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solve below question 2 x + 1 = - 15 | "find the pattern of the remainders after each power : ( 2 ^ 1 ) / 7 remainder 2 ( 2 ^ 2 ) / 7 remainder 4 ( 2 ^ 3 ) / 7 remainder 1 - - > this is where the cycle ends ( 2 ^ 4 ) / 7 remainder 2 - - > this is where the cycle begins again ( 2 ^ 5 ) / 7 remainder 4 continuing the pattern to ( 2 ^ 14 ) / 7 gives us a remainder of 4 final answer : d ) 4" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | reminder(power(2, 14), 7) | power(n0,n1)|reminder(#0,n2)| | general |
if 4 men working 10 hours a day earn rs . 1600 per week , then 9 men working 6 hours a day will earn how much per week ? | "1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 45 / 4 = 11 ¼ * 2 = 22 ½ days answer : b" | a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 12 ½ days , e ) none of these | b | add(divide(const_1, 18), divide(const_1, 30)) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)| | physics |
how many seconds will a 650 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ? | "let the additional invested amount for 8 % interest be x ; equation will be ; 2600 + 0.05 * 2600 + x + 0.08 x = 2600 + x + 0.06 ( 2600 + x ) 0.05 * 2600 + 0.08 x = 0.06 x + 0.06 * 2600 0.02 x = 2600 ( 0.06 - 0.05 ) x = 2600 * 0.01 / 0.02 = 1300 ans : ` ` c ' '" | a ) 1200 , b ) 3000 , c ) 1300 , d ) 3600 , e ) 2400 | c | divide(subtract(multiply(divide(6, const_100), 2600), multiply(2600, divide(5, const_100))), subtract(divide(8, const_100), divide(6, const_100))) | divide(n3,const_100)|divide(n1,const_100)|divide(n2,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(#2,#0)|subtract(#3,#4)|divide(#6,#5)| | general |
a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by a are ? | "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e" | a ) 96 , b ) 240 , c ) w = 256 , d ) w = 384 , e ) w = 480 | e | multiply(multiply(16, const_2), 15) | multiply(n1,const_2)|multiply(n2,#0)| | general |
if x is an integer and 2.134 × 10 ^ x is less than 2 , 200,000 , what is the greatest possible value for x ? | "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 40 + ( 11 - 1 ) * 1 } = 11 * 45 = 495 = x number of even number = ( 50 - 40 ) / 2 + 1 = 6 = y x + y = 495 + 6 = 501 d" | a ) 171 , b ) 281 , c ) 391 , d ) 501 , e ) 613 | d | add(multiply(divide(add(40, 50), const_2), add(subtract(50, 40), const_1)), add(divide(subtract(50, 40), const_2), const_1)) | add(n0,n1)|subtract(n1,n0)|add(#1,const_1)|divide(#1,const_2)|divide(#0,const_2)|add(#3,const_1)|multiply(#2,#4)|add(#5,#6)| | general |
in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 4000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ? | "28 - - - 4 ds = 7 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 7 + 4 ) / 2 = 5.5 answer : e" | a ) 6.5 , b ) 8.6 , c ) 7.5 , d ) 9.2 , e ) 5.5 | e | divide(add(divide(16, 4), divide(28, 4)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | physics |
a mixture contains milk and water in the ratio 5 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 5 : 3 . the quantity of milk in the original mixture is ? | alice and bob complete 200 km / 4 hours = 50 km / hour bob ' s speed is 50 - 30 = 20 km / hour the answer is a . | a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36 | a | subtract(divide(add(100, 100), subtract(11, 7)), 30) | add(n1,n1)|subtract(n4,n2)|divide(#0,#1)|subtract(#2,n0) | physics |
how many odd numbers between 10 and 1,000 are the squares of integers ? | "explanation : given year 2040 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2040 + 28 = 2068 answer : e" | a ) 2063 , b ) 2061 , c ) 2111 , d ) 2191 , e ) 2068 | e | add(multiply(subtract(multiply(const_4, const_4), const_2), const_2), 2040) | multiply(const_4,const_4)|subtract(#0,const_2)|multiply(#1,const_2)|add(n0,#2)| | gain |
a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 22 per kg , then his gain percent is | "5 , 15,25 , 35,40 , 50,55 , 65,75 , 85,95 so there are total 11 such type of numbers . answer : c" | a ) 10 , b ) 12 , c ) 11 , d ) 20 , e ) 25 | c | divide(100, const_10) | divide(n1,const_10)| | general |
a , b and c rents a pasture for rs . 480 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? | "sol . speed = [ 144 x 5 / 18 ] m / sec = 40 m / sec . time taken = ( 100 / 40 ) sec = 2.5 sec . answer a" | a ) 2.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) none | a | divide(100, multiply(144, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1004 in total compensation , how many total hours did he work that week ? | "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 25 2 x + 3 x = 600 x = 120 km answer is d" | a ) 24 km , b ) 30 km , c ) 48 km , d ) 120 km , e ) 15 km | d | divide(multiply(multiply(subtract(10, 2), add(10, 2)), 25), add(subtract(10, 2), add(10, 2))) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|multiply(n2,#3)|divide(#4,#2)| | physics |
the sector of a circle has radius of 14 cm and its perimeter 50 cm . find its central angel ? | "the total number of ways to choose 4 children from 8 is 8 c 4 = 70 the number of ways to choose 2 boys and 2 girls is 4 c 2 * 4 c 2 = 6 * 6 = 36 p ( 2 boys and 2 girls ) = 36 / 70 = 18 / 35 the answer is d ." | a ) 12 / 29 , b ) 14 / 31 , c ) 16 / 33 , d ) 18 / 35 , e ) 20 / 37 | d | divide(multiply(choose(4, const_2), choose(4, const_2)), choose(add(4, 4), 4)) | add(n0,n0)|choose(n0,const_2)|choose(n0,const_2)|choose(#0,n2)|multiply(#1,#2)|divide(#4,#3)| | probability |
average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ? | explanation : number = ( 800 * 300 * 600 ) / 8 * 3 * 2 = 3000000 answer : d | a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 3000000 , e ) none of these | d | divide(multiply(multiply(multiply(const_4.0, const_100), multiply(3, const_100)), multiply(const_4.0, const_100)), multiply(multiply(8, 3), 3)) | multiply(n2,const_100)|multiply(n1,const_100)|multiply(const_4.0,n1)|multiply(#0,#1)|multiply(n1,#2)|multiply(#3,#0)|divide(#5,#4)| | physics |
