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a van takes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | 25 ^ 5 Γ 5 ^ ( - 1 ) = ( 125 ) ^ x ( 5 ^ 2 ) ^ 5 Γ 5 ^ ( - 1 ) = 5 ^ 3 x 5 ^ 10 x 5 ^ ( - 1 ) = 5 ^ 3 x ; since all of the bases are the same now , we can equate the exponents in the next step 10 - 1 = 3 x 9 = 3 x x = 3 ans . b ) 3 | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | b | divide(subtract(multiply(const_2, 5), 1), const_3) | multiply(n1,const_2)|subtract(#0,n3)|divide(#1,const_3) | general |
a pyramid has a square base of 6 cm , and the four lateral faces are four congruent equilateral triangles . what is the total surface area of the pyramid in square cm ? | p ___ 50 _____ r ___ 50 _____ s ____ 50 ___ q the above figure gives the locations of p , r , s & q in relation to each other . answer : a | a ) 150 km , b ) 200 km , c ) 250 km , d ) 125 km , e ) 155 km | a | add(multiply(50, const_2), divide(multiply(50, const_2), const_2)) | multiply(n0,const_2)|divide(#0,const_2)|add(#1,#0) | physics |
if a > x > y > z on the number line , y is halfway between x and z , and x is halfway between w and z , then ( y - x ) / ( y - a ) = | "start with the prime factorization : 250 = 2 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 250 . answer : b ." | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8 | b | add(add(add(const_4, const_2), const_1), const_1) | add(const_2,const_4)|add(#0,const_1)|add(#1,const_1)| | other |
a , b and c start a business each investing 20,000 . after 10 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 71400 was recorded . find the share of b . | "add the numbers of highlighters . 24 + 28 + 25 = 77 . answer is c ." | a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88 | c | add(add(24, 28), 25) | add(n0,n1)|add(n2,#0)| | general |
rs 50000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ? | "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 50 / 20 = x / 10 x = 50 m . answer : option d" | a ) 30 m . , b ) 40 m . , c ) 60 m . , d ) 50 m . , e ) 70 m . | d | multiply(50, subtract(const_2, const_1)) | subtract(const_2,const_1)|multiply(n1,#0)| | physics |
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 ? | "let the required numbers be 33 a and 33 b . then 33 a + 33 b = 528 \ inline \ fn _ jvn \ rightarrow a + b = 16 . now , co - primes with sum 16 are ( 1,15 ) , ( 3,13 ) , ( 5,11 ) and ( 7,9 ) . \ inline \ fn _ jvn \ therefore required numbers are ( 33 x 1 , 33 x 15 ) , ( 33 x 3 , 33 x 13 ) , ( 33 x 5 , 33 x 11 ) , ( 33 x 7 , 33 x 9 ) the number of such pairs is 4 answer : a" | a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | a | multiply(divide(add(528, 33), add(const_1, const_1)), subtract(divide(add(528, 33), add(const_1, const_1)), 33)) | add(n0,n1)|add(const_1,const_1)|divide(#0,#1)|subtract(#2,n1)|multiply(#2,#3)| | general |
gary drove from point a to point b at 60 km / h . on his way back he took a train travelling at 110 km / h and therefore his trip back lasted 5 hours less . what is the distance ( in km ) between a and b ? | "total age of 50 students = 50 * 10 = 500 total age of 51 persons = 51 * 11 = 561 age of teacher = 561 - 500 = 61 years answer is c" | a ) 59 , b ) 55 , c ) 61 , d ) 45 , e ) 36 | c | subtract(add(add(multiply(50, 10), 1), 50), multiply(50, 10)) | multiply(n0,n1)|add(n2,#0)|add(n0,#1)|subtract(#2,#0)| | general |
bottle r contains 250 capsules and costs $ 5.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ? | "let the numerator be x . then the denominator is x + 6 . x + 1 / x + 7 = 4 / 5 . 5 x + 5 = 4 x + 28 . x = 23 . the original fraction is 23 / 29 . the answer is b ." | a ) 17 / 23 , b ) 23 / 29 , c ) 29 / 35 , d ) 31 / 37 , e ) 33 / 39 | b | divide(divide(subtract(multiply(4, add(1, 6)), 5), subtract(5, 4)), add(divide(subtract(multiply(4, add(1, 6)), 5), subtract(5, 4)), 6)) | add(n0,n1)|subtract(n3,n2)|multiply(n2,#0)|subtract(#2,n3)|divide(#3,#1)|add(n0,#4)|divide(#4,#5)| | general |
the average of first six multiples of 3 is | explanation : if n = 1 , then the set t 1 = { 1 , 23 , 45 } , and it does not have 6 or any multiples . n = 2 to n = 6 has 6 in the set . n = 7 , has the set t 7 = { 7 , 89 , 1011 } , and no 6 or multiples . so 1 in every 6 members do not have 6 or multiples of 6 . so , till n = 96 , there are 16 sets of β 6 members β ( 16 * 6 = 96 ) and 16 sets do not have 6 or its multiples , while the remaining 80 sets have . answer : a | a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84 | a | multiply(divide(add(const_2, const_3), 6), 96) | add(const_2,const_3)|divide(#0,n8)|multiply(n7,#1) | general |
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 ? | the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 55 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 44 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 44 miles / gallon * 10 gallons = 440 miles . answer e . | a ) 320 , b ) 375.2 , c ) 400 , d ) 408.3 , e ) 440 | e | multiply(multiply(subtract(const_1, divide(20, const_100)), 55), 10) | divide(n2,const_100)|subtract(const_1,#0)|multiply(n0,#1)|multiply(n4,#2) | gain |
if y is 90 % greater than x , than x is what % less than y ? | basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 1050 ( e ) | a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 360 , e ) $ 1050 | e | multiply(70, divide(multiply(360, 605), divide(multiply(360, 605), const_10))) | multiply(n1,n2)|divide(#0,const_10)|divide(#0,#1)|multiply(n0,#2)| | geometry |
a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction t of the sum of the 21 numbers in the list ? | "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter t must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b" | a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120 | b | square_perimeter(divide(20, power(add(const_1, const_1), inverse(const_2)))) | add(const_1,const_1)|inverse(const_2)|power(#0,#1)|divide(n0,#2)|square_perimeter(#3)| | geometry |
