Cheukting/mathqa huggingface dataset:
Question (physics): by travelling at 40 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 20 kmph , b ) 17 kmph , c ) 15 kmph , d ) 14 kmph , e ) 13 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 40 * 3 x = 120 x km he covered 2 / 3 * 120 x = 80 x km in 1 / 3 * 3 x = x hours so , the remaining 40 x km , he has to cover in 2 x hours . required speed = 40 x / 2 x = 20 kmph . answer : a"
Answer: a
Question (gain): the present population of a town is 260 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 226 , e ) 286
Rationale: "p = 260 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 260 * ( 1 + 10 / 100 ) = 260 * ( 11 / 10 ) = 286 answer is e"
Answer: e
Question (general): 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 . 3025 . , the number of the member is the group is :
Options: a ) 55 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 30.25 x 100 ) paise = 3025 paise . number of members = square root of 3025 = 55 . answer : option a"
Answer: a
Question (general): in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons ' 1996 tax totals $ 2108 , find their property tax for the year 1995
Options: a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500
Rationale: tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b
Answer: b
Question (general): in an election , candidate douglas won 64 percent of the total vote in counties x and y . he won 76 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 10 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 76 % voted means 76 * 200 = 152 votes combined for xy has 300 voters and voted 64 % so total votes = 192 balance votes = 192 - 152 = 40 as y has 100 voters so 40 votes means 40 % of votes required ans e"
Answer: e
Question (physics): how many seconds will a 900 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 287 , b ) 288 , c ) 500 , d ) 400 , e ) 121
Rationale: "let length of tunnel is x meter distance = 900 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 900 + x = ( 65 / 3 ) * 60 900 + x = 20 * 65 = 1300 x = 1300 - 900 = 400 meters answer : d"
Answer: d
Question (general): 16 * 16 * 16 * 16 * 16 = 4 ^ ?
Options: a ) 8 , b ) 6 , c ) 10 , d ) 4 , e ) 3
Rationale: 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 = 4 ^ ( 2 + 2 + 2 + 2 + 2 ) = 4 ^ 10 answer : 10 option : c
Answer: c
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.82 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.82 9.9 - 45 x + 36 x = 8.82 9 x = 1.08 x = 0.12 the answer is d ."
Answer: d
Question (general): when average age of 25 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 24 , c ) 21 , d ) 23 , e ) 25
Rationale: "average of 25 numbers = 0 . sum of 25 numbers ( 0 x 25 ) = 0 . it is quite possible that 24 of these numbers may be positive and if their sum is a then 25 th number is ( - a ) answer is 24 ( b )"
Answer: b
Question (physics): the length of the bridge , which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 meters , b ) 225 meters , c ) 245 meters , d ) 250 meters , e ) 300 meters
Rationale: "given , length of the train = 130 meters speed of the train = 45 km / hr = 45 * 518 m / sec = 252 m / sec time = 30 secs let the length of the bridge be x meters . the distance travelled by the train while crossing the bridge will be sum of the length of train and length of the bridge = ( x + 130 ) meters so , 252 = x + 13030 = 30 * 25 = 2 x + 260 = 750 - 260 = 2 x = 490 = 2 x = x = 245 meters . answer c"
Answer: c
Question (physics): sakshi can do a piece of work in 10 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 8 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 10 : x ⇒ x = ( 10 x 4 / 5 ) ⇒ x = 8 days . hence , tanya takes 8 days is complete the work . answer a"
Answer: a
Question (gain): there were two candidates in an election . winner candidate received 65 % of votes and won the election by 300 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 255 , d ) 650 , e ) 231
Rationale: "w = 65 % l = 35 % 65 % - 35 % = 30 % 30 % - - - - - - - - 300 65 % - - - - - - - - ? = > 650 answer : d"
Answer: d
Question (gain): a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 6.00 ?
Options: a ) 72 , b ) 60 , c ) 90 , d ) 120 , e ) 240
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 6 ( 1 / 12 ) * x = 6 x = 72 answer : a"
Answer: a
Question (gain): in a recent election , geoff received 1 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,571 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 54 , c ) 56 , d ) 60 , e ) 60.5
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 60 votes he needs 3571 more votes so : 60 + 3571 = 3631 now what ' s the problem wants ? ? a x % . . . . . . . . 3631 is what % of total votes 6000 . . . . . . . . translating : 3631 = x / 100 * 6000 - - - > x = 60.51666666 x = 60.5 % . . . . . . . . . . e"
Answer: e
Question (general): what is the value of 3 x ^ 2 − 1.8 x + 0.4 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.4 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.4 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.4 = 0 + 0.4 = 0.4 answer : c"
Answer: c
Question (general): 2500 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 2982 , d ) 2450 , e ) none of these
Rationale: "2500 - 50 = 2450 answer : d"
Answer: d
Question (geometry): what is the probability of getting equilateral triangles from the vertices of regular hexagon ?
