regisss/math_qa huggingface dataset:
Problem: what is the square root of 83,521 ?
Options: a ) 476 , b ) 489 , c ) 289 , d ) 511 , e ) 311
Rationale: "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) c = 489 ^ 2 and e = 511 ^ 2 c = ( 300 - 11 ) ^ 2 and e = ( 300 + 11 ) ^ 2 since we need the answer less than 90000 = > e is out . thus we have c as the ans ."
Answer: c
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 4 : 5
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 16 : 9 = 4 : 3 . answer : b"
Answer: b
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 3 of the juniors is equal to 1 / 2 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 3 / 7 , d ) 2 / 7 , e ) 7 / 2
Rationale: "let total number of juniors = j total number of seniors = s ( 2 / 3 ) j = ( 1 / 2 ) s = > s = 4 / 3 j total number of students = j + s = ( 7 / 3 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 7 / 3 ) j ] = 3 / 7 answer c"
Answer: c
Problem: a meal cost $ 34.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: 10 % ( 34.5 ) = 3.45 15 % ( 34.5 ) = 5.175 total amount could have been 34.5 + 3.45 and 34.5 + 5.175 = > could have been between 37.95 and 39.675 = > approximately between 38 and 40 answer is c .
Answer: c
Problem: in an examination , questions were asked in 5 sections . out of the total students , 5 % candidates cleared the cut - off in all the sections and 5 % cleared none . of the rest , 25 % cleared only one section and 20 % cleared 4 sections . if 24.5 % of the entire candidates cleared two sections and 300 candidates cleared 3 sections . find out how many candidates appeared at the examination ?
Options: a ) 1000 , b ) 1200 , c ) 1500 , d ) 2000 , e ) 1800
Rationale: solution : passed in none = 5 % passed in all = 5 % passed in four = 20 % 0 f 90 % = 18 % passed in three = 24.5 % passed in three = ( 100 - 5 - 5 - 22.5 - 24.5 - 18 ) = 25 % . but given 300 students passed in three . hence , 25 % = 300 . so , 100 % = 1200 . 1200 students must have appeared . answer : option b
Answer: b
Problem: a carpenter worked alone for 1 day on a job that would take him 4 more days to finish . he and another carpenter completed the job in 2 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 14 , e ) 24
Rationale: "a carpenter worked only 1 day on something that takes him 4 more days . means ; carpenter finishes his work in 5 days . let his buddy finish the same task in x days . respective rates per day : 1 / 5 and 1 / x to complete 1 work : first guy worked for 3 days @ rate = 1 / 5 per day . second one worked for 2 days @ rate = 1 / x per day expression : days * rate = work 3 * 1 / 5 + 2 * 1 / x = 1 3 x + 10 = 5 x 2 x = 10 x = 5 days . ans : a"
Answer: a
Problem: g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( z ) is divisible by 4 ^ 11 , what is the smallest possible value for z ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: g ( z ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b
Answer: b
Problem: if 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a 7 - percent vinegar solution , what was the concentration of the original solution ?
Options: a ) 19.3 % , b ) 17 % , c ) 36.17 % , d ) 15.5 % , e ) 12.5 %
Rationale: let x be the quantity of non - vinegar in the strong vinegar solution thus vinegar quantity will be 12 - x when 50 ounces of water were added the percentage of vinegar becomes 7 % , thus ( 12 - x ) / 62 = 7 / 100 from this equation x = 7.66 answer ( 12 - 7.66 ) / 12 = 36.17 % answer : c
Answer: c
Problem: if ( a + b ) = 5 , ( b + c ) = 6 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 5 b + c = 6 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 5 - 6 + 3 = 2 . option d . . ."
Answer: d
Problem: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 25 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 10.89 , b ) 14.81 , c ) 14.8 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 25 inch = ( 136 ã — 25 ) / 312 = 10.89 km answer : a"
Answer: a
Problem: a garrison of 400 men had a provision for 31 days . after 27 days 200 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 8 days , d ) 16 days , e ) 18 days
Rationale: 400 - - - 31 400 - - - 4 200 - - - ? 400 * 4 = 200 * x = > x = 8 days . answer : c
Answer: c
Problem: a salesman commission is 10 % on all sales upto $ 5000 and 5 % on all sales exceeding this . he remits $ 15000 to his parent company after deducting his commission . find the total sales ?