in a certain pond , 90.00001 fish were caught , tagged , and returned to the pond . a few days later , 90 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ? | "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 6 = 54 minutes . answer : e" | a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 54 min | e | multiply(add(const_3, 6), 6) | add(const_3,n2)|multiply(n1,#0)| | physics |
how much is 80 % of 40 is greater than 4 / 5 of 30 ? | "solution : let average expenditure of 20 people be x . then , 20 x = 12 * 70 + 8 * ( x + 4 ) ; or , 20 x = 12 * 70 + 8 x + 32 ; or , x = 72.667 ; so , total money spent = 72.67 * 20 = rs . 1453.4 . answer : option c" | a ) 1628.4 , b ) 1534 , c ) 1453 , d ) 1496 , e ) none of these | c | multiply(divide(add(multiply(12, 70), multiply(subtract(20, 12), 4)), subtract(20, subtract(20, 12))), 20) | multiply(n1,n2)|subtract(n0,n1)|multiply(n3,#1)|subtract(n0,#1)|add(#0,#2)|divide(#4,#3)|multiply(n0,#5)| | general |
rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ? | "not sure if this is the shortest . . but this is how i did this there are 8 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . 405 | 504 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 4 sets with 10 such number in each set will give 4 x 10 = 40 integers . a" | a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | a | multiply(const_10, subtract(const_10, const_2)) | subtract(const_10,const_2)|multiply(#0,const_10)| | general |
a library has an average of 425 visitors on sundays and 325 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : | "let the two numbers be 5 x and 6 x . let the numbers added to both so that their ratio becomes 7 : 8 be k . ( 5 x + k ) / ( 6 x + k ) = 7 / 8 = > 40 x + 8 k = 42 x + 7 k = > k = 2 x . 6 x - 5 x = 10 = > x = 10 k = 2 x = 20 . answer : c" | a ) 17 , b ) 14 , c ) 10 , d ) 16 , e ) 20 | c | subtract(multiply(multiply(6, 6), 6), multiply(add(multiply(7, 6), 6), 8)) | multiply(n1,n1)|add(n1,#0)|multiply(n2,#0)|multiply(n3,#1)|subtract(#2,#3)| | other |
a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ? | "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1060 820 x + 1060 * 441 x = 570.07 so , value of each installment = rs . 570.07 answer : option c" | a ) 993.2 , b ) 551.25 , c ) 570.07 , d ) 543.33 , e ) 646.33 | c | divide(multiply(power(add(divide(5, const_100), const_1), 2), 1060), 2) | divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|divide(#3,n1)| | gain |
a dealer offers a cash discount of 16 % and still makes a profit of 25 % when he further allows 60 articles to be sold at the cost price of 50 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ? | "answer β΅ 50 % of p = 23040 β΄ p = ( 23040 x 100 ) / 50 = 46080 correct option : d" | a ) 32256 , b ) 24000 , c ) 44936 , d ) 46080 , e ) none | d | multiply(divide(const_100, 50), 23040) | divide(const_100,n0)|multiply(n1,#0)| | general |
difference between the length & breadth of a rectangle is 10 m . if its perimeter is 206 m , then its area is ? | 2 ( l + 300 ) = 1400 = > l = 400 m answer : b | a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700 | b | subtract(divide(1400, const_2), 300) | divide(n0,const_2)|subtract(#0,n1)| | physics |
a rectangle with width 8 and diagonal 30 . find the area ? | "let initial price be 100 price in day 1 after 4 % discount = 96 price in day 2 after 4 % discount = 92.16 price in day 3 after 10 % discount = 82.94 so , price in day 3 as percentage of the sale price on day 1 will be = 82.94 / 96 * 100 = > 86.4 % answer will definitely be ( d )" | a ) 82.5 % , b ) 89.9 % , c ) 87.7 % , d ) 86.4 % , e ) 83.3 % | d | add(multiply(divide(divide(10, const_100), subtract(1, divide(1, 4))), const_100), 2) | divide(n5,const_100)|divide(n1,n0)|subtract(n1,#1)|divide(#0,#2)|multiply(#3,const_100)|add(n2,#4)| | gain |
paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to paul and 40 % of his income to quentin , paul ' s new income would be what fraction of quentin ' s new income ? | "solution - simply substitute 3 and 4 in equation in the place of a and b respectively . 3 # 4 = 3 * 4 - 4 + 4 ^ 2 = 12 - 4 + 16 = 24 . ans d" | a ) 2 , b ) 8 , c ) 15 , d ) 24 , e ) 35 | d | add(subtract(multiply(3, 4), 4), power(4, 2)) | multiply(n1,n2)|power(n2,n0)|subtract(#0,n2)|add(#1,#2)| | general |
what will be the remainder when 17 ^ 200 is divided by 18 ? | "4 : 1 = x : 100 x = 4 * 100 x = 400 answer : c" | a ) 40 , b ) 200 , c ) 400 , d ) 800 , e ) 4000 | c | multiply(100, 4) | multiply(n0,n2)| | other |
what is the greatest prime factor of 5 ^ 6 - 1 ? | "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5535 ( 27 / 40 ) * x = 5535 x = 5535 * 40 / 27 = 8200 the answer is b ." | a ) 7900 , b ) 8200 , c ) 8500 , d ) 8800 , e ) 9100 | b | divide(5535, subtract(subtract(const_1, divide(10, const_100)), multiply(subtract(const_1, divide(10, const_100)), divide(25, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|subtract(const_1,#0)|multiply(#1,#2)|subtract(#2,#3)|divide(n2,#4)| | gain |
a work as fast as b . if b can complete a work in 24 days independently , the number of days in which a and b can together finish the work in ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 5 x = 40 = > x = 8 hence , b ' s age = 2 x = 16 years . answer : a" | a ) 16 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | a | multiply(divide(subtract(42, const_2), add(const_3, const_2)), const_2) | add(const_2,const_3)|subtract(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)| | general |
