subtract(const_1, divide(add(10, 10), 20))) | add(n2,n2)|divide(#0,n0)|subtract(const_1,#1)|divide(n2,#2)| | physics |
a money lender lent rs . 800 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years . | ( 800 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 Γ’ β β t = 3.72 answer b | a ) 3.5 , b ) 3.72 , c ) 4 , d ) 4.25 , e ) 4.5 | b | divide(350, add(divide(multiply(3, 800), const_100), divide(multiply(1400, 5), const_100))) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|add(#2,#3)|divide(n4,#4)| | gain |
two watches are set for an alarm at 10 0 ' clock in the night . one watch gains 2 minutes per hour . when the faster watch shows 4 : 12 in the morning when the alarm rings what does the correct watch show ? | the faster watch gains 2 minutes per hour the two watches show 10 : 00 at 10 0 ' clock at 11 0 ' clock - the correct watch is at 11 : 00 the faster watch is at 11 : 02 ( 1 hour + gains 2 minutes per hour ) at 12 midnight - the correct watch is at 12 : 00 the faster watch is at 12 : 04 ( 2 hours + gains 4 minutes per 2 ... | a ) 5 : 00 , b ) 4 : 00 , c ) 4 : 10 , d ) 5 : 20 , e ) 6 : 00 | b | subtract(add(4, 12), multiply(subtract(add(4, 12), 10), 2)) | add(n3,n4)|subtract(#0,n0)|multiply(n2,#1)|subtract(#0,#2) | physics |
if 3 x β 5 y = 5 and x / x + y = 5 / 7 , then what is the value of x β y ? | 3 x β 5 y = 5 . . . ( i ) and xx + y = 57 xx + y = 57 β 7 x = 5 x + 5 y β 2 x = 5 y . . . ( ii ) from ( i ) and ( ii ) , x = 5 and y = 2 β΄ x β y = 3 answer d | a ) 9 , b ) 6 , c ) 4 , d ) 3 , e ) none of these | d | subtract(divide(5, subtract(3, multiply(subtract(inverse(divide(5, 7)), const_1), 5))), multiply(subtract(inverse(divide(5, 7)), const_1), divide(5, subtract(3, multiply(subtract(inverse(divide(5, 7)), const_1), 5))))) | divide(n1,n4)|inverse(#0)|subtract(#1,const_1)|multiply(n1,#2)|subtract(n0,#3)|divide(n1,#4)|multiply(#5,#2)|subtract(#5,#6) | general |
a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 300 when the rate to profit rises from 5 to 7 percent . find the capital of b ? | "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 300 b capital = 22500 * 1 / 6 = 3750 . answer : a" | a ) 3750 , b ) 7799 , c ) 2500 , d ) 2772 , e ) 2912 | a | divide(multiply(300, const_100), 2) | multiply(n2,const_100)|divide(#0,n0)| | general |
john borrowed 3 soccer boots from jake , and forgot them on the field , if peter came across a total of 15 boots on the field jake ' s boots inclusive , and he took 4 boots at random , what is the probability that jake ' s boots were not amongst the 4 taken ? . | since jake owns 3 of the boots , the subset from which the 4 boots should be chosen are the 12 boots not owned by jake from the universe of 15 . the first boot can be one of the 12 from the 15 with probability 12 / 15 . the second boot can be one of the 11 from the 14 remaining with probability 11 / 14 . the third boot... | a ) 12 / 91 , b ) 3 / 15 , c ) 12 / 15 , d ) 33 / 91 , e ) 3 / 91 | d | divide(choose(subtract(15, 3), 4), choose(15, 4)) | choose(n1,n2)|subtract(n1,n0)|choose(#1,n2)|divide(#2,#0) | probability |
a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 40 marks , find the maximum marks set for the test . | 30 % = 120 marks 1 % = 4 marks 100 % = 400 marks the answer is a . | a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800 | a | divide(add(80, 40), divide(30, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1) | gain |
set a consists of the integers from 5 to 10 , inclusive , while set b consists of the integers from 1 to 8 , inclusive . how many distinct integers do belong to the both sets at the same time ? | "a = { 5,6 , 7 , 8 , 9 , 10 } b = { 1,2 , 3,4 , 5,6 , 7,8 } common elements = { 5,6 , 7 , 8 } = 4 elements answer : option e ." | a ) 5 , b ) 10 , c ) 8 , d ) 2 , e ) 4 | e | add(1, 5) | add(n0,n2)| | other |
he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg . answer : b" | a ) 75 kg , b ) 95 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg | b | add(multiply(2.5, 8), 75) | multiply(n0,n1)|add(n2,#0)| | general |
