Cheukting/mathqa huggingface dataset:
Question (general): in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22500 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b .
Answer: b
Question (physics): a train 150 meters long completely crosses a 240 meters long bridge in 42 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 33 , c ) 88 , d ) 66 , e ) 09
Rationale: "s = ( 150 + 240 ) / 42 = 390 / 42 * 18 / 5 = 33 answer : b"
Answer: b
Question (general): on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent t of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before t = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b"
Answer: b
Question (physics): if 2 men or 3 women can reap a field in 8 days how long will 3 men and 4 women take to reap it ?
Options: a ) 2 / 16 , b ) 1 / 16 , c ) 3 / 24 , d ) 5 / 16 , e ) 6 / 26
Rationale: "explanation : 2 men reap 1 / 8 field in 1 day 1 man reap 1 / ( 2 x 8 ) 3 women reap 1 / 8 field in 1 day 1 woman reap 1 / ( 3 x 8 ) 3 men and 4 women reap ( 3 / ( 2 x 8 ) + 4 / ( 3 x 8 ) ) = 5 / 16 in 1 day 3 men and 4 women will reap the field in 5 / 16 days answer : option d"
Answer: d
Question (physics): if 15 men , working 9 hours a day , can reap a field in 16 days , in how many days will 18 men reap the field , working 8 hours a day ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) none of them
Rationale: let the required number of days be x . more men , less days ( indirect proportion ) less hours per day , more days ( indirect proportion ) men 18 : 15 hours per day 8 : 9 } : : 16 : x ( 18 x 8 x x ) = ( 15 x 9 x 16 ) = x = ( 44 x 15 ) 144 = 15 hence , required number of days = 15 . answer is b .
Answer: b
Question (general): find the sum the difference between the compound and s . i . on a certain sum of money for 5 years at 50 % per annum is rs . 200 of money ?
Options: a ) 1256 , b ) 2000 , c ) 3600 , d ) 8400 , e ) 4566
Rationale: "p = 200 ( 100 / 50 ) 5 = > p = 2000 answer : b"
Answer: b
Question (general): a small beaker is 1 / 2 filled with salt water . another beaker , which has 5 times the capacity of the small beaker , is 1 / 5 filled with fresh water . after dumping all of the salt water from the small beaker into the large beaker , to what fraction of its capacity will the large beaker be filled ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 5 , d ) 3 / 10 , e ) 7 / 20
Rationale: 1 / 2 of the small beaker is 1 / 10 of the large beaker . 1 / 10 + 1 / 5 = 3 / 10 the answer is d .
Answer: d
Question (geometry): a football field is 9600 square yards . if 800 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?
Options: a ) 450 , b ) 600 , c ) 750 , d ) 2400 , e ) 300
Rationale: "answer e ) 9600 yards need 1200 lbs 1 yard will need 800 / 9600 = 1 / 12 lbs 3600 yards will need 1 / 12 * 3600 yards = 300 lbs"
Answer: e
Question (general): 4.036 divided by 0.04 gives
Options: a ) 1.009 , b ) 100.09 , c ) 10.9 , d ) none of these , e ) can not be determined
Rationale: "solution 4.036 / 0.04 = 403.6 / 4 = 100.9 answer a"
Answer: a
Question (general): sum of the squares of 3 numbers is 222 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 22 , b ) 25 , c ) 26 , d ) 28 , e ) 29
Rationale: ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 222 + 2 * 131 a + b + c = √ 484 = 22 a
Answer: a
Question (physics): a train 410 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 49 sec , e ) 60 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 410 + 140 = 550 m required time = 550 * 2 / 25 = 44 sec answer : c"
Answer: c
Question (general): the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 4 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 4 of that new total price : p = 1 / 4 * $ 3,000 = $ 750 . plug this value in the first equation : c + 750 = $ 2,500 - - > c = $ 1,750 answer : c ."
Answer: c
Question (general): 3 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.08333 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 3 / 36 = . 08 something answer ( b )"
Answer: b
Question (general): n ^ ( n / 2 ) = 6 is true when n = 6 in the same way what is the value of n if n ^ ( n / 2 ) = 9 ?