the tailor has a 10 meter long piece of fabric for which to sew a ball room dress . she has to cuts this fabric into strips of 200 centimeters each . how long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ? | "interest for 1 st year = 7000 * 5 / 100 = 350 interest for 2 nd year = 7350 * 5 / 100 = 367.50 total = 7000 + 350 + 367.50 = 7717.50 answer : b" | a ) $ 7727.50 , b ) $ 7717.50 , c ) $ 7737.50 , d ) $ 7747.50 , e ) $ 7757.50 | b | add(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 5), const_100)), divide(multiply(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 5), const_100)), 5), const_100)) | multiply(n2,const_3)|multiply(#0,const_100)|multiply(#1,const_10)|multiply(n1,#2)|divide(#3,const_100)|add(#4,#2)|multiply(n1,#5)|divide(#6,const_100)|add(#5,#7)| | gain |
if 150 ! / 10 ^ n is an integer , what is the largest possible value of n ? | let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b | a ) $ 27000 , b ) $ 22000 , c ) $ 33000 , d ) $ 16000 , e ) $ 43000 | b | multiply(20000, add(const_1, divide(10, const_100))) | divide(n3,const_100)|add(#0,const_1)|multiply(n1,#1) | general |
two pipes a and b can separately fill a tank in 10 and 15 minutes respectively . a third pipe c can drain off 20 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ? | "explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 4 % answer : option b" | a ) 3 % , b ) 4 % , c ) 7 % , d ) 8 % , e ) 9 % | b | multiply(divide(subtract(subtract(65, multiply(65, divide(10, const_100))), 56.16), subtract(65, multiply(65, divide(10, const_100)))), const_100) | divide(n2,const_100)|multiply(n0,#0)|subtract(n0,#1)|subtract(#2,n1)|divide(#3,#2)|multiply(#4,const_100)| | gain |
the product of x and y is a constant . if the value of x is increased by 60 % , by what percentage must the value of y be decreased ? | c . 50 cents yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 50 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 25 cents . fraction of spirit is 1 / 2 . 25 = k * ( 1 / 2 ) k = 50 cost per liter = 50 * ( 1 / 4 ) ( 1 part spirit , 3 parts water ) cost for 4 liters = 50 * ( 1 / 4 ) * 4 = 50 cents d . 50 cents | ['a ) 13', 'b ) 33', 'c ) 56', 'd ) 50', 'e ) 52'] | d | multiply(multiply(50, divide(1, add(1, 3))), add(1, 3)) | add(n0,n4)|divide(n0,#0)|multiply(n2,#1)|multiply(#0,#2) | geometry |
the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 42 kmph , find the speed of the stream ? | "explanation : distance covered = 120 + 120 = 240 m time = 12 s let the speed of each train = x . then relative velocity = x + x = 2 x 2 x = distance / time = 240 / 12 = 20 m / s speed of each train = x = 20 / 2 = 10 m / s = 10 * 18 / 5 km / hr = 36 km / hr option b" | a ) 30 km / hr , b ) 36 km / hr , c ) 80 km / hr , d ) 90 km / hr , e ) none of these | b | multiply(const_3_6, divide(divide(add(120, 120), 12), const_2)) | add(n0,n0)|divide(#0,n1)|divide(#1,const_2)|multiply(#2,const_3_6)| | physics |
- 24 * 29 + 1240 = ? | "sides are 8 , 15 and 21 . . . thus it is right angle triangle since 21 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 21 + 15 + 8 / 2 = 22 thus , 60 = 22 * r and hence r = in - radius = 2.6 option b" | a ) 8.5 units , b ) 2.6 units , c ) 3 units , d ) 5 units , e ) 12 units | b | divide(triangle_area_three_edges(8, 15, 21), divide(triangle_perimeter(8, 15, 21), const_2)) | triangle_area_three_edges(n0,n1,n2)|triangle_perimeter(n0,n1,n2)|divide(#1,const_2)|divide(#0,#2)| | geometry |
a , b and c invested rs . 6000 , rs . 4000 and rs . 10000 respectively , in a partnership business . find the share of a in profit of rs . 11000 after a year ? | "( 4 - x ) = x * ( 5 + x ) ( 4 - x ) = 5 x + x ^ 2 0 = x ^ 2 + 6 x - 4 the answer is b ." | a ) - 3 , b ) 0 , c ) 2 , d ) 4 , e ) 6 | b | subtract(multiply(4, 2), 4) | multiply(n2,n0)|subtract(#0,n0)| | general |
exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ? | "for 40 hrs = 40 * 16 = 640 excess = 1004 - 640 = 364 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 364 / 28 = 13 total hrs = 40 + 13 = 53 answer e 53" | a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 53 | e | add(40, divide(subtract(1004, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100))) | add(n3,const_100)|multiply(n0,n1)|multiply(n0,#0)|subtract(n4,#1)|divide(#2,const_100)|divide(#3,#4)|add(n1,#5)| | general |
a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 50 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ? | step one : first you want to make 3 trips of 1,000 grapes 333 kilometers . you will be left with 2,001 grapes and 667 kilometers to go . step two : next you want to take 2 trips of 1,000 grapes 500 kilometers . you will be left with 1,000 grapes and 167 kilometers to go ( you have to leave a grape behind ) . step three : finally , you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland . correct answer is a ) 833 | a ) 833 , b ) 765 , c ) 665 , d ) 679 , e ) 874 | a | subtract(1000, subtract(subtract(1000, floor(divide(1000, const_3))), divide(1000, const_2))) | divide(n1,const_3)|divide(n1,const_2)|floor(#0)|subtract(n1,#2)|subtract(#3,#1)|subtract(n1,#4) | physics |
two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every fourth , starting with the fourth , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ? | "the sum of the odd numbers from - 19 to + 19 is 0 . let ' s add the remaining numbers . 21 + 23 + 25 + 27 + 29 = 5 ( 25 ) = 125 the answer is a ." | a ) 125 , b ) 135 , c ) 150 , d ) 175 , e ) 235 | a | add(add(add(add(19, const_2), add(add(19, const_2), const_2)), add(add(add(19, const_2), const_2), const_2)), 29) | add(n0,const_2)|add(#0,const_2)|add(#0,#1)|add(#1,const_2)|add(#2,#3)|add(n1,#4)| | physics |
the simple interest on rs . 10 for 4 months at the rate of 3 paise per rupeeper month is | "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 now , there are 25 oranges , so to get to 6 oranges , we should remove 25 - 6 = 19 oranges . answer d" | a ) 3 , b ) 6 , c ) 14 , d ) 19 , e ) 20 | d | subtract(add(14, 25), divide(14, divide(70, const_100))) | add(n0,n1)|divide(n2,const_100)|divide(n0,#1)|subtract(#0,#2)| | general |