a rectangle a has an area of 30 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ? | i guess it ' s mean that square b is placed within rectangle a entirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 30 - 16 = 14 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favora... | ['a ) 9 / 30', 'b ) 14 / 30', 'c ) 4 / 9', 'd ) 3 / 5', 'e ) 6 / 25'] | b | divide(subtract(30, square_area(square_edge_by_perimeter(16))), 30) | square_edge_by_perimeter(n1)|square_area(#0)|subtract(n0,#1)|divide(#2,n0) | geometry |
a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.40 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer wil... | "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c" | a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3 | c | add(add(multiply(const_2, 32.25), multiply(const_1, 20.40)), multiply(const_1, 13.85)) | multiply(n5,const_2)|multiply(n3,const_1)|multiply(n1,const_1)|add(#0,#1)|add(#3,#2)| | general |
the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 20 . find the sum : | "sol . ( d ) let the sum be 100 . therefore , si = 100 Γ 5 Γ 2100 = 10100 Γ 5 Γ 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 β 100100 ( 1 + 5100 ) 2 β 100 β΄ = 100 Γ 21 Γ 2120 Γ 20 β 100 = 414 = 100 Γ 21 Γ 2120 Γ 20 β 100 = 414 difference of ci and si = 41 β 4 - 10 = 1 β 4 if the difference is 1 β 4 , the sum = 100 = > if the ... | a ) 4500 , b ) 7500 , c ) 5000 , d ) 8000 , e ) none of these | d | divide(20, subtract(power(add(const_1, divide(5, const_100)), 2), add(const_1, multiply(2, divide(5, 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 the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 8400 ? | "required difference = [ 3 Β½ % of rs . 8400 ] β [ 3 1 / 3 % of rs . 8400 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 8400 = 1 / 6 % of rs . 8400 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 8400 ] = rs . 14 . answer is c ." | a ) rs . 12 , b ) rs . 16 , c ) rs . 14 , d ) rs . 10 , e ) rs . 18 | c | divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 8400), const_100) | divide(n1,n2)|divide(n1,n0)|add(n0,#0)|add(n0,#1)|subtract(#2,#3)|multiply(n6,#4)|divide(#5,const_100)| | general |
how many two - digit whole numbers yield a remainder of 2 when divided by 12 and also yield a remainder of 2 when divided by 6 ? | "the possible number n can be written as follow : n = multiple of lcm ( 12,6 ) + 1 st such number n = 12 x + 2 possible values = 2 , 26,38 , 50,62 , 86,98 answer : 6 such 2 digit number . c ." | a ) none , b ) five , c ) six , d ) seven , e ) eight | c | add(add(2, 2), 2) | add(n0,n0)|add(n0,#0)| | general |
find ( 7 x + 8 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ? | x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 8 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 8 y ) / ( 3 y - 2 y ) = > 29 y / y = 29 answer : e | a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29 | e | divide(add(multiply(multiply(divide(3, 2), 2), 7), 8), subtract(multiply(divide(3, 2), 2), 2)) | divide(n4,n2)|multiply(n2,#0)|multiply(n0,#1)|subtract(#1,n2)|add(n1,#2)|divide(#4,#3) | general |
kramer can pack 10 boxes of cigarettes per minute . if there are 5 boxes of cigarettes in one case , how many cases can kramer pack in 2 hours ? | kramer can pack 10 boxes per min . therefore in 2 hrs ( 120 mins ) he can pack 120 * 10 = 1200 boxes . if there are 5 boxes in one case then then the total number of cases packed by kramer = 1200 / 5 = 240 answer is c | a ) 100 , b ) 120 , c ) 240 , d ) 150 , e ) 200 | c | divide(multiply(multiply(const_60, 2), 10), 5) | multiply(n2,const_60)|multiply(n0,#0)|divide(#1,n1) | physics |
what number should replace the question mark ? 11 , 15 , 16 , 12 , 21 , 9 , - - - ? | "answer : e 11 , 15 , 16 , 12 , 21 , 9 , - - - ? there are two alternate sequences : + 5 and - 3 ." | a ) 21 , b ) 29 , c ) 28 , d ) 27 , e ) 26 | e | add(add(add(const_2.0, 11), 11), 11) | add(const_2.0,n0)|add(n0,#0)|add(#1,n0)| | general |
list d consists of 12 consecutive integers . if - 4 is the least integer in list d , what is the range of positive integers in list d ? | since - 4 is the least integer in list d , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b . | a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12 | b | subtract(subtract(subtract(12, const_1), 4), const_1) | subtract(n0,const_1)|subtract(#0,n1)|subtract(#1,const_1) | general |