Options: a ) 16 , b ) 14 , c ) 18 , d ) 6 , e ) 9
Rationale: n ^ ( n / 2 ) = 9 apply log n / 2 logn = log 9 nlogn = 2 log 9 = log 9 ^ 2 = log 81 logn = log 81 now apply antilog n = 81 / n now n = 9 . answer : e
Answer: e
Question (general): y and z are in a relay race . y runs the first leg of the course in 58 seconds . z runs the second leg of the course in 26 seconds . what was the average time they took to run a leg of the course ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: ( 58 seconds + 26 seconds ) / 2 = 42 seconds correct option is : d
Answer: d
Question (general): a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 5 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 9 / 16 , d ) 5 / 7 , e ) 3 / 4
Rationale: the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 5 / 8 * c : ( b + c ) / 2 = ( 5 / 8 ) * c b = ( 1 / 4 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 4 * c ) / 2 = ( 1 / 8 ) * c median = ( a + c ) / 2 = ( 1 / 8 * c + c ) / 2 = ( 9 / 8 ) * c / 2 = ( 9 / 16 ) * c ( answer c )
Answer: c
Question (general): the mean of 30 values was 180 . it was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 148 , e ) 180.67
Rationale: "corrected mean = 180 × 30 − 135 + 155 / 30 = 5400 − 135 + 155 / 30 = 5420 / 30 = 180.67 answer e"
Answer: e
Question (geometry): three interviewers , x , y , and z are interviewing 40 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer x admitted 15 applicants , y admitted 17 applicants , and z admitted 20 applicants , at least how many applicants get the admission ?
Options: a ) 0
b ) 2
c ) 6
d ) 8
e ) 12
Rationale: if x admitted 15 are overlapping with y admission of 17 but z does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : a
Answer: a
Question (gain): a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 6480 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 16000 , d ) rs 18000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 6480 â ˆ — 100 / 12 â ˆ — 3 = rs 18000 option d"
Answer: d
Question (physics): how long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak , but due to the leak it will take one additional hour to be filled ?
Options: a ) 12 hours , b ) 111 hours , c ) 15 hours , d ) 14 hours , e ) 11 hours
Rationale: part filled without leak in 1 hour = 1 / 3 part filled with leak in 1 hour = 1 / 4 work done by leak in 1 hour = 1 / 3 â ˆ ’ 1 / 4 = 12 hours answer : a
Answer: a
Question (general): the security gate at a storage facility requires a 5 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be even , how many lock codes are possible ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440
Rationale: x - x - x - x - x - - > there are 3 even digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 3 - x - x - x - 2 . other x ' s can take following values : 3 - 5 - 4 - 3 - 2 - - > 3 * 5 * 4 * 3 * 2 = 360 . answer : c .
Answer: c
Question (general): if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 5 m + n ?
Options: a ) 65 , b ) 18 , c ) 20 , d ) 25 , e ) 33
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 5 * 10 + 15 = 65 answer : a"
Answer: a
Question (other): the h . c . f . of two numbers is 59 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is :
Options: a ) 678 , b ) 944 , c ) 456 , d ) 323 , e ) 899
Rationale: : explanation : clearly , the numbers are ( 59 x 13 ) and ( 59 x 16 ) . { \ color { blue } \ therefore } larger number = ( 59 x 16 ) = 944 . answer : b ) 944
Answer: b
Question (general): 0.012 x 0.5 = ?
Options: a ) 0.0006 , b ) 0.06 , c ) 0.6 , d ) 0.006 , e ) 6.0
Rationale: "12 x 5 = 60 . sum of decimal places = 4 0.012 x 0.5 = 0.006 answer : option d"
Answer: d
Question (general): the rate of interest on a sum of money is 5 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,500 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 5 ) / 100 = 3 p / 20 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 3 p / 20 + 4 p / 25 + p / 20 = 540 9 p / 25 = 540 p = 1500 answer : option a"
Answer: a
Question (general): a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 10 per item . if the manufacturer ’ s selling price per item is $ 15 , how many items the manufacturer produce and sell to earn an annual profit of $ 150,000 ?