the population of a town is 10000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ? | "a rate = 1 / 8 b rate = 1 / 24 ( a + b ) rate = ( 1 / 8 ) + ( 1 / 24 ) = 1 / 6 a & b finish the work in 6 days correct option is e" | a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6 | e | divide(multiply(8, 24), add(8, 24)) | add(n0,n1)|multiply(n0,n1)|divide(#1,#0)| | physics |
after decreasing 24 % in the price of an article costs rs . 1140 . find the actual cost of an article ? | "16 raise to 8 = 2 raise to 32 , now highest power of 2 divisible by 50 ! is 25 + 12 + 6 + 3 + 1 = 47 since 2 raise to 47 is divisible , 2 raise to 32 also will be divisible answer : a" | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | reminder(multiply(16, 50), 8) | multiply(n0,n1)|reminder(#0,n2)| | general |
for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score w for the exam ? | "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 1250 + 1250 = 2500 m . required time = 2500 * 6 / 125 = 120 sec . answer : e" | a ) 228 , b ) 278 , c ) 48 , d ) 27 , e ) 120 | e | add(45, 30) | add(n1,n2)| | physics |
on average , the boys in the class have 20 pencils and the girls have 38 pencils . if the overall class average is 30 pencils , what is the ratio of boys to girls in the class ? | "let c . p . of each pencil be re . 1 . then , c . p . of 100 pencils = rs . 100 ; s . p . of 100 pencils = rs . 140 . gain % = 40 / 100 * 100 = 40 % answer : e" | a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40 | e | divide(const_100, divide(100, subtract(140, 100))) | subtract(n0,n1)|divide(n1,#0)|divide(const_100,#1)| | gain |
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds . the length of the train ( in metres ) is : | "mother + daughter + child = 140 kg daughter + child = 60 kg mother = 140 - 60 = 80 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 80 = 16 kg so now daughter = 140 - ( mother + child ) = 140 - ( 80 + 16 ) = 44 kg answer : a" | a ) 44 , b ) 47 , c ) 48 , d ) 49 , e ) 50 | a | subtract(60, divide(subtract(140, 60), 5)) | subtract(n0,n1)|divide(#0,n3)|subtract(n1,#1)| | general |
alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,200 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ? | "( 3 x - 9 ) : ( 5 x - 9 ) = 5 : 2 x = 1 = > 3 x = 3 answer : a" | a ) a ) 3 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62 | a | add(multiply(3, divide(9, multiply(3, 5))), multiply(5, divide(9, multiply(3, 5)))) | multiply(n0,n1)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(#2,#3)| | other |
irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 170 cookies , what percent of the cookies did irin bake ? | we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c . | a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 1 / 8 | c | divide(add(const_1, divide(3, 5)), add(5, 3)) | add(n0,n1)|divide(n0,n1)|add(#1,const_1)|divide(#2,#0) | general |
boys and girls in a class are writing letters . there are twice as many girls as boys in the class , and each girl writes 3 more letters than each boy . if boys write 24 of the 90 total letters written by the class , how many letters does each boy write ? | "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 65 5 x = 35 x = 7 . x + 12 = 7 + 12 = 19 b" | a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21 | b | divide(add(add(add(add(const_2.0, const_4), add(3, const_4)), add(const_4, const_4)), 65), 5) | add(const_2.0,const_4)|add(const_4,const_4)|add(#0,#0)|add(#2,#1)|add(n2,#3)|divide(#4,n0)| | general |
a pupil ' s marks were wrongly entered as 83 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ? | let the cost price of book = x selling price of book = 24 $ markup % = 20 ( 120 / 100 ) x = 24 = > x = 20 answer e | a ) $ 14.40 , b ) $ 14.00 , c ) $ 10.00 , d ) $ 9.60 , e ) $ 20.00 | e | subtract(24, multiply(divide(20, const_100), 24)) | divide(n0,const_100)|multiply(n1,#0)|subtract(n1,#1) | gain |
when 242 is divided by a certain divisor the remainder obtained is 12 . when 698 is divided by the same divisor the remainder obtained is 16 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 10 . what is the value of the divisor ? | "the profit 0 f 2009 in terms of 2008 = 0.9 * 15 / 10 * 100 = 135 % c" | a ) 80 % , b ) 105 % , c ) 135 % , d ) 124.2 % , e ) 138 % | c | multiply(divide(multiply(15, subtract(const_1, divide(10, const_100))), 10), const_100) | divide(n3,const_100)|subtract(const_1,#0)|multiply(n4,#1)|divide(#2,n1)|multiply(#3,const_100)| | gain |
10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ? | "p = $ 10000 r = 6 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 6 * 1 / 100 = $ 600 answer is c" | a ) $ 410 , b ) $ 500 , c ) $ 600 , d ) $ 710 , e ) $ 1000 | c | multiply(10000, divide(6, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
what is the ratio between perimeters of two squares one having 8 times the diagonal then the other ? | "milk : water = 5 : 2 5 x : 2 x + 10 = 5 : 3 3 [ 5 x ] = 5 [ 2 x + 10 ] 15 x = 10 x + 50 15 x - 10 x = 50 x = 10 the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 x = 70 short cut method : milk : water = 5 : 2 after adding 10 liters of water milk : water = 5 : 3 milk is same but water increse 10 liters then the water ratio is increse 1 parts 1 part - - - - - > 10 liters the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 parts - - - - - > 70 liters ( answer is = 70 ) short cut method - 2 : for only milk problems milk : water 5 : 2 5 : 3 milk ratio same but water ratio 1 part incress per 10 liters 1 part of ratio - - - - - - - > 10 liters 7 part of ratio - - - - - - - > 70 liters c )" | a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70 | c | divide(multiply(10, divide(const_2.0, const_3.0)), subtract(divide(3, add(5, 2)), multiply(divide(2, add(5, 2)), divide(2, 5)))) | add(n4,n1)|divide(n3,n4)|divide(n0,#0)|divide(n1,#0)|multiply(n2,#1)|multiply(#3,#1)|subtract(#2,#5)|divide(#4,#6)| | general |