Options: a ) 15456 , b ) 14758 , c ) 15789 , d ) 13250 , e ) 12450
Rationale: "let his total sales be x total sales - commission = $ 15000 x - [ ( 10 % of 5000 ) + 5 % of ( x - 5000 ) ] = 15000 95 x / 100 = 15000 x = 15789 approximately answer is c"
Answer: c
Problem: ( 7.5 × 7.5 + 3.75 + 2.5 × 2.5 ) is equal to
Options: a ) 30 , b ) 60 , c ) 80 , d ) 100 , e ) 90
Rationale: "solution given expression = ( 7.5 x 7.5 + 2 × 7.5 × 2.5 + 2.5 × 2.5 ) ² = ( a ² + 2 ab + b ² ) = ( a + b ) ² = ( 7.5 + 2.5 ) ² = 10 ² = 100 . answer d"
Answer: d
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 40 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 30 % , e ) 20 %
Rationale: "expensive item = $ 100 ; cheap item = $ 60 ; we must increase $ 60 to $ 100 , so by $ 40 , which is approximately 60 % increase : ( 100 - 60 ) / 60 = 2 / 3 = ~ 0.66 . answer : c ."
Answer: c
Problem: a owes b rs . 50 . he agrees to pay b over a number of consecutive days on a monday , paying single note or rs . 10 or rs . 20 on each day . in how many different ways can a repay b .
Options: a ) 2 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: he can pay by all 10 rupee notes = 1 way 3 ten rupee + 1 twenty rupee = 4 ! 3 ! × 1 ! 4 ! 3 ! × 1 ! = 4 ways 1 ten rupee + 2 twenty rupee notes = 3 ! 2 ! × 1 ! 3 ! 2 ! × 1 ! = 3 ways total ways = 1 + 4 + 3 = 8 answer : b
Answer: b
Problem: if two positive numbers are in the ratio 1 / 12 : 1 / 9 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 33.33 % , d ) 50 % , e ) 65 %
Rationale: "given ratio = 1 / 12 : 1 / 9 = 9 : 12 let first number be 9 x and the second number be 12 x . the second number is more than first number by 3 x . required percentage = 3 x / 9 x * 100 = 33.33 % . answer : c"
Answer: c
Problem: a and b invests rs . 10000 each , a investing for 6 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4500 , find their shares ?
Options: a ) 1500,6000 , b ) 4500,3000 , c ) 3500,3000 , d ) 1500,3000 , e ) 2500,3000
Rationale: "the ratio of their profits a : b = 6 : 12 = 1 : 2 share of a in the total profit = 1 / 3 * 4500 = rs . 1500 share of b in the total profit = 2 / 3 * 4500 = rs . 3000 answer : d"
Answer: d
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 32.49 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "explanation : money collected = ( 32.49 x 100 ) paise = 3249 paise . ∴ number of members = √ ( 3249 ) = 57 . answer : a"
Answer: a
Problem: q ' = 3 q - 3 , what is the value of ( 6 ' ) ' ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240
Rationale: ( 6 ' ) ' = ( 3 * 6 - 3 ) ' = 15 ' = 15 * 15 - 15 = 210 answer d
Answer: d
Problem: in 1979 approximately 1 / 3 of the 38.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.6
Rationale: number of passengers using kennedy airport = 38 / 3 = ~ 12.67 passengers using miami airport = 12.67 / 2 = ~ 6.3 passengers using logan airport = 6.3 / 4 = ~ 1.58 so e
Answer: e
Problem: when n is divided by 24 , the remainder is 3 . find thee difference between previous remainder and the remainder when 9 n is divided by 7 ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 6
Rationale: "let n = 3 ( leaves a remainder of 3 when divided by 24 ) 9 n = 9 ( 3 ) = 27 , which leaves a remainder of 6 when divided by 7 . difference = 6 - 3 = 3 . answer d"
Answer: d
Problem: the initial price of an article is rs . 6000 which increases 40 % increse in its price in the first year , a 20 % decrease in the second year and a 20 % increase in the next year . what is the final price of the article ?