each of the three people individually can complete a certain job in 3 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ? | u / i = 7 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 35 : 21 : 2 i . e . u : b = 35 : 2 answer : option e | a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 35 : 2 | e | divide(multiply(7, 5), multiply(1, 2)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1) | other |
calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 13 km / hr downstream and 10 km / hr upstream . | "13 / 3 = 4 . xxx 83 / 6 = 13 . xxx so we need to find prime numbers between 4 ( exclusive ) - 12 ( inclusive ) there are 2 prime numbers 7 11 hence answer will be ( b ) 2 b" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | floor(const_2) | floor(const_2)| | general |
joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 2 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ? | "increase = ( 20 / 60 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b" | a ) 15 % , b ) 33.33 % , c ) 17.8 % , d ) 19 % , e ) 21 % | b | multiply(divide(subtract(80, 60), 60), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
the class mean score on a test was 40 , and the standard deviation was 15 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ? | "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 600 x = 10 the numbers are 3 * 10 , 4 * 10 , 5 * 10 hence required h . c . f . = 10 answer is a" | a ) 10 , b ) 30 , c ) 40 , d ) 50 , e ) 60 | a | add(multiply(multiply(3, 5), const_100), multiply(4, 5)) | multiply(n0,n2)|multiply(n1,n2)|multiply(#0,const_100)|add(#2,#1)| | other |
john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 65 miles per hour , what is v in miles per hour ? | "explanation : speed in downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed in upstream = ( 14 Γ’ β¬ β 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 Γ’ β‘ β x / 18 + x / 20 = 19 Γ’ β‘ β x = 180 km . answer : a" | a ) 180 km , b ) 127 km , c ) 178 km , d ) 188 km , e ) 111 km | a | divide(19, add(divide(const_1, add(14, 4)), divide(const_1, multiply(subtract(14, 4), const_2)))) | add(n1,n2)|subtract(n2,n1)|divide(const_1,#0)|multiply(#1,const_2)|divide(const_1,#3)|add(#2,#4)|divide(n0,#5)| | physics |
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 | "explanation : 18 * 43 + 12 = 786 answer : d" | a ) 586 , b ) 766 , c ) 796 , d ) 786 , e ) 686 | d | add(multiply(18, 43), 12) | multiply(n0,n1)|add(n2,#0)| | general |
carl is facing very difficult financial times and can only pay the interest on a $ 30,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ? | "remainder = 0.60 - - > 60 / 100 - - > can be written as ( 60 / 4 ) / ( 100 / 4 ) = 15 / 25 so remainders can be 15 , 30 , 45 , 60 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 15 + 30 + 45 + 60 + 75 + 90 = 315 answer : a" | a ) 315 , b ) 616 , c ) 672 , d ) 900 , e ) 1024 | a | add(multiply(divide(const_3, const_2), const_100), add(multiply(add(const_2, const_3), 50.60), const_3)) | add(const_2,const_3)|divide(const_3,const_2)|multiply(n0,#0)|multiply(#1,const_100)|add(#2,const_3)|add(#4,#3)| | general |
the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 507 sq m , then what is the breadth of the rectangular plot ? | "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 60 + 10 x 1.5 60 + 15 = 75 kg ans : ' d '" | a ) 80 kg , b ) 83 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg | d | add(60, multiply(10, add(1, divide(const_1, 1)))) | divide(const_1,n1)|add(n1,#0)|multiply(n0,#1)|add(n2,#2)| | general |
the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 20 % ? | "let x be the cost price . 1.2 x = 1050 x = 1050 / 1.2 = 875 the answer is e ." | a ) $ 835 , b ) $ 845 , c ) $ 855 , d ) $ 865 , e ) $ 875 | e | multiply(const_100.0, divide(const_100, add(1050, 20))) | add(n1,const_100)|divide(const_100,#0)|multiply(n0,#1)| | gain |
evaluate 35 % of 450 + 45 % of 350 | we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a | a ) 8 / 9 , b ) 11 / 12 , c ) 8 / 13 , d ) 11 / 13 , e ) 12 / 13 | a | divide(add(40, 40), add(add(40, 40), const_10)) | add(n3,n3)|add(#0,const_10)|divide(#0,#1) | general |
a man can do a job in 15 days . his father takes 20 days and his son finishes it in 15 days . how long will they take to complete the job if they all work together ? | 2 a * 4 b = 10 * 10 = 100 8 ab = 100 i . e . 40 ab = 500 answer : option e | a ) 50 , b ) 100 , c ) 250 , d ) 450 , e ) 500 | e | multiply(40, multiply(divide(10, 2), divide(10, 4))) | divide(n2,n0)|divide(n2,n1)|multiply(#0,#1)|multiply(n3,#2) | general |
if 2 ^ k + 2 ^ k = ( 2 ^ 9 ) ^ ( 2 ^ 9 ) - 2 ^ k , then k = ? | "average price per book = ( 1200 + 480 ) / ( 52 + 32 ) = 1680 / 84 = rs . 20 answer : d" | a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 20 , e ) s . 10 | d | divide(add(1200, 480), add(52, 32)) | add(n1,n3)|add(n0,n2)|divide(#0,#1)| | general |
due to construction , the speed limit along an 10 - 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 ? | "time upstream = d / 2 time downstream = d / 6 total time = d / 2 + d / 6 = 2 d / 3 average speed = 2 d / ( 2 d / 3 ) = 3 km / hr the answer is d ." | a ) 6 , b ) 4 , c ) 9 , d ) 3 , e ) 2 | d | divide(add(subtract(4, const_0.5), add(4, 2)), const_2) | add(n0,const_0.5)|subtract(n0,n1)|add(#0,#1)|divide(#2,const_2)| | general |
11 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ? | "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 4 * 4 = 208 smash d" | a ) 26 , b ) 39 , c ) 42 , d ) 208 , e ) 156 | d | multiply(multiply(multiply(power(2, 2), 4), divide(13, 2)), 2) | divide(n4,n0)|power(n0,n0)|multiply(n2,#1)|multiply(#0,#2)|multiply(n0,#3)| | general |
four machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ? | "3 < x < 6 < y < 11 ; 3 < x y < 11 3 + y < x + 11 y - x < 8 . positive integer difference is 7 ( for example y = 10.5 and x = 3.5 ) answer : e ." | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | subtract(subtract(11, 3), const_1) | subtract(n2,n0)|subtract(#0,const_1)| | general |