Options: a ) 2,858 , b ) 18,667 , c ) 21,429 , d ) 35,000 , e ) 56,000
Rationale: let the items manufactured or sold bex 130000 + 10 x = 15 x - 150000 5 x = 280000 x = 56000 ans : e
Answer: e
Question (gain): the difference between simple and compound interest on rs . 1700 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.25 , b ) 4.25 , c ) 9.25 , d ) 3.25 , e ) 2.25
Rationale: "s . i . = ( 1700 * 10 * 1 ) / 100 = rs . 170 c . i . = [ 1700 * ( 1 + 5 / 100 ) 2 - 1700 ] = rs . 174.25 difference = ( 174.25 - 174 ) = rs . 4.25 . answer : b"
Answer: b
Question (other): two whole numbers whose sum is 24 is the ratio
Options: a ) 1 : 3 , b ) 2 : 8 , c ) 1 : 6 , d ) 2 : 3 , e ) 2 : 5
Rationale: a ) 1 : 3
Answer: a
Question (gain): vijay sells a cupboard at 16 % below cost price . had he got rs . 1800 more , he would have made a profit of 16 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 5625 , d ) 7500 , e ) none of these
Rationale: explanation : cost price = 1800 / ( 0.16 + 0.16 ) = 1800 / 0.32 = rs . 5625 answer c
Answer: c
Question (general): if a : b = 4 : 7 and b : c = 5 : 9 , then a : c = ?
Options: a ) 28 : 37 , b ) 18 : 37 , c ) 16 : 53 , d ) 20 : 63 , e ) 15 : 48
Rationale: a / b = 4 / 7 and b / c = 5 / 9 a / b * b / c = 4 / 7 * 5 / 9 = 20 / 63 so a / c = 20 / 63 20 : 63 answer d
Answer: d
Question (probability): there are 7 red balls and 5 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that 3 balls selected are red balls ?
Options: a ) 19 / 44 , b ) 5 / 44 , c ) 3 / 41 , d ) 13 / 44 , e ) 7 / 44
Rationale: "probability = favorable outcomes / total outcomes probability = 7 c 3 / 12 c 3 or ( 7 / 12 ) * ( 6 / 11 ) * ( 5 / 10 ) = 7 / 55 answer option e"
Answer: e
Question (gain): on the first of the year , james invested x dollars at proudstar bank in an account that yields 3 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 22.04 % , b ) 16.12 % , c ) 12.5 % , d ) 18.25 % , e ) 10 %
Rationale: per quarter , interest = 3 % so for a year , interest = 12 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 12 % answer = 12.5 % = answer : c
Answer: c
Question (physics): the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of rs . 800 per sq . meter .
Options: a ) rs . 12000 , b ) rs . 19500 , c ) rs . 18000 , d ) rs . 16500 , e ) rs . 17500
Rationale: "explanation : area = 5.5 × 3.75 sq . metre . cost for 11 sq . metre . = rs . 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : option d"
Answer: d
Question (general): a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 42 . , b ) 46 . , c ) 50 . , d ) 54 . , e ) 58 .
Rationale: "n = 4 k + 1 = 7 j + 2 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 2 . 1 , 5 , 9 = 7 ( 1 ) + 2 the next such number is 9 + 4 * 7 = 37 . 9 + 37 = 46 the answer is b ."
Answer: b
Question (geometry): the breath of a rectangular landscape is 8 times its length . there is a playground in it whose area is 3200 square mtr & which is 1 / 9 rd of the total landscape . what is the breath of the landscape ?
Options: a ) 420
b ) 430
c ) 280
d ) 360
e ) 480
Rationale: sol . 8 x * x = 9 * 3200 x = 60 length = 8 * 60 = 480 e
Answer: e
Question (physics): machine c takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine c to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of c is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and c reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of c . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Question (gain): jim is able to sell a hand - carved statue for $ 670 which was a 25 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 536.00 , c ) $ 555.40 , d ) $ 574.90 , e ) $ 588.20
Rationale: "670 = 1.25 * x x = 670 / 1.25 = 536 $ 536 , which is ( b ) ."
Answer: b
Question (gain): sandy had $ 224 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 260 , b ) $ 290 , c ) $ 320 , d ) $ 350 , e ) $ 380
Rationale: "let the money sandy took for shopping be x . 0.7 x = 224 x = 320 the answer is c ."
Answer: c
Question (general): if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 4 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 4
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 4 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 4 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 4 = e"
Answer: e
Question (gain): each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 72 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 24 % , b ) 16 % , c ) 11 % , d ) 7 % , e ) 5 %
Rationale: let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.4 i + 0.8 f = 0.72 ( i + f ) 0.08 f = 0.32 i f = 4 i this means that for every 1 incandescent bulb , there are 4 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.4 i / ( 0.4 i + 0.8 f ) = 0.4 i / ( 0.4 i + 0.8 * 4 i ) = 0.4 i / 3.6 i = 1 / 9 which is about 11 % . the answer is c .