Options: a ) rs . 5392 , b ) rs . 6392 , c ) rs . 8392 , d ) rs . 7392 , e ) rs . 9392
Rationale: "the initial price of the article is rs . 6000 . in the 1 st year , price of the article = 6000 + 2400 = rs . 8400 . in the 2 nd year , price = 8400 - 20 % of 8400 = 8400 - 1680 = rs . 6720 . in the 3 rd year , price = 6720 + 10 % of 6720 = 6720 + 672 = rs . 7392 required price = = rs . 7392 . answer : d"
Answer: d
Problem: a and b can finish a work in 16 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 80 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 16 – 1 / 20 = 1 / 80 = > 80 days answer : c"
Answer: c
Problem: one side of a rectangular field is 13 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 100 , b ) 141.7 , c ) 150 , d ) 180 , e ) none
Rationale: "solution other side = √ ( 17 ) 2 - ( 13 ) 2 = √ 289 - 169 = √ 120 = 10.9 m . ∴ area = ( 13 x 10.9 ) m 2 = 141.7 m 2 . answer b"
Answer: b
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 16000 left with him . find salary . .
Options: a ) $ 10800 , b ) $ 18000 , c ) $ 160000 , d ) $ 1800 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 16000 , = [ 1 - 9 / 10 ] * total salary = $ 16000 , total salary = $ 16000 * 10 = $ 160000 , correct answer ( c )"
Answer: c
Problem: a has 10000 chocolates . 20 % of the chocolates are eaten . what percentage of the uneaten chocolates must be eaten so that 3 / 2 of all chocolates are eaten ?
Options: a ) 39.25 , b ) 37.25 , c ) 37.26 , d ) 38.21 , e ) 38.32
Rationale: number of chocolates = 10,000 currently eaten = 10,000 * 20 / 100 = 2000 uneaten chocolates = 10000 - 2000 = 8000 2 / 3 of all chocolates = 5000 the number of chocolates to be eaten to make 2 / 3 of all chocolates eaten = 5000 - 2000 = 3000 so now the question remains - 3000 is how much percentage of uneaten chocolates ( 8000 ) = 3000 * 100 / 8000 = 37.5 answer ( b )
Answer: b
Problem: a school has 4 section of chemistry in class x having 60 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50 , b ) 52 , c ) 51 , d ) 53 , e ) none of the above
Rationale: "required average marks = 60 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 60 + 35 + 45 + 42 = 3000 + 2100 + 2475 + 1890 / 182 = 9465 â  „ 182 = 52 answer b"
Answer: b
Problem: the number of employees in obelix menhir co . is a prime number and is less than 300 . the ratio of the number of employees who are graduates and above , to that of employees who are not , can possibly be : -
Options: a ) 101 : 88 , b ) 87 : 100 , c ) 110 : 111 , d ) 85 : 98 , e ) 97 : 84
Rationale: explanation : going through the given options , option 1 : - 101 : 88 = > 189 . [ divisible by 3 ] option 2 : - 87 : 100 = > 187 . [ divisible by 11 ] option 3 : - 85 : 98 = > 183 . [ divisible by 3 ] option 4 : - 97 : 84 = > 181 . [ prime number ] hence , only 181 is the prime number i . e the total number of employee in the company and the required ratio is 97 : 84 . answer : e
Answer: e
Problem: rs . 825 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 825 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1055 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 825 ) = rs . 131 rate = ( 100 x 131 / 825 x 3 ) = 524 / 99 % new rate = ( 524 / 99 + 4 ) % = 920 / 99 % new s . i . = rs . ( 825 x 920 / 99 x 3 / 100 ) rs . 230 . ∴ new amount = rs . ( 825 + 230 ) = rs . 1055 . answer c"
Answer: c
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 496.80 ?
Options: a ) 22 , b ) 27 , c ) 20 , d ) 21 , e ) 12
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 496.80 , discount = 621 - 496.80 = 124.20 discount % = 124.2 / 621 * 100 = 20 % . answer : c"
Answer: c
Problem: a 45 ° - 45 ° - 90 ° right triangle has hypotenuse of length h . what is the area of the triangle t in terms of h ?