the charge for a single room at hotel p is 30 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? | chris present age = x after 20 years = x + 20 5 years back = x - 5 x + 20 = 5 ( x - 5 ) x = 5 answer is e | a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 5 | e | subtract(divide(add(multiply(5, 5), 20), subtract(5, const_1)), subtract(divide(add(multiply(5, 5), 20), subtract(5, const_1)), 5)) | multiply(n1,n1)|subtract(n1,const_1)|add(n0,#0)|divide(#2,#1)|subtract(#3,n1)|subtract(#3,#4) | general |
two men are going along a track rail in the opposite direction . one goods train crossed the first person in 20 sec . after 10 min the train crossed the other person who is coming in opposite direction in 18 sec . after the train has passed , when the two persons will meet ? | "x is an integer and 2.134 Γ 10 x is less than 2 , 200,000 , what is the greatest possible value for x ? for 2.134 Γ 10 x is less than 2 , 200,000 to remain true , the greatest number is 2 , 134,000 , which makes x = 6 b . 6" | a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | b | floor(divide(log(divide(2, 2.134)), log(10))) | divide(n2,n0)|log(n1)|log(#0)|divide(#2,#1)|floor(#3)| | general |
an auction house charges a commission of 17 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ? | "1 / 2 * d ( 15 + 9 ) = 636 d = 53 answer : a" | a ) 53 , b ) 28 , c ) 27 , d ) 80 , e ) 25 | a | divide(divide(divide(636, divide(add(15, 9), const_2)), 9), const_2) | add(n0,n1)|divide(#0,const_2)|divide(n2,#1)|divide(#2,n1)|divide(#3,const_2)| | physics |
tim and Γ© lan are 60 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and Γ© lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets Γ© lan ? | "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 24 = 360 m . let the length of the platform be x m . then , ( x + 360 ) / 36 = 15 = > x = 180 m . answer : c" | a ) 767 m , b ) 240 m , c ) 180 m , d ) 176 m , e ) 186 m | c | multiply(24, multiply(54, const_0_2778)) | multiply(n2,const_0_2778)|multiply(n1,#0)| | physics |
by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ? | let weight of jar filled with beans = 100 g weight of jar = 30 g weight of coffee beans = 70 g weight of jar and remaining beans = 60 g weight of remaining beans = 30 g fraction remaining = 30 / 70 = 3 / 7 answer is e . | a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 7 | e | divide(subtract(60, 30), subtract(const_100, 30)) | subtract(n1,n0)|subtract(const_100,n0)|divide(#0,#1) | gain |
the ratio of the area of a square to that of the square drawn on its diagonal is | "explanation : it will 12.5 * 1 / 100 = 1 / 8 answer : option d" | a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 8 , e ) none of above | d | divide(circle_area(divide(12.5, const_2)), const_2) | divide(n0,const_2)|circle_area(#0)|divide(#1,const_2)| | gain |
a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x β 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number w of people surveyed by the company ? | "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 15 % = 115 % 115 % - - - - - - - > 1150 ( 115 Γ 100 = 1150 ) 100 % - - - - - - - > 1000 ( 100 Γ 100 = 1000 ) b )" | a ) 250 , b ) 1000 , c ) 450 , d ) 500 , e ) 520 | b | divide(1150, add(const_1, divide(15, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | gain |
the principal that amounts to rs . 4903 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ? | "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 390 ) / 36 * 5 / 18 = 51 min . answer : c" | a ) 19 , b ) 27 , c ) 51 , d ) 47 , e ) 28 | c | divide(add(390, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36)) | multiply(n0,const_0_2778)|multiply(n1,#0)|add(n2,#1)|divide(#2,#0)| | physics |
two trains start simultaneously from opposite ends of a 175 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 175 - km trip in 4 hours . train y , travelling at a constant rate , completes the 175 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ? | "explanation : average of new numbers = 23 * 5 = 115 answer : option d" | a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 115 , e ) e ) 145 | d | multiply(23, 5) | multiply(n1,n2)| | general |
if a boat is rowed downstream for 24 km in 4 hours and upstream for 48 km in 24 hours , what is the speed of the boat and the river ? | "in 4 miles , initial 1 / 5 mile charge is $ 3 rest of the distance = 4 - ( 1 / 5 ) = 19 / 5 rest of the distance charge = 19 ( 0.2 ) = $ 3.8 ( as the charge is 0.2 for every 1 / 5 mile ) = > total charge for 4 miles = 3 + 3.8 = 6.8 answer is a" | a ) $ 6.80 , b ) $ 6.50 , c ) $ 16.80 , d ) $ 6.85 , e ) $ 61.80 | a | add(3.00, multiply(subtract(divide(3.00, divide(1, 5)), 1), 0.20)) | divide(n1,n2)|divide(n6,#0)|subtract(#1,n1)|multiply(n3,#2)|add(n0,#3)| | general |
coconuts were purchased at 150 per 100 and sold at 2 per coconut . if 2000 coconuts were sold , what was the total profit made ? | "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 35 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 35 = 1 / 420 so , 20 women work = 20 / 420 = 1 / 21 ans : 21 days answer : e" | a ) 10 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 21 days | e | inverse(add(divide(6, multiply(8, 35)), divide(11, multiply(12, 35)))) | multiply(n0,n2)|multiply(n1,n2)|divide(n3,#0)|divide(n4,#1)|add(#2,#3)|inverse(#4)| | physics |
the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ? | "given that a + b = 182 + b + c = > a Γ’ β¬ β c = 18 + b Γ’ β¬ β b = 18 = > c is younger than a by 18 years answer : e" | a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 18 years | e | multiply(18, const_1) | multiply(n0,const_1)| | general |