of the 100 people in a room , 4 / 5 are women . if 3 / 5 of the people are married , what is the maximum number of women in the room who could be unmarried ? | let ' s see , the way i did it was 12 / 25 are clerical out of 3600 so 1728 are clerical 1728 reduced by 1 / 4 is 1728 * 1 / 4 so it reduced 432 people , so there is 1296 clerical people left but since 432 people left , it also reduced from the total of 3600 so there are 3168 people total since 1296 clerical left / 3168 people total you get ( a ) 40 % | a ) 40 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 % | a | multiply(divide(multiply(divide(12, 25), subtract(1, divide(1, 4))), add(multiply(divide(12, 25), subtract(1, divide(1, 4))), subtract(const_1, divide(12, 25)))), const_100) | divide(n1,n2)|divide(n3,n4)|subtract(n3,#1)|subtract(const_1,#0)|multiply(#0,#2)|add(#4,#3)|divide(#4,#5)|multiply(#6,const_100) | general |
if the cost price is 96 % of the selling price , then what is the profit percent ? | "in such a case there is always a loss loss % = ( 13 / 10 ) ^ 2 = 120 / 71 = 1.69 % answer is a" | a ) 1.69 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 % | a | multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 13)), 675958), multiply(divide(const_100, subtract(const_100, 13)), 675958)), add(675958, 675958)), add(multiply(divide(const_100, add(const_100, 13)), 675958), multiply(divide(const_100, subtract(const_100, 13)), 675958))), const_100) | add(n1,const_100)|add(n0,n0)|subtract(const_100,n1)|divide(const_100,#0)|divide(const_100,#2)|multiply(n0,#3)|multiply(n0,#4)|add(#5,#6)|subtract(#7,#1)|divide(#8,#7)|multiply(#9,const_100)| | gain |
if 0.5 : x : : 5 : 8 , then x is equal to : | "30 / 3 = 10 the three numbers are 9 , 10 , and 11 . the answer is d ." | a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | d | add(divide(subtract(30, 3), 3), const_2) | subtract(n1,n0)|divide(#0,n0)|add(#1,const_2)| | physics |
in township k each property is taxed at 12 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ? | solution : sum of pass students of first , second and third class , = ( 45 % of 10 ) + ( 60 % of 15 ) + ( 80 % of 25 ) = 4.5 + 9 + 20 = 33.5 total students appeared , = 10 + 15 + 25 = 50 pass average , = 33.5 * 100 / 50 = 67 % . answer : option c | a ) 74 % , b ) 75 % , c ) 67 % , d ) 72 % , e ) none | c | divide(multiply(add(add(divide(multiply(10, 45), const_100), divide(multiply(15, 60), const_100)), divide(multiply(25, 80), const_100)), const_100), add(add(10, 15), 25)) | add(n1,n3)|multiply(n1,n2)|multiply(n3,n4)|multiply(n5,n6)|add(n5,#0)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|add(#5,#6)|add(#8,#7)|multiply(#9,const_100)|divide(#10,#4) | general |
two employees x and y are paid a total of rs . 750 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ? | "the triangle with sides 20 cm , 12 cm and 16 cm is right angled , where the hypotenuse is 20 cm . area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d" | a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92 | d | divide(multiply(12, 16), const_2) | multiply(n1,n2)|divide(#0,const_2)| | geometry |
in a lottery there are 100 prizes and 300 blanks . a lottery is drawn at random . what is the probability of getting a prize ? | "d = 100 + 150 = 250 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 25 sec . answer : c" | a ) 2 , b ) 28 , c ) 25 , d ) 99 , e ) 12 | c | divide(add(150, 100), multiply(36, const_0_2778)) | add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)| | physics |
john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 16 , what was the price before the first discount ? | 34.94 240.016 + 23.98 - - - - - - - - 298.936 answer is a . | a ) 298.936 , b ) 298.694 , c ) 289.496 , d ) 289.469 , e ) 298.964 | a | add(add(34.94, 240.016), 23.98) | add(n0,n1)|add(n2,#0) | general |
how many of the positive factors of 24 are not factors of 27 | total cost of items : 2000 / - amount paid : 3000 / - balance receivable : 3000 - 2000 = 1000 / - answer is b | a ) 650 , b ) 1000 , c ) 1500 , d ) 800 , e ) 750 | b | subtract(3000, 2000) | subtract(n3,n2) | general |
what is the least integer greater than – 4 + 0.5 ? | "correct average = 35 x 72 + ( 86 - 36 ) / 35 ≈ 72 + 1.43 = 73.43 answer d" | a ) 73.41 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) can not be determined | d | divide(subtract(multiply(35, 72), subtract(86, 36)), 35) | multiply(n0,n2)|subtract(n4,n3)|subtract(#0,#1)|divide(#2,n0)| | general |
1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = ? | or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder e as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 68 and 10 is 121 . c | a ) 21 , b ) 41 , c ) e = 121 , d ) 241 , e ) 481 | c | add(lcm(10, lcm(6, 8)), const_1) | lcm(n2,n3)|lcm(n4,#0)|add(#1,const_1) | general |
after decreasing 25 % in the price of an article costs rs . 1500 . find the actual cost of an article ? | "anyways , one can infer that he ' steals ' 30 % from suppliers and then charges 40 % extra to customers so basically 1.3 * 1.4 = 1.82 given that 1 is start point , we get 21 % more hence answer is b" | a ) 28 % , b ) 82 % , c ) 24.33 % , d ) 29.109 % , e ) 78 % | b | subtract(multiply(divide(add(const_100, 40), const_100), add(const_100, 30)), const_100) | add(n0,const_100)|add(n1,const_100)|divide(#1,const_100)|multiply(#0,#2)|subtract(#3,const_100)| | gain |
a rectangular grass field is 70 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ? | "milk quantity = 3 / 4 * 60 = 45 water quantity = 60 - 45 = 15 new ratio of m : w = 45 : 15 + x = 3 : 2 45 + 3 x = 90 x = 15 answer is b" | a ) 1 , b ) 15 , c ) 7 , d ) 5 , e ) 12 | b | multiply(subtract(divide(multiply(divide(3, add(3, 1)), 60), divide(3, add(3, 2))), 60), divide(add(const_10, 1), const_10)) | add(const_10,n2)|add(n1,n2)|add(n1,n4)|divide(#0,const_10)|divide(n1,#1)|divide(n1,#2)|multiply(n0,#4)|divide(#6,#5)|subtract(#7,n0)|multiply(#3,#8)| | general |