Options: a ) h / √ 2
b ) h / 2
c ) h / 4
d ) ( h ) ^ 2
e ) ( h ) ^ 2 / 4
Rationale: if . . . each of the two shorter sides = 3 , then the hypotenuse = h = 3 ( root 2 ) . the area t = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 3 ) ( 3 ) = 9 / 2 . so we ' re looking for an answer that = 9 / 2 when h = 3 ( root 2 ) . there ' s only one answer that matches . . . e
Answer: e
Problem: the perimeter of a triangle is 40 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 50
Rationale: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e"
Answer: e
Problem: a man swims downstream 54 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "54 - - - 3 ds = 18 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 18 + 6 ) / 2 = 12 answer : e"
Answer: e
Problem: the average of 11 results is 52 , if the average of first 6 results is 49 and that of the last 6 is 52 . find the sixth result ?
Options: a ) a ) 46 , b ) b ) 34 , c ) c ) 66 , d ) d ) 76 , e ) e ) 74
Rationale: 1 to 11 = 11 * 52 = 572 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 – 572 = 34 answer : b
Answer: b
Problem: sum of the squares of 3 no . is 138 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 21 , c ) 25 , d ) 26 , e ) 27
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 * 131 a + b + c = √ 400 = 20 a"
Answer: a
Problem: the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is :
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 × ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . answer : d"
Answer: d
Problem: 120 liters of a mixture contains milk and water in the ratio 4 : 2 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 8 : 6 , b ) 9 : 3 , c ) 9 : 4 , d ) 9 : 6 , e ) 8 : 2
Rationale: quantity of milk in 120 liters if mix = 120 * 4 / 6 = 80 liters quantity of milk in 130 liters of new mix = 80 + 10 = 90 liters quantity of water in it = 130 - 90 = 40 liters ratio of milk and water in new mix = 90 : 40 = 9 : 4 answer is c
Answer: c
Problem: 170 kg of an alloy a is mixed with 250 kg of alloy b . if alloy a has lead and tin in the ratio 1 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?
Options: a ) 210.6 kg , b ) 221.3 kg , c ) 229.5 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 170 kg of a = 170 * 3 / 4 = 127.5 kg quantity of tin in 250 kg of b = 250 * 3 / 8 = 93.75 kg quantity of tin in the new alloy = 127.5 + 93.75 = 221.25 kg answer is b"
Answer: b
Problem: a train 360 m long can cross an electric pole in 30 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 43 kmph , c ) 72 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "length = speed * time speed = l / t s = 360 / 30 s = 12 m / sec speed = 12 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 43 kmph answer : b"
Answer: b
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours
Rationale: "a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 2 ) = 3 / 4 b ' s 1 hour work = ( 3 / 4 - 1 / 2 ) = 1 / 4 b alone will take 4 hours to do the work . answer : c"
Answer: c
Problem: the maximum number of student amoung them 1204 pens and 840 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 28 , c ) 56 , d ) 89 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1204 and 840 = 28 . answer b"
Answer: b
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 7 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 105
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 7 * 180 / 12 = 105 ounces of water e"
Answer: e
Problem: the product of three consecutive numbers is 120 . then the sum of the smallest two numbers is ?
Options: a ) 9 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 120 120 = 2 * 2 * 5 * 6 = 4 * 5 * 6 so , the three numbers are 4,5 and 6 . and sum of smallest of these two = 4 + 5 = 9 . answer : option a"
Answer: a
Problem: a company pays 12.5 % dividend to its investors . if an investor buys rs . 40 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 20 , b ) 66 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 12.5 * 40 ) / 100 = rs . 5 rs . 25 is income on an investment of rs . 100 rs . 5 is income on an investment of rs . ( 5 * 100 ) / 25 = rs . 20 answer : a"
Answer: a
Problem: how many even number in the range between 10 to 140 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 44
Rationale: we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 140 using ap formula , we can say 140 = 10 + ( n - 1 ) * 2 or n = 66 . for 6 , 12,18 , . . . 138 using ap formula , we can say 138 = 12 + ( n - 1 ) * 6 or n = 22 . hence , only divisible by 2 but not 3 = 66 - 22 = 44 . hence , answer e
Answer: e
Problem: the average of 15 result is 55 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th result ?