a train 125 m long passes a man , running at 15 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ? | "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 15 ) km / hr . x - 15 = 45 = > x = 60 km / hr . answer : option c" | a ) 40 , b ) 50 , c ) 60 , d ) 79 , e ) 80 | c | divide(divide(subtract(125, multiply(multiply(15, const_0_2778), 15)), 15), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)| | physics |
the ratio of the volumes of two cubes is 729 : 1000 . what is the ratio of their total surface areas ? | "ratio of the sides = Β³ β 729 : Β³ β 1000 = 9 : 10 ratio of surface areas = 92 : 102 = 46 : 51 answer : c" | a ) 1 : 12 , b ) 81 : 13 , c ) 46 : 51 , d ) 86 : 16 , e ) 56 : 13 | c | power(divide(729, 1000), divide(const_1, const_3)) | divide(n0,n1)|divide(const_1,const_3)|power(#0,#1)| | geometry |
the average weight of 9 person ' s increases by 5.5 kg when a new person comes in place of one of them weighing 86 kg . what might be the weight of the new person ? | "total weight increased = ( 9 x 5.5 ) kg = 49.5 kg . weight of new person = ( 86 + 49.5 ) kg = 135.5 kg . answer : option c" | a ) 72 kg , b ) 77.5 kg , c ) 135.5 kg , d ) data inadequate , e ) none of these | c | add(multiply(9, 5.5), 86) | multiply(n0,n1)|add(n2,#0)| | general |
in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 50 more than the correct answer . find the number . | "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 50 25 * x / 48 = 50 x = 96 answer a" | a ) 96 , b ) 280 , c ) 384 , d ) 400 , e ) 500 | a | divide(multiply(multiply(50, 16), 6), subtract(multiply(5, 16), multiply(5, 6))) | multiply(n1,n4)|multiply(n0,n1)|multiply(n0,n3)|multiply(n3,#0)|subtract(#1,#2)|divide(#3,#4)| | general |
a rectangle having length 150 cm and width 40 cm . if the length of the rectangle is increased by fifteen percent then how much percent the breadth should be decreased so as to maintain the same area . | "explanation : solution : ( 15 / ( 150 + 15 ) * 100 ) % = 9.09 % answer : b" | a ) 25 % , b ) 9.09 % , c ) 40 % , d ) 75 % , e ) none of these | b | multiply(add(const_1, divide(divide(multiply(150, 40), add(150, divide(multiply(multiply(const_3, const_10), 150), const_100))), 40)), const_10) | multiply(n0,n1)|multiply(const_10,const_3)|multiply(n0,#1)|divide(#2,const_100)|add(n0,#3)|divide(#0,#4)|divide(#5,n1)|add(#6,const_1)|multiply(#7,const_10)| | geometry |
two numbers n and 12 have lcm = 42 and gcf = 6 . find n . | "the product of two integers is equal to the product of their lcm and gcf . hence . 12 * n = 42 * 6 n = 42 * 6 / 12 = 21 correct answer c" | a ) 35 , b ) 56 , c ) 21 , d ) 87 , e ) 24 | c | divide(multiply(42, 6), 12) | multiply(n1,n2)|divide(#0,n0)| | physics |
ajay spends 45 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 7.5 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income . | "let the monthly income of ajay be rs . x savings of ajay = x - ( 45 + 25 + 7.5 ) / 100 * x = 22.5 / 100 x 22.5 / 100 x = 9000 x = 40000 . answer : a" | a ) rs . 40000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these | a | divide(9000, divide(subtract(const_100, add(add(45, 25), 7.5)), const_100)) | add(n0,n1)|add(n2,#0)|subtract(const_100,#1)|divide(#2,const_100)|divide(n3,#3)| | gain |
the average of numbers 0.44204 , 0.44203 , 0.44202 and 0.44201 is ? | "answer average = ( 0.44204 + 0.44203 + 0.44202 + 0.44201 ) / 4 = 1.7681 / 4 = 0.442025 correct option : d" | a ) 0.44202 , b ) 0.44204 , c ) 0.442022 , d ) 0.442025 , e ) none | d | divide(add(multiply(0.44204, 0.44203), multiply(0.44204, 0.44202)), 0.44204) | multiply(n0,n1)|multiply(n0,n2)|add(#0,#1)|divide(#2,n0)| | general |
the length of the bridge , which a train 145 metres long and travelling at 45 km / hr can cross in 30 seconds , is : | "let the length of the bridge : l the equation now is l + 145 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 230 m answer : b" | a ) 200 m , b ) 230 m , c ) 245 m , d ) 250 m , e ) 270 m | b | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 145) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ? | "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 19 - 1 then 18 * ( 18 - 3 ) / 2 = 135 correct option : a" | a ) 135 , b ) 125 , c ) 120 , d ) 110 , e ) 140 | a | divide(multiply(subtract(19, const_1), subtract(subtract(19, const_1), const_3)), const_2) | subtract(n0,const_1)|subtract(#0,const_3)|multiply(#0,#1)|divide(#2,const_2)| | geometry |