what least number must be added to 1145 , so that the sum is completely divisible by 23 ? | "2 / 2 = 1 and 13 / 2 = 6 6 - 1 = 5 5 + 1 = 6 numbers . answer : e" | a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 6 | e | add(divide(subtract(multiply(floor(divide(13, 2)), 2), multiply(add(floor(divide(2, 2)), const_1), 2)), 2), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | general |
the hcf and lcm of two numbers m and n are respectively 8 and 200 . if m + n = 84 , then 1 / m + 1 / n is equal to | "26 + 20 - 17 = 29 37 - 29 = 8 play neither answer is b" | a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14 | b | subtract(37, subtract(add(26, 20), 17)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)| | other |
together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours e would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ? | "speed of boat in still water = 15 km / hr speed of the stream = 6 km / hr speed downstream = ( 15 + 6 ) = 21 km / hr time taken to travel 86 km downstream = 86 â „ 16 = 17 â „ 4 = 4.1 hours answer is a" | a ) 4.1 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr | a | divide(86, add(15, 6)) | add(n0,n1)|divide(n2,#0)| | physics |
the sum of ages of 5 children born at the intervals of 3 years each is 80 years . what is the age of the youngest child ? | "let x be the number and y be the quotient . then , x = 357 * y + 38 = ( 17 * 21 * y ) + ( 17 * 2 ) + 4 = 17 * ( 21 y + 2 ) + 4 . required number = 4 . answer is a" | a ) 4 , b ) 5 , c ) 8 , d ) 7 , e ) 2 | a | multiply(subtract(divide(power(38, const_2), 357), floor(divide(power(38, const_2), 357))), 357) | power(n1,const_2)|divide(#0,n0)|floor(#1)|subtract(#1,#2)|multiply(n0,#3)| | general |
average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ? | given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 12 % ( 700 ) = rs . 84 answer : c | a ) 62 , b ) 140 , c ) 84 , d ) 60 , e ) 123 | c | multiply(subtract(divide(300, divide(30, const_100)), 300), divide(12, const_100)) | divide(n1,const_100)|divide(n0,const_100)|divide(n2,#1)|subtract(#2,n2)|multiply(#0,#3) | gain |
what percent is 36 paisa ' s of 12 rupees ? | "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 15 * 10 = 150 m . the time taken to pass the platform = ( 150 + 370 ) / 10 = 52 seconds the answer is d ." | a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54 | d | divide(add(multiply(multiply(36, const_0_2778), 15), 370), multiply(36, const_0_2778)) | multiply(n0,const_0_2778)|multiply(n1,#0)|add(n2,#1)|divide(#2,#0)| | physics |
how long does a train 250 meters long running at the rate of 72 km / hr take to cross a bridge 150 meters in length ? | "work done by the tank in 1 hour = ( 1 / 3 - 3 1 / 3 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : c" | a ) 17 hr , b ) 19 hr , c ) 30 hr , d ) 14 hr , e ) 16 hr | c | inverse(subtract(divide(1, 3), inverse(divide(add(multiply(3, 3), 1), 3)))) | divide(n2,n0)|multiply(n0,n3)|add(n2,#1)|divide(#2,n3)|inverse(#3)|subtract(#0,#4)|inverse(#5)| | physics |
let c be defined as the sum of all prime numbers between 0 and 30 . what is c / 3 | "soln : - 13 x = 45 - - > 87 / 77 * x = 45 - - > x = 45 * 77 / 87 = 677 / 17 = ~ 40 . answer : c ." | a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42 | c | multiply(divide(const_100, add(const_100, 13)), 45) | add(n4,const_100)|divide(const_100,#0)|multiply(n7,#1)| | gain |
a rectangle with width 8 and diagonal 30 . find the area ? | "let the universal set be x = { all students in the graduate physics course } , such that n ( x ) = 100 it will contain 2 mutually exclusive sets ; m ( all male students ) & f ( all female students ) , where n ( m ) = 70 , n ( f ) = 30 now 2 / 7 of all male students are married , implying their number = 20 . however the total number of married students = 30 , implying 10 married females . therefore 20 single females ; = 2 / 3 of total females . answer : d" | a ) 2 / 7 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7 | d | divide(const_10, 30) | divide(const_10,n1)| | gain |
in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 5 years older than b , the present age of b is | "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio r of ann ' s time to bob ' s time is 3 : 2 . answer : b ." | a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8 | b | divide(const_2, add(const_1, divide(const_1, const_3))) | divide(const_1,const_3)|add(#0,const_1)|divide(const_2,#1)| | general |
today is thursday . i came home from a trip 3 days before the day after last monday . how many days have i been home ? | "eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 4 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 4 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 14 ( 2 ) simplify - b + d = 7 b - d = - 7 ( b - d ) ^ 2 = ( - 7 ) ^ 2 = 49 my answer : a" | a ) 49 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 . | a | power(subtract(4, divide(add(18, 4), 2)), 2) | add(n0,n1)|divide(#0,n2)|subtract(n1,#1)|power(#2,n2)| | general |
if â € œ * â € is called â € œ + â € , â € œ / â € is called â € œ * â € , â € œ - â € is called â € œ / â € , â € œ + â € is called â € œ - â € . 240 / 80 â € “ 60 * 40 - 10 = ? | given that the total purchase of two items cost 800 . so the average purchase of one item will cost 800 / 2 = 400 . its given as total shirt cost 400 $ less . hence total shirt cost = 400 - 200 and total trouser cost = 400 + 200 5 shirts = 200 $ = = > one shirt = 40 $ one trouser = 40 + 20 = 60 $ total trousers = 600 / 60 = 10 . e | a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10 | e | divide(subtract(800, multiply(5, add(20, 20))), add(add(20, 20), 20)) | add(n3,n3)|add(n3,#0)|multiply(n2,#0)|subtract(n0,#2)|divide(#3,#1) | general |