Options: a ) 760 , b ) 720 , c ) 700 , d ) 786 , e ) 797
Rationale: "sum of all the 13 results = 15 * 55 = 825 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 825 + 399 - 427 = 797 . e"
Answer: e
Problem: a train of length 250 m crosses a bridge of length 150 m in 32 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 25 , d ) 22 , e ) 45
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 32 x speed speed = 400 / 32 = 12.5 m / s = 45 km / h answer = e"
Answer: e
Problem: a cricketer scored 142 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 57.75 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 142 - ( 12 x 4 + 2 x 6 ) = 142 - ( 60 ) = 82 now , we need to calculate 82 is what percent of 142 . = > 82 / 142 * 100 = 57.75 % answer : a"
Answer: a
Problem: a train running at the speed of 54 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 279 , c ) 135 , d ) 272 , e ) 150
Rationale: "speed = 54 * 5 / 18 = 15 m / sec length of the train = speed * time = 15 * 9 = 135 m answer : c"
Answer: c
Problem: one half of a two digit number exceeds its one third by 6 . what is the sum of the digits of the number ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: "explanation : x / 2 – x / 3 = 6 = > x = 6 3 + 6 = 9 b )"
Answer: b
Problem: a box contains 5 pairs of shoes ( 10 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 92
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 20 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 9 ( as after taking one at random there are 9 shoes left and only one is the pair of the first one ) = 1 / 9 answer : c ."
Answer: c
Problem: in a company of 16 employees , 8 employees earn $ 38,000 , 4 employees earn $ 42,000 , and the 4 highest - paid employees earn the same amount . if the average annual salary for the 16 employees is $ 44,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 54,000 , b ) $ 55,000 , c ) $ 56,000 , d ) $ 57,000 , e ) $ 58,000
Rationale: "8 * 38,000 + 4 * 42,000 + 4 x = 16 * 44,000 4 x = 704,000 - 304,000 - 168,000 4 x = 232,000 x = 58,000 the answer is e ."
Answer: e
Problem: if the price of petrol increases by 32 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 24.2 % , d ) 33.33 % , e ) none of these
Rationale: explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 32 ) i . e 132 . now , his consumption should be reduced to : - = ( 132 − 100 ) / 132 ∗ 100 . hence , the consumption should be reduced to 24.2 % . answer : c
Answer: c
Problem: 108 . triangle a ’ s base is 7 % greater than the base of triangle b , and a ’ s height is 7 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less , b ) 1 % less , c ) equal to each other , d ) 1 % more , e ) 2.1 % more
Rationale: "wish the question specified that we are talking about corresponding height . base of a = 8 / 7 * base of b height of a = 6 / 7 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 8 / 7 * 6 / 7 * area of b = 48 / 49 * area of b area of a is 2.1 % more than the area of b . answer ( e )"
Answer: e
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 64 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 8
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 64 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 65 incorrect c . 2 / 2 = 2 / 3 + 2 / 66 incorrect d . 2 / 3 = 2 / 4 + 2 / 69 incorrect e . 2 / 4 = 2 / 5 + 2 / 72 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Problem: praveen starts business with rs . 3360 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8640 , c ) s . 8500 , d ) s . 9000 , e ) s . 6000
Rationale: let hari ’ s capital be rs . x . then , 3360 * 12 / 7 x = 2 / 3 = > 14 x = 120960 = > x = 8640 . answer : b
Answer: b
Problem: the average ( arithmetic mean ) of 10 , 20 , and 60 is 5 more than the average of 10 , 40 , and what number ?
Options: a ) 25 , b ) 60 , c ) 50 , d ) 30 , e ) 40
Rationale: "a 1 = 90 / 3 = 30 a 2 = a 1 - 5 = 25 sum of second list = 25 * 3 = 75 therefore the number = 75 - 50 = 25 a"
Answer: a
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: solution : first of all , notice the magic word “ approximately ” — the test - writer is letting us know estimation is perfectly fine . furthermore , the answer choices are nicely spread out , which will facilitate estimating . ok , get ready for some fast & furious estimation . the interest rate 3.96 % is an ugly number , so i ’ m going to approximate that as 4 % . it compounds semiannually , so that means that there ’ s 2 % every six months , and that happens four times in two years . well , 2 % of $ 10000 is $ 200 . if you get $ 200 , or a little more , on four occasions , that ’ s a little more than $ 800 in interest . we expect an answer slightly higher than $ 10800 , so of course ( b ) is just right . notice , i estimated so that everything up until the last sum was single - digit math . single - digit calculations are a good standard for which to strive when you are practicing estimation . by the way , if you find the bank that will do answer ( e ) , double your money in only two years , that ’ s terrific , but it probably is something wildly illegal , a ponzi scheme or worse ! in the real world , that just doesn ’ t happen . on word problems , especially in financial situations , you should always have your antenna up for what ’ s realistic or unrealistic . answer ( b )
Answer: b
Problem: 250 men work for 16 days and finish a work . how many men would do a job 3 times the previous one in 20 days ?