sachin is younger than rahul by 7 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ? | "let rahul ' s age be x years . then , sachin ' s age = ( x - 7 ) years . therefore ( x - 7 ) / x = 7 / 9 9 x - 63 = 7 x 2 x = 63 x = 31.5 hence , sachin ' s age = ( x - 7 ) = 24.5 years . answer : b" | a ) 22.5 years , b ) 24.5 years , c ) 12.5 years , d ) 28.5 years , e ) 29.5 years | b | multiply(divide(7, subtract(9, 7)), 7) | subtract(n2,n1)|divide(n0,#0)|multiply(n1,#1)| | other |
a train running at the speed of 72 km / hr crosses a pole in 9 sec . what is the length of the train ? | "speed = 72 * 5 / 18 = 20 m / sec length of the train = speed * time = 20 * 9 = 180 m answer : e" | a ) 288 , b ) 279 , c ) 277 , d ) 272 , e ) 180 | e | multiply(divide(multiply(72, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
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 |
a set consists of 20 numbers , all are even or multiple of 5 . if 9 numbers are even and 12 numbers are multiple of 5 , how many numbers is multiple of 10 ? | "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 20 = 9 + 12 - { both } + 0 ; { both } = 1 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : b ." | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5 | b | subtract(20, 12) | subtract(n0,n3)| | general |
united telephone charges a base rate of $ 6.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ? | "lets take number of minutesx . given that , 6 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 120 minutes ans c" | a ) 20 minutes , b ) 110 minutes , c ) 120 minutes , d ) 140 minutes , e ) 160 minutes | c | divide(subtract(12.00, 6.00), subtract(0.25, 0.20)) | subtract(n2,n0)|subtract(n1,n3)|divide(#0,#1)| | general |
the ratio of three numbers is 1 : 3 : 4 and the sum of their squares is 2600 . the sum of the numbers is ? | "let the numbers be x , 3 x , 4 x then , x ^ 2 + 9 x ^ 2 + 16 x ^ 2 = 2600 26 x ^ 2 = 2600 x ^ 2 = 100 x = 10 answer is a" | a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9 | a | sqrt(divide(2600, add(power(4, 3), add(power(1, const_2), power(3, 3))))) | power(n0,n1)|power(n1,const_2)|power(n2,n1)|add(#0,#1)|add(#3,#2)|divide(n3,#4)|sqrt(#5)| | other |
a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18000 . a ' s share is ? | "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18000 = 6000 answer : c" | a ) rs . 7500 , b ) rs . 7200 , c ) rs . 6000 , d ) rs . 5750 , e ) rs . 6750 | c | multiply(multiply(const_1, const_12), divide(18000, add(add(multiply(const_1, const_12), multiply(subtract(const_12, 6), const_2)), multiply(subtract(const_12, 8), const_3)))) | multiply(const_1,const_12)|subtract(const_12,n0)|subtract(const_12,n1)|multiply(#1,const_2)|multiply(#2,const_3)|add(#0,#3)|add(#5,#4)|divide(n2,#6)|multiply(#7,#0)| | gain |
the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and 15 as remainder . what is the smaller number ? | "let the smallest number be x . then larger number = ( x + 1365 ) x + 1365 = 6 x + 15 = 5 x = 1350 x = 270 smaller number = 270 . answer : b" | a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 365 | b | divide(add(1365, 15), subtract(6, const_1)) | add(n0,n2)|subtract(n1,const_1)|divide(#0,#1)| | general |
in a 100 m race , sam beats john by 4 seconds . on the contrary , if sam allowed john to start 24 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ? | "their difference is 4 second but this difference is 0 if john allows sam to start the race from 24 m ahead . that means jhon was 24 m away from finishing line when they started together . so he will cover 24 m in 4 seconds . so his speed = 24 / 4 = 6 metre / second . so time taken = 100 / 4 = 25 seconds . so sam took ... | a ) 4 seconds , b ) 25 seconds , c ) 19 seconds , d ) 21 seconds , e ) 6.25 seconds | c | divide(subtract(100, 24), 4) | subtract(n0,n2)|divide(#0,n1)| | physics |