when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ? | "the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 1 = 1 / 2 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 2 = 1 / 2 - - > time taken for the 2 nd pump to finish : 1 : 1 / 2 = 2 / 1 = 2 hours . c" | a ) 1 hour , b ) 1.2 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours | c | divide(const_1, subtract(const_1, divide(const_1, multiply(1, const_2)))) | multiply(n0,const_2)|divide(const_1,#0)|subtract(const_1,#1)|divide(const_1,#2)| | physics |
a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 40 now , the son age 5 years back was | "explanation : required number = h . c . f . of ( 1657 - 9 ) and ( 2037 - 5 ) = h . c . f . of 1648 and 2032 = 16 . answer : a" | a ) 16 , b ) 127 , c ) 235 , d ) 305 , e ) 505 | a | gcd(subtract(2037, 5), subtract(1657, 9)) | subtract(n1,n3)|subtract(n0,n2)|gcd(#0,#1)| | general |
darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 5 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ? | "l * 30 = 1200 l = 40 40 + 30 + 50 = 120 120 * 10 = 1200 e" | a ) 2387 , b ) 1298 , c ) 1128 , d ) 1237 , e ) 1200 | e | multiply(add(add(30, divide(1200, 30)), sqrt(add(power(30, 2), power(divide(1200, 30), 2)))), 10) | divide(n1,n3)|power(n3,n2)|add(n3,#0)|power(#0,n2)|add(#1,#3)|sqrt(#4)|add(#2,#5)|multiply(n0,#6)| | geometry |
let f ( x , y ) be defined as the remainder when ( x β y ) ! is divided by x . if x = 16 , what is the maximum value of y for which f ( x , y ) = 0 ? | "if the width is 4 in and the length is 2 times the width , then the length is 2 * 4 = 8 in the area is given by 4 * 8 = 32 square inches correct answer e" | a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 32 square inches | e | rectangle_area(4, multiply(2, 4)) | multiply(n0,n1)|rectangle_area(n1,#0)| | geometry |
9.009 / 1.001 | "c . p . = rs . 4 x and s . p . = rs . 7 x . then , gain = rs . 3 x required ratio = 3 x : 4 x = 3 : 4 a" | a ) 3 : 4 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25 | a | divide(subtract(7, 4), 4) | subtract(n0,n1)|divide(#0,n1)| | other |
a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ? | "let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.02 = 1200 ans : ` ` a ' '" | a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400 | a | divide(subtract(multiply(divide(6, const_100), 2400), multiply(2400, 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 |
the difference between a number and its two - fifth is 510 . what is 20 % of that number ? | "probability of a speaks truth p ( a ) = 3 / 10 ; false = 7 / 10 probability of b speaks truth p ( b ) = 4 / 10 ; false = 6 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 7 / 10 ) * ( 6 / 10 ) ] = 1 - 42 / 100 = 1 - 0.42 = 0.58 answer : a" | a ) 0.58 , b ) 0.9 , c ) 1.9 , d ) 2.2 , e ) 2.3 | a | multiply(divide(30, multiply(multiply(const_4, const_5), const_5)), divide(40, multiply(multiply(const_4, const_5), const_5))) | multiply(const_4,const_5)|multiply(#0,const_5)|divide(n0,#1)|divide(n1,#1)|multiply(#2,#3)| | gain |
during a sale , the price of a pair of shoes is marked down 10 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ? | basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 154.1 ( e ) | a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 360 , e ) $ 154.1 | e | multiply(30, divide(multiply(370, 605), divide(multiply(370, 605), const_10))) | multiply(n1,n2)|divide(#0,const_10)|divide(#0,#1)|multiply(n0,#2)| | geometry |
tom , working alone , can paint a room in 16 hours . peter and john , working independently , can paint the same room in 8 hours and 4 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ? | explanation : let the ten digit be x , unit digit is y . then ( 10 x + y ) - ( 10 y + x ) = 36 = > 9 x - 9 y = 36 = > x - y = 4 . option b | a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 14 | b | divide(36, subtract(const_10, const_1)) | subtract(const_10,const_1)|divide(n0,#0) | general |
what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 21 units ? | "average in 10 matches = ( 6 * 27 + 4 * 32 ) / 6 + 4 = 162 + 128 / 10 = 290 / 10 = 29 answer is d" | a ) 25 , b ) 27 , c ) 30 , d ) 29 , e ) 42 | d | divide(add(multiply(6, 27), multiply(4, 32)), 10) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|divide(#2,n4)| | general |
a and b can do a piece of work in 11 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ? | "( 900 * 3 * 3 ) / 100 = 81 920 + 81 = 1001 answer : b" | a ) rs . 1056 , b ) rs . 1001 , c ) rs . 2056 , d ) rs . 1026 , e ) rs . 1856 | b | multiply(power(add(const_1, divide(3, const_100)), 3), 900) | divide(n3,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | gain |
x and y are both integers . if x / y = 59.60 , then what is the sum of all the possible two digit remainders of x / y ? | "income of 10 months = ( 10 Γ 85 ) β debt = 850 β debt income of the man for next 4 months = 4 Γ 60 + debt + 30 = 270 + debt β΄ income of 10 months = 1120 average monthly income = 1120 Γ· 10 = 112 answer c" | a ) 180 , b ) 100 , c ) 112 , d ) 110 , e ) none of the above | c | divide(add(add(multiply(85, 10), multiply(60, 4)), 30), add(10, 4)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|add(n4,#3)|divide(#4,#0)| | general |
jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 36 , what is the probability that the next one she draws will be pink ? | "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 5 c 3 * 5 c 3 = 10 * 10 = 100 p ( selling 3 bottles of apple juice ) = 100 / 210 = 10 / 21 the answer is d ." | a ) 4 / 9 , b ) 6 / 11 , c ) 8 / 15 , d ) 10 / 21 , e ) 12 / 25 | d | divide(choose(5, 3), choose(10, 5)) | choose(n1,n3)|choose(n0,n1)|divide(#0,#1)| | probability |
the speed of a boat in still water in 37 km / hr and the rate of current is 13 km / hr . the distance travelled downstream in 10 minutes is : | 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 = 136 = > . 1 x + 3 / 4 x = 136 = > x = 160 160 - 136 = pure gala = 24 . a | a ) 24 , b ) 33 , c ) 55 , d ) 77 , e ) 88 | a | subtract(divide(136, add(divide(10, const_100), divide(3, 4))), 136) | divide(n0,const_100)|divide(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,n1) | general |