Options: a ) 700 , b ) 666 , c ) 600 , d ) 400 , e ) 800
Rationale: number of men needed to finish the required work ( variation , proportion method ) = 3 * 16 * 250 / 20 = 600 answer : c
Answer: c
Problem: solution for 1.35 + . 123 + . 321
Options: a ) 2.91 , b ) 1.794 , c ) 1.338 , d ) 1.986 , e ) 1.999
Rationale: "1.35 + . 123 + . 321 = 0 0 = 0 - 1.35 - 0.123 - 0.321 0 = - 1.794 answer : b"
Answer: b
Problem: the population of a town increases 25 % and 15 % respectively in two consecutive years . after the growth the present population of the town is 1150 . then what is the population of the town 2 years ago ?
Options: a ) a ) 400 , b ) b ) 500 , c ) c ) 600 , d ) d ) 700 , e ) e ) 800
Rationale: explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1150 * 100 / 125 * 100 / 115 = 800 answer : option e
Answer: e
Problem: if 16 machine can finish a job in 45 days , then how many more machines would be needed to finish the job in one - third less time ?
Options: a ) a . 3 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 16 machines ( identical ones , i assume ) work simultaneously for 45 days , they will do a total of 16 * 45 machine - days of work . so the job requires 16 * 45 days of machine work in total . we instead want the job done in 1 / 3 less time , so in 30 days . so we ' ll need 16 * 36 / 30 = 19.2 ~ = 19 machines , or 3 additional machines . a"
Answer: a
Problem: two trains start simultaneously from opposite ends of a 160 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 160 - km trip in 5 hours . train y , travelling at a constant rate , completes the 160 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 56 , b ) 58 , c ) 60 , d ) 62 , e ) 64
Rationale: if the two trains cover a total distance d , then train x travels ( 3 / 8 ) * d while train y travels ( 5 / 8 ) * d . if the trains travel 160 km to the meeting point , then train x travels ( 3 / 8 ) * 160 = 60 km . the answer is c .
Answer: c
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the total share of a & b in profit of rs . 12100 after a year ?
Options: a ) rs . 6030 , b ) rs . 4050 , c ) rs . 6050 , d ) rs . 7050 , e ) rs . 6080
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 a ' share = 3 / 10 * 12100 = 3630 b ' s share = 2 / 10 * 12100 = 2420 required total share = 3630 + 2420 = 6050 answer : c"
Answer: c
Problem: an athlete runs 200 metres race in 40 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 18 , d ) 30 , e ) 28
Rationale: "speed = distance / time = 200 / 40 = 5 m / s = 5 * 18 / 5 = 3618 km / hr answer : c"
Answer: c
Problem: company p had 15 percent more employees in december than it had in january . if company p had 490 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 426 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 490 j = 490 / 1.15 j = 49,000 / 115 = 426 thus b is the correct answer ."
Answer: b
Problem: the present worth of rs . 1404 due in two equal half - yearly instalments at 8 % per annum simple interest is :
Options: a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) none
Rationale: solution required sum = p . w . of rs . 702 due 6 month hence + p . w . of rs . 702 due 1 year hence = rs . [ ( 100 x 702 / 100 + 8 x 1 / 2 ) + ( 100 x 702 / 100 + ( 8 x 1 ) ) ] = rs . ( 675 + 650 ) = rs . 1325 . answer a
Answer: a
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 3 type b widgets , and the weight of 5 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: "5 b = 7 c and so b = 7 c / 5 7 a = 3 b and so a = 3 b / 7 = 3 c / 5 a + b = 3 c / 5 + 7 c / 5 = 10 c / 5 b + c = 7 c / 5 + c = 12 c / 5 the ratio of a + b : b + c = 10 : 12 = 5 : 6 the answer is e ."