the contents of a certain box consist of 14 apples and 20 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ? | the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right n... | a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20 | c | subtract(add(14, 20), divide(14, divide(70, const_100))) | add(n0,n1)|divide(n2,const_100)|divide(n0,#1)|subtract(#0,#2) | general |
a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 500 , what is the reduced price for kg ? | "a 500 * ( 25 / 100 ) = 125 - - - - 5 ? - - - - 1 = > rs . 25" | a ) 25 , b ) 60 , c ) 70 , d ) 80 , e ) 20 | a | divide(divide(multiply(500, 25), const_100), 5) | multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)| | gain |
there are two concentric circles with radii 8 and 6 . if the radius of the outer circle is increased by 25 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ? | "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 64 pi . the area of the small circle is 36 pi . the area a 1 between the circles is 28 pi . when the big circle ' s radius increases , the new area is 100 pi . when the small circle ' s radius decreases , the new area is 9 pi . the... | a ) 225 , b ) 250 , c ) 275 , d ) 300 , e ) 325 | a | multiply(divide(subtract(subtract(power(multiply(8, divide(add(const_100, 25), const_100)), const_2), power(multiply(6, divide(subtract(const_100, 50), const_100)), const_2)), subtract(power(8, const_2), power(6, const_2))), subtract(power(8, const_2), power(6, const_2))), const_100) | add(n2,const_100)|power(n0,const_2)|power(n1,const_2)|subtract(const_100,n3)|divide(#0,const_100)|divide(#3,const_100)|subtract(#1,#2)|multiply(n0,#4)|multiply(n1,#5)|power(#7,const_2)|power(#8,const_2)|subtract(#9,#10)|subtract(#11,#6)|divide(#12,#6)|multiply(#13,const_100)| | gain |
the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 100 meters ? | the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 100 meters = 100 / 5 = 20 seconds . the answer is d . | a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22 | d | divide(100, multiply(add(15, 3), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1) | physics |
3 people decided to put a down payment on a car for 3500 dollars . how much money do they each have to pay , given that that they have to pay the same amount , and they can not use any bills below $ 1 ? | to keep the amount exact when dividing for 3 , we have to work backwards through division . dividing 3500 by 3 will give us 1166.66 then by subtracting . 66 , we get 1166 , and we multiply it by 3 to get 3498 . to get enough for the down payment , we add 3 to 3498 . dividing the result by 3 gives us our answer . correc... | a ) $ 1166 , b ) $ 1168 , c ) $ 1166.6 , d ) $ 1167 , e ) none of the above | d | divide(3500, 3) | divide(n1,n0) | general |
a biker covered half the distance between two towns in 2 hr 30 min . after that he increased his speed by 2 km / hr . he covered the second half of the distance in 2 hr 20 min . find the distance between the two towns and the initial speed of the biker . | let x km / hr be the initial speed of the biker , then his speed during the second part of the trip is x + 2 km / hr . half the distance between two cities equals 23060 β
x km and 22060 β
( x + 2 ) km . from the equation : 23060 β
x = 22060 β
( x + 2 ) we get x = 28 km / hr . the intial speed of the biker is 28 km / h ... | a ) 140 , b ) 120 , c ) 130 , d ) 150 , e ) 160 | a | multiply(2, multiply(add(2, divide(30, const_60)), divide(multiply(add(2, divide(20, const_60)), 2), subtract(add(2, divide(30, const_60)), add(2, divide(20, const_60)))))) | divide(n1,const_60)|divide(n4,const_60)|add(n0,#0)|add(n0,#1)|multiply(n0,#3)|subtract(#2,#3)|divide(#4,#5)|multiply(#2,#6)|multiply(n0,#7) | physics |
the diagonal of a square is 40 m . the area of the square is : | arear = 1 / 2 Γ ( diagonal ) ( power ) 2 = ( 1 / 2 Γ 40 Γ 40 ) m ( power ) 2 = 1600 / 2 = 800 m ( power ) 2 answer is c . | ['a ) 600', 'b ) 900', 'c ) 800', 'd ) 500', 'e ) 400'] | c | divide(power(40, const_2), const_2) | power(n0,const_2)|divide(#0,const_2) | geometry |
on dividing 16698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ? | "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 16698 - 14 ) / 89 = 187 answer ( c )" | a ) 743 , b ) 154 , c ) 187 , d ) 741 , e ) 785 | c | divide(subtract(16698, 14), 89) | subtract(n0,n2)|divide(#0,n1)| | general |