if the given two numbers are respectively 7 % and 28 % of a third number , then what percentage is the first of the second ? | "males who did not arrive on time are 1 / 5 * 1 / 3 = 1 / 15 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 3 = 1 / 9 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 15 + 1 / 9 = 8 / 45 the answer is e ." | a ) 1 / 6 , b ) 2 / 15 , c ) 3 / 20 , d ) 7 / 30 , e ) 8 / 45 | e | add(multiply(subtract(const_1, divide(5, 6)), subtract(const_1, divide(1, 3))), multiply(subtract(const_1, divide(4, 5)), divide(1, 3))) | divide(n4,n5)|divide(n0,n1)|divide(n2,n3)|subtract(const_1,#0)|subtract(const_1,#1)|subtract(const_1,#2)|multiply(#3,#4)|multiply(#1,#5)|add(#6,#7)| | general |
a constructor estimates that 8 people can paint mr khans house in 3 days . if he uses 4 people instead of 8 , how long will they take to complete the job ? | "let c . p . be $ 100 . then , s . p . = $ 130 let marked price be $ x . then , 95 / 100 x = 130 x = 13000 / 95 = $ 136.8 now , s . p . = $ 136.8 , c . p . = $ 100 profit % = 136.8 % . d" | a ) 140 , b ) 120 , c ) 130 , d ) 136.8 , e ) 150 | d | multiply(const_100, divide(add(const_100, 30), subtract(const_100, 5))) | add(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)|multiply(#2,const_100)| | gain |
ram , who is half as efficient as krish , will take 18 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ? | "the smallest amount that the company can spend is the lcm of 300 and 200 , which is 600 for each , which is total 1200 . the number of 1 st type of computers which costing $ 300 = 600 / 300 = 2 . the number of 2 nd type of computers which costing $ 200 = 600 / 200 = 3 . total = 2 + 3 = 5 answer is b ." | a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11 | b | add(divide(lcm(300, 200), 300), divide(lcm(300, 200), 200)) | lcm(n0,n1)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)| | general |
a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ? | "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 14 = 36 n ^ 2 + 12 n + 1 + 14 = 36 n ^ 2 + 12 n + 12 + 3 if p = 6 n - 1 , then p ^ 2 + 14 = 36 n ^ 2 - 12 n + 1 + 14 = 36 n ^ 2 - 12 n + 12 + 3 when divided by 12 , it must leave a remainder of 3 . the answer is c ." | a ) 6 , b ) 1 , c ) 3 , d ) 8 , e ) 7 | c | subtract(add(14, power(add(const_1, const_4), 2)), multiply(12, 3)) | add(const_1,const_4)|multiply(n0,n3)|power(#0,n1)|add(n2,#2)|subtract(#3,#1)| | general |
the total marks obtained by a student in mathematics and physics is 80 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . | "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { hhh , hth , thh , hht } p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 answer is d" | a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 1 / 2 , e ) 1 / 8 | d | negate_prob(divide(const_1, power(const_2, const_3))) | power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)| | probability |
during the second quarter of 1984 , a total of 3 , 976000 domestic cars were sold . if this was 32 % greater than the number sold during the first quarter of 1984 , how many were sold during the first quarter ? | "here both numbers are less than 100 . so they are deficient of - 5 and - 2 compared with 100 . so answer : d" | a ) 93 / 198 , b ) 93 / 12 , c ) 93 / 13 , d ) 93 / 10 , e ) 93 / 11 | d | divide(95, 98) | divide(n0,n1)| | general |
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 ? | d | a ) 9 , b ) 12 , c ) 20 , d ) 10 , e ) 0 | d | multiply(divide(5, 5), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 14 , what was the price before the first discount ? | "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were right - handed - - > 12 * 1 / 3 = 4 were right - handed and 8 left - handed . the number of right - handed players who were not at practice that day is 9 - 4 = 5 . the number of left - handed players who were not at practice that days is 9 - 8 = 1 . the ratio = 5 / 1 . answer : b" | a ) 1 / 3 , b ) 5 / 1 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2 | b | divide(subtract(divide(const_1, const_2), subtract(subtract(const_1, divide(const_1, const_3)), multiply(divide(const_1, const_3), subtract(const_1, divide(const_1, const_3))))), subtract(divide(const_1, const_2), multiply(divide(const_1, const_3), subtract(const_1, divide(const_1, const_3))))) | divide(const_1,const_2)|divide(const_1,const_3)|subtract(const_1,#1)|multiply(#1,#2)|subtract(#2,#3)|subtract(#0,#3)|subtract(#0,#4)|divide(#6,#5)| | general |
recently , i decided to walk down an escalator of a tube station . i did some quick calculation in my mind . i found that if i walk down 20 ` ` 6 steps , i require thirty seconds to reach the bottom . however , if i am able to step down thirty ` ` 4 stairs , i would only require eighteen seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time i step off the last step at the bottom ? | "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 42 = 6 k + 4 p = > k = 5 , p = 3 total red ' s in bag a will be 2 k = 10 d" | a ) 1 , b ) 3 , c ) 4 , d ) 10 , e ) 12 | d | divide(42, add(multiply(3, 2), 4)) | multiply(n1,n2)|add(n5,#0)|divide(n6,#1)| | other |
what is the remainder when 1250 * 1040 * 1057 * 1145 is divided by 32 ? | "explanation : let number of hens = h and number of cows = c number of heads = 42 = > h + c = 42 - - - ( equation 1 ) number of feet = 124 = > 2 h + 4 c = 124 = > h + 2 c = 62 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 62 - 42 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 42 = > h = 42 - 20 = 22 i . e . , number of hens = 22 answer : a" | a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28 | a | divide(subtract(multiply(42, const_4), 124), const_2) | multiply(n0,const_4)|subtract(#0,n1)|divide(#1,const_2)| | general |