Options: a ) 1 / 10 , b ) 2 / 10 , c ) 3 / 10 , d ) 4 / 10 , e ) 5 / 10
Rationale: total no . of triangles that can b made with the vetices hexagon = 6 c 3 = 20 no . of possible outcomes i . e . no . of equality triangles = 2 . . ' . probability = 2 / 20 = 1 / 10 answer : a
Answer: a
Question (general): solomon taken a loan rs . 15000 / - from co - operative society with an interest @ 11.5 % per month . at the same time he deposited rs . 10000 / - as fixed deposit with an interest @ 9.5 % per month . after one week sam asked the manager to calculate the interest to be paid . what is the interest amount for 7 days ?
Options: a ) a ) 165 , b ) b ) 220 , c ) c ) 310 , d ) d ) 185 , e ) e ) 181
Rationale: loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be paid by solomon = 403 - 222 = 181 / - for 7 days answer is e
Answer: e
Question (general): the sum of the first 50 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 50 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 5000 + 2500 = 7500 b is the answer ."
Answer: b
Question (physics): johnny makes $ 2.35 per hour at his work . if he works 5 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 11.75
Rationale: 2.35 * 5 = 11.75 . answer is e .
Answer: e
Question (physics): a and b together can plough a field in 10 hours but by himself a requires 15 hours . how long would b take to plough the same field ?
Options: a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: if a and b together can do a piece of work in x days and a alone can do the same work in y days , then b alone can do the same work in x y / y – x days . therefore , the no . of hours required by b = 10 × 15 / 15 – 10 = 150 / 5 = 30 hours . answer : c
Answer: c
Question (geometry): the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 576 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 36 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 576 x ^ 2 = 144 x = 12 length = 4 * 12 = 48 difference = 48 - 12 = 36 c is the answer"
Answer: c
Question (physics): if two girls starting from same point , walking in the opposite directions with 7 km / hr and 3 km / hr as average speeds respectively . then the distance between them after 12 hours is ?
Options: a ) 120 , b ) 121 , c ) 122 , d ) 123 , e ) 124
Rationale: explanation : total distance = distance traveled by person a + distance traveled by person b = ( 7 ã — 12 ) + ( 3 ã — 12 ) = 84 + 36 = 120 km answer : a
Answer: a
Question (physics): two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 7 days ?
Options: a ) 2 / 5 , b ) 7 / 18 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 7 days = 7 ( 1 / 18 ) = 7 / 18 . answer b"
Answer: b
Question (general): how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol ?
Options: a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 8 , e ) 300 / 17
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 32 % of ( 100 + x ) or 20 + x = ( 100 + x ) 8 / 25 500 + 25 x = 800 + 8 x 17 x = 300 x = 300 / 17 ans : e"
Answer: e
Question (physics): 24 men working 8 hours a day can finish a work in 10 days . working at the rate of 10 hours a day , the number of men required to finish the same work in 6 days is
Options: a ) 30 , b ) 36 , c ) 34 , d ) 32 , e ) none of these
Rationale: m 1 × d 1 × t 1 × w 2 = m 2 × d 2 × t 2 × w 1 24 × 10 × 8 × 1 = m 2 × 6 × 10 × 1 ⇒ m 2 = 24 × 10 × 8 / 6 × 10 = 32 men answer d
Answer: d
Question (general): n and m are each 3 - digit integers . each of the numbers 3,4 , 5 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: "you have 6 digits : 3 , 4 , 5 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 3 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . 487 and 536 ( difference is 49 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 685 and 734 ( difference is 49 ) b"
Answer: b
Question (general): a jogger running at 9 km / hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 88 , b ) 27 , c ) 36 , d ) 31 , e ) 12
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 190 + 120 = 310 m . time taken = 310 / 10 = 31 sec . answer : d"
Answer: d
Question (gain): a fruit seller sells mangoes at the rate of rs . 11 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 10 % ?
Options: a ) rs . 13.44 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 90 : 11 = 110 : x x = ( 11 ã — 110 / 90 ) = rs . 13.44 hence , s . p per kg = rs . 13.44 answer a"
Answer: a
Question (general): when 1 / 20 % of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 598 , e ) 400
Rationale: "1 / 20 % of 6000 = 3 1 / 10 of 6000 = 600 600 - 3 = 598 ans : d"
Answer: d
Question (physics): a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 620 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 7 , e ) 4
Rationale: "30 * 25 = 750 620 - - - - - - - - - - - 130 25 + 7.50 = 32.5 130 / 32.5 = 4 e"
Answer: e
Question (general): in 1982 and 1983 , company b ’ s operating expenses were $ 13.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 46 1 / 6 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 13 = 2.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 2.6 ) / 2.6 * 100 % = 46 1 / 6 % answer b"
Answer: b
Question (gain): the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 80 respectively . the sum is :
Options: a ) rs . 1800 , b ) rs . 1450 , c ) rs . 1360 , d ) rs . 6800 , e ) none
Rationale: "solution sum = s . i xt . d / ( s . i ) - ( t . d ) = 85 x 80 / 85 - 80 = rs . 1360 . answer c"
Answer: c
Question (general): a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 75 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 69.55 $ , b ) 50.63 $ , c ) 60.95 $ , d ) 52.15 $ , e ) 53.15 $
Rationale: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 75 x = 60.95 hence , the correct option is c"
Answer: c
Question (general): the age of father 5 years ago was 4 times the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
Options: a ) 5 : 4 , b ) 7 : 4 , c ) 5 : 2 , d ) 5 : 3 , e ) 7 : 5
Rationale: let the ages of father and son 5 years ago be 4 x and x years respectively . then , ( 4 x + 5 ) + 5 = 2 [ ( x + 5 ) + 5 ] 4 x + 10 = 2 x + 20 x = 5 . required ratio = ( 4 x + 5 ) : ( x + 5 ) = 25 : 10 = 5 : 2 . answer : option c
Answer: c
Question (general): the average of 11 numbers is 50 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ?