a box contains 4 black , 3 red and 6 green marbles . 2 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ? | explanation : total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random . therefore , n ( s ) = 13 c 2 = 78 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 4 c 2 + 3 c 2 + 6 c... | a ) 24 / 78 , b ) 24 / 709 , c ) 24 / 76 , d ) 24 / 71 , e ) 24 / 72 | a | divide(add(add(3, 6), add(const_10, add(3, 2))), multiply(add(const_10, const_3), 6)) | add(n1,n2)|add(n1,n3)|add(const_10,const_3)|add(#1,const_10)|multiply(n2,#2)|add(#0,#3)|divide(#5,#4) | other |
when an amount was distributed among 14 boys , each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys . what was the amount ? | let the total amount be rs . x the , x / 14 - x / 18 = 80 < = > 2 x / 126 = 80 < = > x / 63 = 63 x 80 = 5040 . hence the total amount is 5040 answer is d . | a ) 5000 , b ) 5030 , c ) 5010 , d ) 5040 , e ) 5020 | d | divide(80, subtract(divide(const_1, 14), divide(const_1, 18))) | divide(const_1,n0)|divide(const_1,n2)|subtract(#0,#1)|divide(n1,#2) | general |
sum of the squares of 3 no . is 156 and the sum of their products taken two at a time is 50 . find the sum ? | ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 156 + 2 * 50 a + b + c = Γ’ Λ Ε‘ 256 = 16 answer b | a ) 18 , b ) 16 , c ) 19 , d ) 21 , e ) 15 | b | sqrt(add(156, multiply(50, const_2))) | multiply(n2,const_2)|add(n1,#0)|sqrt(#1) | general |
two trains of length 150 m and 250 m are 150 m apart . they start moving towards each other on parallel tracks , at speeds 36 kmph and 72 kmph . in how much time will the trains cross each other ? | "relative speed = ( 36 + 72 ) * 5 / 18 = 6 * 5 = 30 mps . the time required = d / s = ( 150 + 150 + 250 ) / 30 = 550 / 30 = 55 / 3 sec . answer : a" | a ) 55 / 3 , b ) 55 / 7 , c ) 55 / 6 , d ) 55 / 8 , e ) 55 / 9 | a | divide(150, multiply(add(36, 72), const_0_2778)) | add(n3,n4)|multiply(#0,const_0_2778)|divide(n2,#1)| | physics |
farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : | "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to (... | a ) 15.502 % , b ) 25.7014 % , c ) 12.502 % , d ) 21.7014 % , e ) none | d | divide(multiply(multiply(divide(500, 3840), const_100), const_100), 60) | divide(n2,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,n0)| | general |
a , b and c started a business with capitals of rs . 6000 , rs . 8000 , and rs . 10000 respectively . at the end of the year , the profit share of b is rs 1000 . the difference between the profit shares of a and c is | ratio of investments of a , b and c is 6000 : 8000 : 10000 = 3 : 4 : 5 . and also given that , profit share of β b β is rs . 1000 . now required difference is 5 β 3 = 2 parts . therefore , required difference = 2 / 4 ( 1000 ) = rs . 500 . answer : c | a ) rs . 400 , b ) rs . 450 , c ) rs . 500 , d ) rs . 550 , e ) rs . 650 | c | multiply(divide(subtract(10000, 6000), 8000), 1000) | subtract(n2,n0)|divide(#0,n1)|multiply(n3,#1) | gain |
the probability that a computer company will get a computer hardware contract is 4 / 5 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ? | "let , a β‘ event of getting hardware contract b β‘ event of getting software contract ab β‘ event of getting both hardware and software contract . p ( a ) = 4 / 5 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b )... | a ) 7 / 20 , b ) 9 / 25 , c ) 11 / 30 , d ) 13 / 35 , e ) 17 / 40 | c | subtract(add(divide(const_3.0, 5), subtract(const_1, divide(4, 5))), divide(5, 6)) | divide(n0,const_4.0)|divide(n0,n3)|divide(n3,n5)|subtract(const_1,#1)|add(#0,#3)|subtract(#4,#2)| | other |
the length of a rectangle is five times of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 16 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 11 units ? | given that the area of the square = 16 sq . units = > side of square = Γ’ Λ Ε‘ 16 = 4 units the radius of the circle = side of the square = 4 units length of the rectangle = 5 * 4 = 20 units given that breadth = 11 units area of the rectangle = lb = 20 * 11 = 220 sq . units answer : e | ['a ) 180 sq . units', 'b ) 11 sq . units', 'c ) 110 sq . units', 'd ) 140 sq . units', 'e ) 220 sq . units'] | e | multiply(multiply(sqrt(16), add(const_2, const_3)), 11) | add(const_2,const_3)|sqrt(n0)|multiply(#0,#1)|multiply(n1,#2) | geometry |