Answer: e
Problem: a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 39 % , c ) 50 % , d ) 35 % , e ) 33 %
Rationale: "the total number of mangoes bought by the shopkeeper be 24 . if he buys 6 a rupee , his cp = 4 he selling at 4 a rupee , his sp = 6 profit = sp - cp = 6 - 4 = 2 profit percent = 2 / 4 * 100 = 50 % answer : c"
Answer: c
Problem: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 60 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.6 * 48 + 0.2 * 52 = ~ 39 , so percent of people who are less than 25 years old is 100 - 39 = 61 . answer : b ."
Answer: b
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 15 m wide at the top and 4 m wide at the bottom and the area of cross - section is 1900 sq m , the depth of cannel is ?
Options: a ) 150 , b ) 200 , c ) 140 , d ) 240 , e ) 145
Rationale: "1 / 2 * d ( 15 + 4 ) = 1900 d = 200 answer : b"
Answer: b
Problem: 20 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "20 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 20 ) * 100 = 180 square feet answer : option b"
Answer: b
Problem: a student scored an average of 60 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 160 , c ) 76 , d ) 140 , e ) 26
Rationale: "given m + p + c = 60 * 3 = 180 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 180 = 140 answer : d"
Answer: d
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 21 - m ) then m = ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "2 m = 21 - m 3 m = 21 m = 7 the answer is c ."
Answer: c
Problem: each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 29 have long fur , 17 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 9
Rationale: no of dogs = 45 long fur = 29 brown = 17 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 29 + 17 - both both = 9 answer e
Answer: e
Problem: set a contains all the even numbers between 42 and 90 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "each term in set b is 20 more than the corresponding term in set a . the difference of the sums = 25 * 20 = 500 . the answer is e ."
Answer: e
Problem: of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 6 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 29.4 % , e ) 11.1 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 6 is 1200 * 1 / 6 so it reduced 200 people , so there is 1000 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 1000 clerical left / 3400 people total you get ( a ) 29.4 % answer : d"
Answer: d
Problem: an artist wishes to paint a circular region on a square poster that is 5 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) 2 / sqrt ( pi ) , d ) sqrt ( 12.5 / pi ) , e ) pi / 2
Rationale: "area of the poster is 5 x 5 = 25 1 / 2 the area = 12.5 pi * r ^ 2 = 12.5 r ^ 2 = 12.5 / pi r = sqrt ( 12.5 / pi ) answer ( d )"
Answer: d
Problem: the tax on a commodity is diminished by 17 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8 % , c ) 4.5 % , d ) 6.5 % , e ) 1.5 %
Rationale: "100 * 100 = 10000 83 * 115 = 9545 - - - - - - - - - - - 10000 - - - - - - - - - - - 455 100 - - - - - - - - - - - ? = > 4.55 % decrease answer : c"
Answer: c
Problem: if x is 20 percent greater than 80 , then x =
Options: a ) 68 , b ) 70.4 , c ) 96 , d ) 105.6 , e ) 108
Rationale: "x is 20 % greater than 80 means x is 1.2 times 80 ( in other words 80 + 20 / 100 * 80 = 1.2 * 80 ) therefore , x = 1.2 * 80 = 96.00 answer : c"
Answer: c
Problem: a pet groomer has 7 animals to groom for the day ( 2 cats and 5 dogs ) . if she randomly selects 4 animals to groom before lunch , what is the probability she will finish all the cats before lunch ?
Options: a ) 3 / 7 , b ) 2 / 7 , c ) 12 / 13 , d ) 5 / 11 , e ) 4 / 7
Rationale: combination probability formula : ncr = n ! / [ r ! ( n - r ) ! ] total possible , select 4 animals from 7 animals = 7 c 4 = 7 ! / [ 4 ! ( 7 - 4 ) ! ] = 35 . to finish all 2 cats there must be 2 dogs , select 2 dogs from 5 = 5 c 2 = 10 . and , select 2 cats from 2 = 2 c 2 = 1 . 2 cats and 2 dogs = ( 1 ) ( 10 ) = 10 probability = ( number outcomes favorable ) / ( total number outcomes ) = 10 / 735 = 2 / 7 answer : b
Answer: b
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.75 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,628 , e ) 2,256
Rationale: "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.75 = 0.45 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer d"
Answer: d
Problem: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 70 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 25 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 70 ⇒ 1.75 x = 70 ⇒ x = 40 coins answer c"
Answer: c
Problem: how many positive integers less than 26 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 21 , c ) 24 , d ) 22 , e ) 20
Rationale: 9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 10 - 1 = 21 . answer : b .