what is the thousandths digit in the decimal equivalent of 64 / 5000 ? | "total age of all students = 24 ã — 23 total age of all students + age of the teacher = 25 ã — 24 age of the teacher = 25 ã — 24 â ˆ ’ 24 ã — 23 = 24 ( 25 â ˆ ’ 23 ) = 24 ã — 2 = 48 answer is c ." | a ) 40 , b ) 41 , c ) 48 , d ) 52 , e ) 43 | c | subtract(multiply(add(24, 1), add(23, 1)), multiply(24, 23)) | add(n0,n2)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
in township k each property is taxed at 10 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ? | "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 45 : : 18 : x [ please pay attention , we have written 27 : 45 rather than 45 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 45 \ times 18 } { 27 } } x = 30 so 30 days will be required to get work done by 27 men . answer : c" | a ) 24 , b ) 77 , c ) 30 , d ) 25 , e ) 13 | c | divide(multiply(18, 45), 27) | multiply(n0,n1)|divide(#0,n2)| | physics |
an article with cost price of 320 is sold at 18 % profit . what is the selling price ? | "( 27 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 60 60 – 27 = 33 answer : a" | a ) 33 , b ) 66 , c ) 88 , d ) 100 , e ) 281 | a | subtract(divide(multiply(divide(multiply(27, 8), 30), 50), 6), 27) | multiply(n0,n1)|divide(#0,n2)|multiply(n3,#1)|divide(#2,n4)|subtract(#3,n0)| | physics |
54671 - 10456 - 33466 = ? | "you have 6 digits : 2 , 3 , 4 , 5 , 6 , 7 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 small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 7 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 376 and 425 ( difference is 49 ) or try and make a pair with ( 5 * * and 6 * * ) . make the 5 * * number as large as possible and make the 6 * * number as small as possible . we get 574 and 623 ( difference is 49 ) b" | a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131 | b | subtract(subtract(const_100, multiply(subtract(7, 2), const_10)), const_1) | subtract(n5,n1)|multiply(#0,const_10)|subtract(const_100,#1)|subtract(#2,const_1)| | general |
{ - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x - 4 ) ( x + 9 ) ( 2 x + 5 ) = 0 ? | "e if we calculate we will get 4749" | a ) 2449 , b ) 5449 , c ) 6749 , d ) 6449 , e ) 4749 | e | subtract(multiply(divide(54671, const_100), 14456), multiply(divide(const_1, const_3), multiply(divide(54671, const_100), 14456))) | divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)| | general |
what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? | "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 4 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 4 * ( 2 / 3 ) ) days = > 45 days answer : e" | a ) 30 , b ) 20 , c ) 15 , d ) 25 , e ) 45 | e | divide(multiply(multiply(15, 21), 8), multiply(multiply(21, 4), divide(2, 3))) | divide(n6,n5)|multiply(n0,n1)|multiply(n1,n3)|multiply(n2,#1)|multiply(#0,#2)|divide(#3,#4)| | physics |
find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ? | "the total number of ways to choose 6 children from 8 is 8 c 6 = 28 the number of ways to choose 3 boys and 3 girls is 4 c 3 * 4 c 3 = 4 * 4 = 16 p ( 3 boys and 3 girls ) = 16 / 28 = 4 / 7 the answer is d ." | a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9 | d | divide(multiply(choose(4, const_2), choose(4, const_2)), choose(add(4, 4), 6)) | add(n0,n0)|choose(n0,const_2)|choose(n0,const_2)|choose(#0,n2)|multiply(#1,#2)|divide(#4,#3)| | probability |
1 , 3,5 , 7,9 , . . 50 find term of sequnce | "d = ( d - r ) / q = ( 21 - 1 ) / 10 = 20 / 10 = 2 b" | a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7 | b | floor(divide(21, 10)) | divide(n0,n1)|floor(#0)| | general |
a pupil ' s marks were wrongly entered as 73 instead of 40 . due to the average marks for the class got increased by half . the number of pupils in the class is ? | side of square = √ 36 = 6 m . length = 6 m and breadth = 3 m area of rectangle = 6 * 3 = 18 sq . m answer a | ['a ) 18', 'b ) 20', 'c ) 27', 'd ) 32', 'e ) 25'] | a | multiply(sqrt(36), divide(sqrt(36), const_2)) | sqrt(n0)|divide(#0,const_2)|multiply(#1,#0) | geometry |
two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days . the number of days required by 1 man to complete the work is | "money paid in cash = rs . 1000 balance payment = ( 70000 - 1000 ) = rs . 69000 answer : c" | a ) 22678 , b ) 26699 , c ) 69000 , d ) 19000 , e ) 26711 | c | subtract(70000, 1000) | subtract(n0,n2)| | gain |
lamp a flashes every 6 seconds , lamp b flashes every 8 seconds , lamp c flashes every 10 seconds . at a certain instant of time all 3 lamps flash simultaneously . during the period of 6 minutes after that how many times will exactly two lamps flash ? ( please include any flash of exactly two lights which occurs at the 6 minute mark . ) | "0.8 * ( 1.2 * 200 ) = $ 192 the answer is a ." | a ) $ 192 , b ) $ 198 , c ) $ 200 , d ) $ 208 , e ) $ 216 | a | subtract(add(200, divide(multiply(200, 20), const_100)), divide(multiply(add(200, divide(multiply(200, 20), const_100)), 20), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)|multiply(n1,#2)|divide(#3,const_100)|subtract(#2,#4)| | general |
a sum of 13,400 amounts to 14,400 in 2 years at the rate of simple interest . what is the rate of interest ? | "998 x 998 = ( 998 ) 2 = ( 1000 - 2 ) 2 = ( 1000 ) 2 + ( 2 ) 2 - ( 2 x 1000 x 2 ) = 1000000 + 4 - 4000 = 1000004 - 4000 = 996004 . c )" | a ) 996000 , b ) 1000000 , c ) 996004 , d ) 4000 , e ) 996008 | c | multiply(divide(998, 998), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