a monkey ascends a greased pole 17 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ? | "let the smaller number be x . then larger number = ( x + 1385 ) . x + 1385 = 6 x + 15 5 x = 1370 x = 274 large number = 274 + 1385 = 1659 e" | a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1659 | e | multiply(divide(subtract(1385, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general |
a train running at the speed of 110 km / hr crosses a pole in 9 sec . what is the length of the train ? | "explanation : age of the teacher = ( 37 * 14 - 36 * 13 ) years = 50 years . answer : e" | a ) 35 years , b ) 45 years , c ) 51 years , d ) 54 years , e ) 50 years | e | add(36, const_1) | add(n0,const_1)| | general |
one fourth of a solution that was 10 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ? | answer 0.30 = 30 / 100 = 3 / 10 correct option : c | a ) 18 / 50 , b ) 16 / 50 , c ) 3 / 10 , d ) 19 / 50 , e ) none | c | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 0.3), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2) | physics |
a train 450 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ? | "total no . of stars on galaxy = 5 * 10 ^ 11 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 5 * 10 ^ 11 / 50 * 10 ^ 6 = 50 * 10 ^ 3 / 5 = 10000 therefore answer is e" | a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 10,000 | e | multiply(divide(multiply(divide(multiply(5, 10), 50), power(10, const_4)), const_1000), 5) | multiply(n0,n1)|power(n1,const_4)|divide(#0,n3)|multiply(#2,#1)|divide(#3,const_1000)|multiply(n0,#4)| | general |
the price of an item is discounted 6 percent on day 1 of a sale . on day 2 , the item is discounted another 6 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ? | let the height be h 2 ( 30 + 24 ) x h β 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d | ['a ) 9.6 m 3', 'b ) 96 m 3', 'c ) 960 m 3', 'd ) 9600 m 3', 'e ) 96000 m 3'] | d | volume_rectangular_prism(30, 24, divide(multiply(rectangle_area(30, 24), const_2), rectangle_perimeter(30, 24))) | rectangle_area(n0,n1)|rectangle_perimeter(n0,n1)|multiply(#0,const_2)|divide(#2,#1)|volume_rectangular_prism(n0,n1,#3) | geometry |
the l . c . m of two numbers is 48 . the numbers are in the ratio 2 : 3 . the sum of numbers is ? | "120 amounts to 180 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 180 120 + 120 * ( r / 100 ) * ( 3 ) = 140 = > r = 50 / 3 150 in 6 years = principal + interest = 300 answer is e ." | a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 300 | e | add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(180, 120), 120), 120), 3)), 120)) | multiply(n3,n4)|subtract(n1,n0)|multiply(#1,n0)|divide(#2,n0)|divide(#3,n2)|multiply(#4,#0)|divide(#5,n0)|add(n3,#6)| | gain |
mary ' s income is 60 % more than tim ' s income and tim ' s income is 60 % less than juan ' s income . what % of juan ' s income is mary ' s income . | "explanation : 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square . answer : e" | a ) 337 , b ) 297 , c ) 266 , d ) 116 , e ) 130 | e | divide(divide(divide(divide(divide(520, const_3), const_3), const_4), const_4), const_4) | divide(n0,const_3)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_4)|divide(#3,const_4)| | geometry |
for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 6 minutes from 9 : 00 in the morning to 6 : 00 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 2 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ? | the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : a . | a ) $ 1.80 , b ) $ 2.00 , c ) $ 2.40 , d ) $ 2.70 , e ) $ 3.00 | a | multiply(divide(150, const_100), 1.2) | divide(n6,const_100)|multiply(n4,#0) | general |
last year a certain bond price with a face value of 5000 yielded 9 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ? | explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 β 5 x = 35 β x = 7 . hence , b ' s age = 2 x = 14 years . answer : d | a ) 7 , b ) 9 , c ) 8 , d ) 14 , e ) 10 | d | divide(multiply(subtract(37, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0) | general |
the length of each side of an equilateral triangle having an area of 4 Γ’ Λ Ε‘ 3 cm 2 is ? | let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | b | multiply(const_2, const_3) | multiply(const_2,const_3) | general |
a snail , climbing a 24 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ? | "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . Ο r 2 = 175600 β ( r ) 2 = ( 175600 x ( 7 / 22 ) ) β r = 236.37 m . circumference = 2 Ο r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 2 ) = rs . 2972 . answer : option a" | a ) 2972 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 4675 | a | multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 2) | divide(n0,const_pi)|sqrt(#0)|multiply(#1,const_100)|circumface(#2)|multiply(#3,n1)| | geometry |
in a certain warehouse , 50 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ? | "30 - - - 3 ds = 10 ? - - - - 1 12 - - - - 3 us = 4 ? - - - - 1 m = ? m = ( 10 + 4 ) / 2 = 7 answer : b" | a ) 8 , b ) 7 , c ) 5 , d ) 2 , e ) 4 | b | divide(add(divide(12, 3), divide(30, 3)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | physics |
what will be the compound interest on rs . 25000 a Ε er 3 years at the rate of 12 % per annum | "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 7 x / ( x / 8 ) = 56 kmph answer : a" | a ) 56 , b ) 18 , c ) 24 , d ) 19 , e ) 12 | a | divide(multiply(40, 7), add(divide(40, 40), divide(multiply(2, 40), 20))) | divide(n0,n0)|multiply(n0,n3)|multiply(n0,n1)|divide(#2,n2)|add(#0,#3)|divide(#1,#4)| | general |
how much is 80 % of 40 is greater than 4 / 5 of 30 ? | "explanation : total of the 6 digits - 6 * 16 = 96 total of the 4 digits - 4 * 10 = 40 total of the remaining 2 digits - 96 - 40 = 56 average of the remaining 2 numbers = 56 / 2 = 28 answer : c" | a ) 36 , b ) 35 , c ) 28 , d ) 33 , e ) 21 | c | divide(subtract(multiply(6, 16), multiply(4, 10)), 2) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)| | general |