Answer: c
Question (physics): a motorcyclist goes from bombay to pune , a distance of 224 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 5 , c ) 4 : 7 , d ) 1 : 1 , e ) 1 : 8
Rationale: "t = 224 / 32 = 7 h t = 7 - 3 = 4 time ratio = 7 : 4 speed ratio = 4 : 7 answer : c"
Answer: c
Question (physics): if a is thrice as fast as b and together can do a work in 12 days . in how many days a alone can do the work ?
Options: a ) 16 , b ) 42 , c ) 28 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 12 = 3 + 1 / 3 x = 4 / 3 x = 1 / 12 x = 12 * 4 / 3 = 16 answer : a"
Answer: a
Question (general): a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 45 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 75 , b ) 80 , c ) 90 , d ) 95 , e ) 100
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 90 + ( d / 2 ) / v d / 180 = d / 2 v and so v = 90 km / hr the answer is c ."
Answer: c
Question (general): in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 6 , − 5 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: first , solve for the slope , m : m = ( y 2 - y 1 ) / ( x 2 - x 1 ) = ( - 5 - 3 ) / ( - 6 - 10 ) = - 8 / - 16 or 1 / 2 then you can re - write the equation as y = ( 1 / 2 ) x + b and plug in one of the points to find b , the y intercept . using point ( 10 , 3 ) : 3 = ( 1 / 2 ) ( 10 ) + b , which can be simplified to 3 = 5 + b . solve for b and you get b = - 2 . the equation now reads : y = ( 1 / 2 ) x - 2 . to find the x intercept , plug in 0 for y : 0 = ( 1 / 2 ) x - 2 , which simplifies to 2 = ( 1 / 2 ) x . from this , we can see that the x intercept = 4 . answer is a .
Answer: a
Question (general): in what ratio p : q should the mixture p of milk and water in the ratio of 5 : 3 be mixed with another mixture q of milk and water in the ratio 1 : 3 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 5 : 2 , b ) 4 : 3 , c ) 3 : 2 , d ) 2 : 1 , e ) 4 : 1
Rationale: "( 5 / 8 ) * p + ( 1 / 4 ) * q = ( 3 / 8 ) * p + ( 3 / 4 ) * q 2 p = 4 q p / q = 2 / 1 the answer is d ."
Answer: d
Question (physics): the ratio between the length and the breadth of a rectangular park is 5 : 3 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then thearea of the park ( in sq . m ) is ?
Options: a ) 124545 m , b ) 134561 m , c ) 156787 m , d ) 15450 m , e ) 150000 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 5 x metres and breadth = 3 x metres . then , 2 ( 5 x + 3 x ) = 1600 or x = 100 . length = 500 m and breadth = 300 m . area = ( 500 x 300 ) m 2 = 150000 m e"
Answer: e
Question (probability): three unbiased coins are tossed . what is the probability of getting all tails ?
Options: a ) 7 / 8 , b ) 1 / 2 , c ) 3 / 8 , d ) 1 / 4 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting two heads then e = { ttt } p ( e ) = n ( e ) / n ( s ) = 1 / 8"
Answer: e
Question (general): a person travels from p to q a speed of 80 km / hr and returns by increasing his speed by 10 % . what is his average speed for both the trips ?
Options: a ) 33 , b ) 77 , c ) 48 , d ) 84 , e ) 21
Rationale: "speed on return trip = 110 % of 80 = 88 km / hr . average speed of trip = 80 + 88 / 2 = 168 / 2 = 84 km / hr answer : d"
Answer: d
Question (gain): a tempo is insured to an extent of 4 / 5 of its original value . if the premium on it at the rate of 1.3 % amounts to $ 910 , the original value of the tempo is ?
Options: a ) 92500 , b ) 75230 , c ) 65990 , d ) 45280 , e ) 87500
Rationale: let the original value of the tempo is $ x 1.3 % of 4 / 5 of x = 910 ( 13 / 10 ) * ( 1 / 100 ) * ( 4 / 5 ) x = 910 x = $ 87500 answer is e
Answer: e
Question (physics): a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 60 meters , what is the height of the building ( in meters ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: the height : length ratio will be equal in both cases . 18 / 45 = x / 60 x = 24 the answer is b .
Answer: b
Question (gain): fresh grapes contain 70 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 30 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 30 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 70 = 30 % of whole weight ) , so 30 * 0.75 = x * 0.3 - - > x = 75 . answer : a ."
Answer: a