what is the speed of the stream if a canoe rows upstream at 6 km / hr and downstream at 12 km / hr | "distance traveled in 2 hours = 2 * 55 = 110 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 110 = 350 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 350 / 5 = 70 mph answer : c" | a ) 60 mph , b ) 56.67 mph , c ) 70 mph , d ) 64 mph , e ) 66.67 mph | c | add(divide(add(multiply(80, 3), multiply(55, 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 |
all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems . how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations ? | let dravid scored point = x then dhoni scored = x + 30 shewag scored = 2 * ( x + 30 ) = 2 x + 60 as given , x + x + 30 + 2 x + 60 = 150 points 4 x + 90 = 150 x = 150 - 90 / 4 = 15 so dhoni scored = x + 30 i . e ) 15 + 30 = 45 answer : e | a ) 50 , b ) 52 , c ) 35 , d ) 40 , e ) 45 | e | divide(add(150, 30), add(add(const_2, const_1), const_1)) | add(n0,n2)|add(const_1,const_2)|add(#1,const_1)|divide(#0,#2) | general |
the average of 5 quantities is 9 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ? | if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d | a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 7 , e ) 1 / 3 | d | divide(1, divide(add(add(2.8, add(2.8, 2.8)), add(2.8, 2.8)), const_2)) | add(n1,n1)|add(n1,#0)|add(#1,#0)|divide(#2,const_2)|divide(n0,#3) | general |
a cube of edge 7 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to : | rate = 10 % time = 2 years s . i . = $ 1200 principal = 100 * 1200 / 10 * 2 = $ 6000 amount = 6000 ( 1 + 10 / 100 ) ^ 2 = $ 7260 c . i . = 7260 - 6000 = $ 1260 answer is a | a ) $ 1260 , b ) $ 1520 , c ) $ 1356 , d ) $ 1440 , e ) $ 1210 | a | subtract(add(divide(multiply(add(divide(multiply(1200, const_100), multiply(10, 2)), divide(multiply(divide(multiply(1200, const_100), multiply(10, 2)), 10), const_100)), 10), const_100), add(divide(multiply(1200, const_100), multiply(10, 2)), divide(multiply(divide(multiply(1200, const_100), multiply(10, 2)), 10), const_100))), divide(multiply(1200, const_100), multiply(10, 2))) | multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|multiply(n0,#2)|divide(#3,const_100)|add(#2,#4)|multiply(n0,#5)|divide(#6,const_100)|add(#5,#7)|subtract(#8,#2) | gain |
the ratio between x and y is 8 / 3 ; x is multiplied by x and y is multiplied by y , what is the ratio between the new values of x and y ? | "let the number be x . then , 50 % of x - 35 % of x = 12 50 / 100 x - 35 / 100 x = 12 x = ( 12 * 100 ) / 15 = 80 . answer : d" | a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 70 | d | divide(12, divide(subtract(50, 35), const_100)) | subtract(n2,n0)|divide(#0,const_100)|divide(n1,#1)| | gain |
in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ? | "explanation : l . c . m of 441 = 3 x 3 x 7 x 7 3 , 7 number of different prime factors is 2 . answer : option b" | a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6 | b | add(const_2, const_2) | add(const_2,const_2)| | other |
tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg | let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 50000 + y so y = 30000 then x = 50000 - 30000 = 20000 first part = 20000 answer : a | a ) 20000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000 | a | divide(subtract(divide(multiply(50000, 20), const_100), 8000), divide(10, const_100)) | divide(n1,const_100)|multiply(n0,n2)|divide(#1,const_100)|subtract(#2,n3)|divide(#3,#0) | gain |
two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days . the number of days required by 1 man to complete the work is | "22 = ( n + n + 2 + n + 4 + . . . + ( n + 18 ) ) / 10 22 = ( 10 n + ( 2 + 4 + . . . + 18 ) ) / 10 220 = 10 n + 2 ( 1 + 2 + . . . + 9 ) 220 = 10 n + 2 ( 9 ) ( 10 ) / 2 220 = 10 n + 90 220 - 90 = 10 n 130 = 10 n n = 13 so the first three numbers are 13 , 15 , 17 13 + 15 + 17 = 45 option b" | a ) 13 , b ) 45 , c ) 17 , d ) 220 , e ) 90 | b | add(divide(subtract(multiply(22, 10), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), const_1))), 10), add(add(add(add(const_1, const_2), const_1), const_1), const_1)) | add(const_1,const_2)|multiply(n0,n1)|add(#0,const_1)|add(#2,const_1)|add(#3,const_1)|add(#4,const_1)|add(#5,const_1)|add(#6,const_1)|add(#7,const_1)|add(#8,const_1)|add(#8,#9)|subtract(#1,#10)|divide(#11,n0)|add(#4,#12)| | general |
if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 6 ? | "easy solution : n = dq 1 + 245 2 n = 2 dq 1 + 490 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 378 d * some integer = 378 checking all options only ( a ) syncs with it . answer a" | a ) 378 , b ) 365 , c ) 380 , d ) 456 , e ) 460 | a | subtract(multiply(245, const_2), 112) | multiply(n0,const_2)|subtract(#0,n1)| | general |
a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ? | given 50 % of 8 employees including 4 who are capable of doing task . 60 % of 5 employeees = 50 / 100 * 4 = 4 employees = = = > 4 employees who are capable of doing the task and no one employee who is not capable . percentage of employees assigned who are not capable answer : e | a ) 43.33 % , b ) 33.33 % , c ) 13.33 % , d ) 38.33 % , e ) none | e | multiply(divide(subtract(5, 4), 5), const_100) | subtract(n2,n0)|divide(#0,n2)|multiply(#1,const_100) | general |
on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 380 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ? | "answer = a please refer diagram below 85 - 10 = 75" | a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95 | a | subtract(85, 10) | subtract(n0,n1)| | general |
a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 36 instead of 86 then find the correct average marks up to two decimal places . | "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e" | a ) 34 , b ) 35 , c ) 56 , d ) 67 , e ) 23.57 | e | divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(16, 14)), const_2)), const_2) | rectangle_perimeter(n0,n1)|square_edge_by_perimeter(#0)|divide(#1,const_2)|circumface(#2)|divide(#3,const_2)| | geometry |