Options: a ) a ) 188 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 50 = 188 answer is a"
Answer: a
Question (general): in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 15 %
Rationale: "d 10 % 100 - [ ( 100 - 85 ) + ( 100 - 80 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 15 + 20 + 25 + 30 ) = 100 - 90"
Answer: d
Question (gain): the population of a town is 20000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 5120 , d ) 5230 , e ) 12800
Rationale: "20000 × 80 / 100 × 80 / 100 = 12800 answer : e"
Answer: e
Question (physics): two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 8 cm above the ground , what is the radius of the other ball ?
Options: a ) 12 cm , b ) 16 cm , c ) 18 cm , d ) 20 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 6 = 6 / r - 6 giving r = 12 . answer : a"
Answer: a
Question (gain): the population of a village is 15540 . it increases annually at the rate of 28 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 25460 , c ) 26709 , d ) 14000 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 15540 × 128 / 100 × 128 / 100 = 25460 b"
Answer: b
Question (general): if x / 4 + 24 / x = 5 , what are the values of 2 x - 7 ?
Options: a ) 8 and 9 , b ) 8 and 24 , c ) 17 and 21 , d ) 12 and 29 , e ) 17 and 9
Rationale: i got the same thing e is the answer 9 or 17
Answer: e
Question (physics): which greatest possible length can be used to measure exactly 12 meter 15 cm , 10 meter 15 cm and 10 meter 65 cm
Options: a ) 45 cm , b ) 25 cm , c ) 4 cm , d ) 5 cm , e ) 50 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1215 cm , 1015 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option d"
Answer: d
Question (gain): the sum of money will be double itself in 10 years and simple interest find rate of interest ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: t = 10 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 10 x = 10 % answer is a
Answer: a
Question (physics): a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 11 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 14 , b ) 15 , c ) 18 , d ) 22 , e ) 33
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 11 t 1 = 11 and so t 2 = 22 . the answer is d ."
Answer: d
Question (general): a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 6 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 36 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 6 = x 5 x + 36 = 6 x x = 36 km answer : option e"
Answer: e
Question (gain): the cost price of a radio is rs . 4500 and it was sold for rs . 3200 , find the loss % ?
Options: a ) 28.9 % , b ) 22 % , c ) 28 % , d ) 45 % , e ) 32 %
Rationale: "4500 - - - - 1300 100 - - - - ? = > 28.9 % answer : a"
Answer: a
Question (other): the ratio of three numbers is 4 : 2 : 5 and their sum is 121 . the second number of the three numbers is ?
Options: a ) 22 , b ) 26 , c ) 27 , d ) 29 , e ) 30
Rationale: "4 : 2 : 5 total parts = 11 11 parts - - > 121 1 part - - - - > 11 the second number of the three numbers is = 2 * 11 = 22 answer : a"
Answer: a
Question (geometry): a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 197 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 9801 , b ) 10,000 , c ) 14,400 , d ) 12,696 , e ) can not be determined
Rationale: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 197 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 197 ( x + y ) ( x - y ) = 197 197 is a prime number and thus it will be ( 99 + 98 ) * ( 99 - 98 ) . thus x = 99 and y = 98 x ^ 2 = 99 ^ 2 = 9801 the answer is a ."
Answer: a
Question (general): a special municipal payroll tax charges not tax on a payroll less than $ 200000 and only 0.2 % on a company ’ s payroll above $ 200000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?
Options: a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 300,000 , e ) $ 2 , 200,000
Rationale: answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000
Answer: d
Question (general): when positive integer n is divided by positive integer p , the quotient is 20 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 2 . what is the value of n ?
Options: a ) 107 , b ) 331 , c ) 511 , d ) 691 , e ) 871
Rationale: "n / p = 10 7 / p = 20 p + 7 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 2 solving these two equations we get p = 5 n = 107 answer is a ."
Answer: a
Question (gain): a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 4 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 600 , c ) 200 , d ) 800 , e ) 700
Rationale: explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 4 = > x = 800 answer : d ) rs 800
Answer: d