second saturday and every sunday is a holiday . how many working days will be there in a month of 30 days beginning on a saturday ? | explanation : mentioned month begins on a saturday and has 30 days sundays = 2 nd , 9 th , 16 th , 23 rd , 30 th = > total sundays = 5 every second saturday is holiday . 1 second saturday in every month total days in the month = 30 total working days = 30 - ( 5 + 1 ) = 24 . answer : option a | a ) 24 , b ) 23 , c ) 18 , d ) 21 , e ) 22 | a | add(multiply(subtract(divide(subtract(30, const_2), const_4), const_2), const_4), const_3) | subtract(n0,const_2)|divide(#0,const_4)|subtract(#1,const_2)|multiply(#2,const_4)|add(#3,const_3) | physics |
if 80 % of 90 is greater than 70 % of a number by 30 , what is the number ? | "explanation : 80 / 100 * 90 - 70 / 100 * x = 30 72 - 70 / 100 * x = 30 72 - 30 = 70 / 100 * x 42 = 70 / 100 * x 42 * 100 / 70 = x 60 = x answer : option b" | a ) 70 , b ) 60 , c ) 10 , d ) 75 , e ) 85 | b | divide(subtract(multiply(divide(80, const_100), 90), 30), divide(70, const_100)) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|subtract(#2,n3)|divide(#3,#1)| | gain |
a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is ... | "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 40 ( 2 ^ 3 * 5 ) , sob = 2 ^ 3 or 2 ^ 3 * 5 ( 8 or 40 ) . combining 2 premises shows the ans... | a ) 8 , b ) 6 , c ) 24 , d ) 32 , e ) 48 | b | sqrt(subtract(power(divide(40, 4), const_2), power(12, const_2))) | divide(n2,n1)|power(n0,const_2)|power(#0,const_2)|subtract(#2,#1)|sqrt(#3)| | geometry |
find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 6 x + 15 5 x = 985 x = 197 large number = 197 + 1365 = 1197 b" | a ) 1345 , b ) 1197 , c ) 1540 , d ) 1600 , e ) 1635 | b | multiply(divide(subtract(1000, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general |
a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be ? | length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a | ['a ) 7744', 'b ) 8844', 'c ) 5544', 'd ) 4444', 'e ) 3444'] | a | power(divide(circumface(56), const_4), const_2) | circumface(n0)|divide(#0,const_4)|power(#1,const_2) | geometry |
a rectangular courtyard , the sides of which are in the ratio of 4 : 3 , cost rs . 600 for paving at 50 p per m 2 ; find the length of the diagonal of the courtyard ? | 1 m 2 - - - - 1 / 2 ? - - - - - 600 = > 1200 m 2 4 x * 3 x = 1200 = > x = 10 answer : b | ['a ) 17 m', 'b ) 45 m', 'c ) 54 m', 'd ) 77 m', 'e ) 34 m'] | b | subtract(sqrt(add(power(multiply(4, sqrt(divide(divide(600, divide(50, const_100)), multiply(4, 3)))), 2), power(multiply(3, sqrt(divide(divide(600, divide(50, const_100)), multiply(4, 3)))), 2))), add(const_2, const_3)) | add(const_2,const_3)|divide(n3,const_100)|multiply(n0,n1)|divide(n2,#1)|divide(#3,#2)|sqrt(#4)|multiply(n0,#5)|multiply(n1,#5)|power(#6,n4)|power(#7,n4)|add(#8,#9)|sqrt(#10)|subtract(#11,#0) | geometry |
if the area of a circle decreases by 42 % , then the radius of a circle decreases by | "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 β 10 β 100 β x ) % = ( 100 β 10 β 100 β 42 ) % = ( 100 β 10 β 58 ) % = 100 - 76 = 24 % answer c" | a ) 20 % , b ) 18 % , c ) 24 % , d ) 64 % , e ) none of these | c | multiply(subtract(const_1, sqrt(divide(subtract(const_100, 42), const_100))), const_100) | subtract(const_100,n0)|divide(#0,const_100)|sqrt(#1)|subtract(const_1,#2)|multiply(#3,const_100)| | geometry |
a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ? | "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c" | a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59 | c | add(subtract(83, multiply(17, 3)), 3) | multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)| | general |
when x is multiplied by 3 , the result is 20 more than the result of subtracting x from 20 . what is the value of x ? | "the equation that can be formed is : 3 x - 20 = 20 - x or , 4 x = 40 or , x = 10 . answer : a" | a ) 10 , b ) - 2 , c ) 11 , d ) 13 , e ) 22 | a | divide(add(20, 20), add(3, const_1)) | add(n1,n2)|add(const_1,n0)|divide(#0,#1)| | general |