by selling 20 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ? | "let height of the building be x meters 40.25 : 28.75 : : 17.5 < = > 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : option b" | a ) 10 m , b ) 12.5 m , c ) 17.5 m , d ) 21.25 m , e ) none | b | multiply(28.75, divide(17.5, 40.25)) | divide(n0,n1)|multiply(n2,#0)| | physics |
a university cafeteria offers 6 flavors of pizza - pork , gobi - manjurian , pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ? | x 1 hour ' s work = 1 / 4 ; y + z ' s hour ' s work = 1 / 3 x + y + z ' s 1 hour ' s work = 1 / 4 + 1 / 3 = 7 / 12 y ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 . y alone will take 12 hours to do the work . c | a ) 5 hours , b ) 10 hours , c ) 12 hours , d ) 24 hours , e ) 15 hours | c | inverse(subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 4)))) | divide(const_1,n1)|divide(const_1,n2)|divide(const_1,n0)|subtract(#1,#2)|subtract(#0,#3)|inverse(#4) | physics |
50 percent of the members of a study group are women , and 30 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ? | "6 % of a 50 liter solution is 3 l which is 10 % of the solution at the end . the solution at the end must be 30 l . we need to evaporate 20 liters . the answer is a ." | a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28 | a | subtract(50, multiply(divide(50, const_100), 10)) | divide(n0,const_100)|multiply(n2,#0)|subtract(n0,#1)| | gain |
a basket contains 9 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ? | "total men in company 40 % means total women in company 60 % ( assume total people in company 100 % ) no of men employees attended picnic = 40 x ( 20 / 100 ) = 8 no of women employees attended picnic = 60 x ( 40 / 100 ) = 24 total percentage of employees attended the picnic = 8 + 24 = 32 % answer : a" | a ) 32 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 % | a | multiply(add(multiply(divide(40, const_100), divide(20, const_100)), multiply(divide(subtract(const_100, 40), const_100), divide(40, const_100))), const_100) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(const_100,n2)|divide(#3,const_100)|multiply(#0,#1)|multiply(#4,#2)|add(#5,#6)|multiply(#7,const_100)| | gain |
when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ? | "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 7 log 7 ( 8 ) = 8 correct answer e" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 8 | e | divide(log(multiply(7, 7)), log(const_10)) | log(const_10)|multiply(n0,n0)|log(#1)|divide(#2,#0)| | other |
the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years . the age of the 15 th student is | "due to stoppages , it covers 14 km less . time taken to cover 14 km = ( 14 / 84 x 60 ) min = 10 min answer : b" | a ) 12 min , b ) 10 min , c ) 15 min , d ) 14 min , e ) 13 min | b | multiply(const_60, divide(subtract(84, 70), 84)) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_60)| | physics |
a truck covers a distance of 288 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 90 km more than that travelled by the truck ? | 40 / 160 × 100 = 25 % answer : e | a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 25 % | e | multiply(divide(40, 160), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
the speed of the boat in still water in 12 kmph . it can travel downstream through 45 kms in 3 hrs . in what time would it cover the same distance upstream ? | "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 57 ) = 465.60 hence answer will be ( e )" | a ) 320.50 $ , b ) 380.50 $ , c ) 425.50 $ , d ) 450.50 $ , e ) 465.60 $ | e | multiply(multiply(0.65, 57), 12) | multiply(n1,n3)|multiply(n2,#0)| | general |
find the simple interest on $ 10000 at 7 % per annum for 12 months ? | answer : c ) 5940 | a ) 5942 , b ) 2887 , c ) 5940 , d ) 2888 , e ) 28881 | c | multiply(multiply(multiply(multiply(const_2, const_2), multiply(multiply(const_3, const_3), const_3)), divide(divide(divide(135, const_3), const_3), const_3)), divide(22, const_2)) | divide(n0,const_2)|divide(n3,const_3)|multiply(const_2,const_2)|multiply(const_3,const_3)|divide(#1,const_3)|multiply(#3,const_3)|divide(#4,const_3)|multiply(#2,#5)|multiply(#6,#7)|multiply(#0,#8) | physics |
x and y are both integers . if x / y = 50.60 , then what is the sum of all the possible two digit remainders of x / y ? | "280 * ( 88 / 100 ) * ( 92 / 100 ) = 226 answer : b" | a ) 288 , b ) 226 , c ) 250 , d ) 230 , e ) 262 | b | subtract(subtract(280, divide(multiply(280, 12), const_100)), divide(multiply(subtract(280, divide(multiply(280, 12), const_100)), 8), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain |
there are 690 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | relative speed = ( 1120 / 12 ) m / s = ( 1120 / 12 ) * ( 18 / 5 ) = 336 kmph speed of goods train = 336 - 40 = 296 kmph answer is b | a ) 295 , b ) 296 , c ) 297 , d ) 298 , e ) 299 | b | subtract(divide(divide(1120, 12), const_0_2778), 40) | divide(n2,n1)|divide(#0,const_0_2778)|subtract(#1,n0) | physics |
a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 35 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ? | "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b" | a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21 | b | divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3)) | divide(n2,n1)|multiply(const_1,const_1)|add(n0,#0)|divide(#2,n1)|multiply(#3,const_2)|subtract(#4,n1)|subtract(#5,const_3)|divide(#1,#6)| | general |
what is the unit digit in the product ( 3 ^ 65 x 6 ^ 59 x 7 ^ 71 ) ? | "= ( 107 ) ^ 2 + ( 93 ) ^ 2 = ( 100 + 7 ) ^ 2 + ( 100 - 7 ) ^ 2 = 2 x [ ( 100 ) ^ 2 + 7 ^ 2 ] = 2 [ 10000 + 49 ] = 2 x 10049 = 20098 answer is c" | a ) 19578 , b ) 19418 , c ) 20098 , d ) 21908 , e ) none of them | c | multiply(107, power(107, 93)) | power(n1,n2)|multiply(n0,#0)| | general |