Answer: b
Problem: how many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 5 percent sugar solution ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let x be the amount that needs to be evaporated . 0.04 ( 50 ) = 0.05 ( 50 - x ) 0.05 x = 2.5 - 2 x = 0.5 / 0.05 = 10 liters the answer is d ."
Answer: d
Problem: a person lent a certain sum of money at 6 % per annum at simple interest and in 8 years the interest amounted to $ 520 less than the sum lent . what was the sum lent ?
Options: a ) 800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "p - 520 = ( p * 6 * 8 ) / 100 p = 1000 the answer is b ."
Answer: b
Problem: there are 30 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 435 , d ) 60 , e ) 90
Rationale: "30 players are there . two players play one game with one another . so 30 c 2 = 30 * 29 / 2 = 435 so option c is correct"
Answer: c
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 1.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 1.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is a ."
Answer: a
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 90 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 18 * 4 = 72 now half on their horses so remaining on the walk so 9 men 9 men has 18 legs so , 18 + 72 = 90 legs walking answer : e"
Answer: e
Problem: 240 is increased by 20 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 180 , d ) 288 , e ) 220
Rationale: explanation final number = initial number + 20 % ( original number ) = 240 + 20 % ( 240 ) = 240 + 48 = 288 . answer d
Answer: d
Problem: convert 20 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 20 miles = 20 * 1760 = 35200 yards answer is b"
Answer: b
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 25 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 25 % , d ) 23 % , e ) can not be determined
Rationale: answer : c .
Answer: c
Problem: the average of 10 consecutive integers is 11 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 5 , b ) 5.5 , c ) 6 , d ) 6.5 , e ) 7
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d ."
Answer: d
Problem: let the number which when multiplied by 15 is increased by 196 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 15 x - x = 196 ‹ = › 14 x = 196 x ‹ = › 14 . answer a"
Answer: a
Problem: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets ?
Options: a ) 36 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 6 * 6 = 36 days to produce 2 w widgets . answer : a"
Answer: a
Problem: a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , then what is the area of the parking space in square feet ?
Options: a ) 46
b ) 81
c ) 126
d ) 252
e ) none of these
Rationale: solution clearly , we have : l = 9 and l + 2 b = 37 or b = 14 . ∴ area = ( l × b ) = ( 9 × 14 ) sq . ft . = 126 sq . ft . answer c
Answer: c
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 64,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.14544 , c ) 0.21978 , d ) 0.35466 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 364000 x \ therefore required percentage = \ inline \ frac { 800 x } { 364000 } \ times 100 = 0.21978 c"
Answer: c
Problem: if p / q = 4 / 5 , then the value of 6 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 10 / 7 , d ) 2 , e ) 3
Rationale: "answer given exp . = 6 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 6 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 6 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 6 / 7 + 6 / 14 = 6 / 7 + 3 / 7 = 10 / 7 correct option : c"
Answer: c
Problem: two persons start at the same point , walk in opposite directions with 6 km / hr and 7 km / hr respectively . what is the distance separated after 3 and half hrs ?
Options: a ) 45.5 km , b ) 27.250 km , c ) 28.250 km , d ) 29.250 km , e ) 25.250 km
Rationale: as the two persons are moving in the opposite direction , so they will be separateed in 1 hour = 6 + 7 = 13 km . they will be separated in 2.5 hours = 13 * 3.5 = 45.5 km answer : a
Answer: a
Problem: on day one , a store sold 86 cups . on each of the next d days , the company sold 50 cups . if the average daily sales of cups over this time period ( including day one ) is 53 cups , what is the value of d ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: 86 + 50 d = 53 ( d + 1 ) . 3 d = 33 . d = 11 . the answer is c .
Answer: c