solution for 2.75 + . 003 + . 158 | "2.75 + . 003 + . 158 = 0 0 = 0 - 2.75 - 0.003 - 0.158 0 = - 2.911 answer : b" | a ) 2.91 , b ) 2.911 , c ) 2.938 , d ) 2.986 , e ) 2.999 | b | add(add(2.75, divide(003, const_1000)), divide(158, const_1000)) | divide(n1,const_1000)|divide(n2,const_1000)|add(n0,#0)|add(#2,#1)| | general |
jane makes toy bears . when she works with an assistant , she makes 70 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane β s output of toy bears per hour by what percent ? | "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional v... | a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 % | b | multiply(divide(10, subtract(subtract(const_100, 70), 10)), const_100) | subtract(const_100,n0)|subtract(#0,n1)|divide(n1,#1)|multiply(#2,const_100)| | physics |
ravi and sunil are partners in a business . ravi invests rs . 9,000 for 8 months and sunil invested rs . 12000 for 9 months then after one year ratio of their profits will be | "= ( 9000 * 8 ) : ( 15000 * 8 ) = 72000 : 108000 = 2 : 3 answer : b" | a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4 | b | divide(multiply(multiply(multiply(multiply(8, const_3), multiply(9, const_2)), const_100), 8), multiply(12000, 9)) | multiply(const_3,n1)|multiply(n3,const_2)|multiply(n2,n3)|multiply(#0,#1)|multiply(#3,const_100)|multiply(n1,#4)|divide(#5,#2)| | gain |
a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 238 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ? | "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 238 = > . 1 x + 3 / 4 x = 238 = > x = 280 280 - 238 = pure gala = 42 . answer d" | a ) 22 , b ) 33 , c ) 55 , d ) 42 , e ) 88 | d | subtract(divide(238, add(divide(10, const_100), divide(3, 4))), 238) | divide(n0,const_100)|divide(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,n1)| | general |
the purchase price of an article is $ 48 . in order to include 25 % of cost for overhead and to provide $ 12 of net profit , the markup should be | cost price of article = 48 $ % of overhead cost = 25 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 25 = 50 % answer a | a ) 50 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 % | a | add(multiply(divide(12, 48), const_100), 25) | divide(n2,n0)|multiply(#0,const_100)|add(n1,#1) | gain |
a car is running at a speed of 90 kmph . what distance will it cover in 15 second ? | "explanation : given : speed = 108 kmph = ( 90 x ( 5 / 18 ) ) m / sec = 25 m / sec distance covered in 15 second = ( 25 x 15 ) m = 375 m . answer : c" | a ) 100 m , b ) 255 m , c ) 375 m , d ) can not be determined , e ) none of these | c | multiply(divide(90, const_3_6), 15) | divide(n0,const_3_6)|multiply(n1,#0)| | physics |
what should be the least number to be added to the 51234 number to make it divisible by 9 ? | "the least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits . sum of digits = 15 . nearest multiple of 9 greater than sum of digits = 18 . hence 3 has to be added . answer : c" | a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2 | c | subtract(9, reminder(51234, 9)) | reminder(n0,n1)|subtract(n1,#0)| | general |
in a 120 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ? | "solution simple out of 120 20 % are male i . e 24 and 25 % are female i . e 30 , so total homeowner is 54 . now min number homeowner is 24 and max is 54 so question ask us to find least and 25 has least value among all option . so ans is 25 . answer : c" | a ) 49 , b ) 47 , c ) 25 , d ) 43 , e ) 41 | c | add(multiply(multiply(divide(25, const_100), 20), multiply(divide(25, const_100), 20)), divide(subtract(120, 20), 20)) | divide(n2,const_100)|subtract(n0,n1)|divide(#1,n1)|multiply(n1,#0)|multiply(#3,#3)|add(#2,#4)| | general |
8 k 8 + k 88 - - - - - - - - 16 t 6 if k and t represent non - zero digits within the integers above , what is t ? | 8 k 8 k 88 - - - - - - - - 16 t 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * *... | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 17 | a | subtract(subtract(16, add(8, const_1)), const_1) | add(n0,const_1)|subtract(n3,#0)|subtract(#1,const_1) | general |
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