a vessel of capacity 2 litre has 16 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ? | "1 percent for 3 years = 66 1 percent for 1 year = 22 = > 100 percent = 2200 answer : c" | a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400 | c | multiply(divide(66, 3), const_100) | divide(n2,n0)|multiply(#0,const_100)| | gain |
excluding stoppages , the average speed of a bus is 120 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ? | "( place value of 6 ) - ( face value of 6 ) = ( 6000 - 6 ) = 5994 answer : option c" | a ) 973 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these | c | subtract(multiply(const_10, 6), 6) | multiply(n0,const_10)|subtract(#0,n0)| | general |
a car going at 40 miles per hour set out on an 60 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ? | ": ( 60 / 100 ) * x + 180 = x 2 x = 900 x = 450 answer : e" | a ) 300 , b ) 277 , c ) 266 , d ) 99 , e ) 450 | e | divide(180, divide(180, const_100)) | divide(n1,const_100)|divide(n1,#0)| | gain |
what is the sum of all 5 digit numbers which can be formed with the digits 0 , 1,2 , 3,4 without repetation ? | ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.82 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.82 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b | a ) $ 1 , b ) $ 1.82 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15 | b | min(divide(add(add(add(add(add(add(1.75, 1.61), 1.79), 2.11), 1.96), 2.09), 1.82), 7), 1.82) | add(n1,n2)|add(n3,#0)|add(n4,#1)|add(n5,#2)|add(n6,#3)|add(n7,#4)|divide(#5,n0)|min(n7,#6) | general |
when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 1 ) ^ 2 is divided by 5 ? | "5 ^ x = 1 / 625 5 ^ x = 1 / 5 ^ 4 5 ^ x = 5 ^ - 4 x = - 4 b" | a ) – 2 , b ) - 4 , c ) 0 , d ) - 1 , e ) 2 | b | divide(log(divide(1, 625)), log(5)) | divide(n2,n0)|log(n1)|log(#0)|divide(#2,#1)| | general |
yearly subscription to professional magazines cost a company $ 940.00 . to make a 25 % cut in the magazine budget , how much less must be spent ? | "2 years answer : a" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | floor(add(divide(log(const_2), log(add(const_1, divide(45, const_100)))), const_1)) | divide(n0,const_100)|log(const_2)|add(#0,const_1)|log(#2)|divide(#1,#3)|add(#4,const_1)|floor(#5)| | general |
48 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ? | still water = 12 km / hr downstream = 45 / 3 = 15 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 15 / 2 = 9 km / hr so time taken in upstream = 45 / 9 = 5 hrs answer : d | a ) 8 hours , b ) 6 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours | d | divide(45, subtract(12, subtract(divide(45, 3), 12))) | divide(n1,n2)|subtract(#0,n0)|subtract(n0,#1)|divide(n1,#2) | physics |
what is the units digit of ( 3 ^ 5 ) ( 4 ^ 13 ) ? | "a + b + c = 3 * 55 = 165 a + b + c + d = 4 * 60 = 240 - - - - ( i ) so , d = 75 & e = 75 + 3 = 78 b + c + d + e = 58 * 4 = 232 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 240 – 232 = 8 a = e + 8 = 78 + 8 = 86 answer : d" | a ) 56 , b ) 65 , c ) 75 , d ) 86 , e ) 90 | d | subtract(multiply(60, const_4), subtract(multiply(58, const_4), add(3, subtract(multiply(60, const_4), multiply(55, 3))))) | multiply(n1,const_4)|multiply(n3,const_4)|multiply(n0,n2)|subtract(#0,#2)|add(n2,#3)|subtract(#1,#4)|subtract(#0,#5)| | general |
the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 7 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ? | "s = 120 / 12 * 18 / 5 = 36 kmph answer : c" | a ) 16 kmph , b ) 88 kmph , c ) 36 kmph , d ) 18 kmph , e ) 19 kmph | c | multiply(const_3_6, divide(120, 12)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
one half of a two digit number exceeds its one third by 4 . what is the sum of the digits of the number ? | "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 32 ( 2 ^ 5 ) , sob = 2 ^ 5 combining 2 premises shows the answer is d ( 32 ) ." | a ) 8 , b ) 16 , c ) 24 , d ) 32 , e ) 48 | d | sqrt(subtract(power(divide(32, 4), const_2), power(12, const_2))) | divide(n2,n1)|power(n0,const_2)|power(#0,const_2)|subtract(#2,#1)|sqrt(#3)| | geometry |
how many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number ? | explanation : hint : a ' s one day work = 1 / 3 b ' s one day work = 1 / 5 c ' s one day work = 1 / 10 ( a + b + c ) ' s one day work = 1 / 3 + 1 / 5 + 1 / 10 = 1 / 1.5 hence , a , b & c together will take 1.5 days to complete the work . answer is a | a ) 1.5 days , b ) 4.5 days , c ) 7 days , d ) 9.8 days , e ) 9 days | a | add(subtract(3, const_2), divide(5, 10)) | divide(n1,n2)|subtract(n0,const_2)|add(#0,#1) | physics |
the average age of 36 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . find out the teacher ' s age in years ? | "in 105 liters of drink a , there are 60 liters of milk and 45 liters of juice . with 60 liters of milk , we need a total of 80 liters of juice to make drink b . we need to add 35 liters of juice . the answer is d ." | a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42 | d | subtract(divide(multiply(multiply(divide(4, add(4, 3)), 105), 4), 3), multiply(divide(3, add(4, 3)), 105)) | add(n0,n1)|divide(n0,#0)|divide(n1,#0)|multiply(n4,#1)|multiply(n4,#2)|multiply(n0,#3)|divide(#5,n1)|subtract(#6,#4)| | general |
if 20 liters of chemical x are added to 80 liters of a mixture that is 15 % chemical x and 85 % chemical y , then what percentage of the resulting mixture is chemical x ? | "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 9 ) ] % = 11.1 % per annum . answer : d" | a ) 12.5 % , b ) 13.5 % , c ) 11.5 % , d ) 11.1 % , e ) 21.5 % | d | divide(const_100, 9) | divide(const_100,n0)| | gain |
a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 28 m * 2 m * 0.75 m ? | "according to order of operations , 12 ÷ 3 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 3 × 2 = 4 × 2 = 8 hence 30 - 12 ÷ 3 × 2 = 30 - 8 = 22 correct answer is b ) 22" | a ) 11 , b ) 22 , c ) 33 , d ) 44 , e ) 55 | b | subtract(30, multiply(multiply(12, const_2.0), 2)) | multiply(n1,const_2.0)|multiply(n3,#0)|subtract(n0,#1)| | general |