regisss/math_qa huggingface dataset:
Problem: in business , a and c invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by a and b was 2 : 3 , if rs 15,0000 was their profit , how much amount did b receive .
Options: a ) 12653 , b ) 14587 , c ) 36975 , d ) 75000 , e ) 12874
Rationale: explanation : a : b = 2 : 3 = 2 : 3 = > a : c = 2 : 1 = 2 : 1 = > a : b : c = 2 : 3 : 1 b share = ( 3 / 6 ) * 150000 = 75000 option d
Answer: d
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2015 ) = ?
Options: a ) 2016 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2015 ) = 2016 ans : a"
Answer: a
Problem: a pair of articles was bought for $ 810 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 300 , b ) $ 500 , c ) $ 350 , d ) $ 450 , e ) $ 600
Rationale: "s . p . of each of the article = 810 / 2 = $ 405 let m . p = $ x 90 % of x = 405 x = 405 * 100 / 90 = $ 450 answer is d"
Answer: d
Problem: a person crosses a 600 m long street in 5 minutes . what is his speed in km per hour ?
Options: a ) 3.6 , b ) 7.2 , c ) 8.4 , d ) 10 , e ) 8
Rationale: "speed = 600 / ( 5 x 60 ) m / sec . = 2 m / sec . converting m / sec to km / hr = ( 2 x ( 18 / 5 ) ) km / hr = 7.2 km / hr . answer : b"
Answer: b
Problem: if a and b are two events such that p ( a ) = 3 / 4 , p ( b ) = 1 / 2 and p ( a n b ) = 3 / 8 , find p ( not a and not b ) .
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 11 , d ) 1 / 13 , e ) 2 / 5
Rationale: p ( not a and not b ) = 1 - ( p ( a ) + p ( b ) - p ( ab ) ) which you might find somewhere in your text . substituting in our probabilities we get : p ( not a and not b ) = 1 - ( 3 / 4 + 1 / 2 - 3 / 8 ) p ( not a and not b ) = 1 - ( 7 / 8 ) p ( not a and not b ) = 1 / 8 . b
Answer: b
Problem: when sourav increases his speed from 20 km / hr to 25 km / hr , he takes one hour less than the usual time to cover a certain distance . what is the distance usually covered by him ?
Options: a ) 125 km , b ) 100 km , c ) 80 km , d ) 120 km , e ) 60 km
Rationale: detailed solution here , the distance travelled by sourav is constant in both the cases . so , 20 x t = 25 x ( t - 1 ) = d = ) 20 t = 25 t - 25 = ) 5 t = 25 = ) t = 5 hrs so , distance travelled = 20 x 5 = 100 km . correct answer b .
Answer: b
Problem: what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 3 , and 4 if each digit can be used only once in each number ?
Options: a ) 1443 , b ) 1554 , c ) 1665 , d ) 1776 , e ) 1887
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 333 ) + 2 ( 444 ) = 1776 the answer is d ."
Answer: d
Problem: 4000 was divided into two parts such a way that when first part was invested at 3 % and the second at 5 % , the whole annual interest from both the investments is rs . 144 , how much was put at 3 % ?
Options: a ) rs . 2500 , b ) rs . 2700 , c ) rs . 2800 , d ) rs . 5000 , e ) rs . 6000
Rationale: explanation : ( x * 3 * 1 ) / 100 + [ ( 4000 - x ) * 5 * 1 ] / 100 = 144 3 x / 100 + 200 â € “ 5 x / 100 = 144 2 x / 100 = 56 ã ¨ x = 2800 answer is c
Answer: c
Problem: if 20 % of a number = 200 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 1200 , e ) 820
Rationale: "let the number x . then , 20 % of x = 200 x = ( 200 * 100 ) / 20 = 1000 120 % of x = ( 120 / 100 * 1000 ) = 1200 . answer : d"
Answer: d
Problem: solve the equation for x : 14 ( - x + z ) + 18 = - 14 ( x - z ) - 10
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: d 1 - 14 x + 14 z + 18 = - 14 x + 14 z - 10 - 28 x + 28 = 0 - 28 x = - 28 = > x = 1
Answer: d
Problem: tea worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg will be :
Options: a ) rs . 169.50 , b ) rs . 170 , c ) rs . 175.50 , d ) rs . 180 , e ) rs . 190
Rationale: explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . 126 + 135 = rs . 130.50 2 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 153 / 22.50 = 1 x - 153 = 22.50 x = 175.50 answer is c
Answer: c
Problem: in an election between two candidates , one got 45 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 2000 , the number of valid votes that the other candidate got , was :
Options: a ) 2200 , b ) 3600 , c ) 3270 , d ) 3700 , e ) 4000
Rationale: "number of valid votes = 80 % of 4000 = 3200 . valid votes polled by other candidate = 55 % of 4000 = ( 55 / 100 ) x 8000 = 2200 answer = a"
Answer: a
Problem: if log 10 2 = 0.30103 , find the value of log 10 50
Options: a ) 1.69897 , b ) 2.69897 , c ) 1.99897 , d ) 0.69897 , e ) 5.69897
Rationale: "log 10 50 = log 10 ( 100 / 2 ) = log 100 - log 2 = 2 log 10 - log 2 = 2 ( 1 ) - 0.30103 = 1.69897 answer : a"
Answer: a
Problem: divide $ 672 among a , b in the ratio 5 : 3 . how many $ that a get ?
Options: a ) $ 120 , b ) $ 500 , c ) $ 420 , d ) $ 610 , e ) $ 315
Rationale: "sum of ratio terms = 5 + 3 = 8 a = 672 * 5 / 8 = $ 420 answer is c"
Answer: c
Problem: the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 5 years ago , the sum of their ages was 75 , what will be the age of aman 10 years from now ?
Options: a ) 17 , b ) 25 , c ) 27 , d ) 35 , e ) 40
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 5 + 8 x - 5 + 7 x - 5 = 75 x = 3 present age of aman = 5 * 3 = 15 aman ' s age 10 years hence = 15 + 10 = 25 answer = b"
Answer: b
Problem: if 1 / 3 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 5 are from africa , 1 / 6 are from asia and the remaining 42 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 240 , b ) 250 , c ) 280 , d ) 300 , e ) 320
Rationale: "1 / 3 + 1 / 8 + 1 / 5 + 1 / 6 = ( 40 + 15 + 24 + 20 ) / 120 = 99 / 120 let x be the number of passengers on the ship . 42 = ( 21 / 120 ) x = 7 x / 40 x = 240 the answer is a ."
Answer: a
Problem: a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 136 , b ) 146 , c ) 166 , d ) 176 , e ) 216
Rationale: area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d
Answer: d
Problem: average expenditure of a person for the first 3 days of a week is rs . 340 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 380 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 340 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 340 + rs . 40 = rs . 380 correct option : c"
Answer: c
Problem: if rs . 400 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 610 , e ) s . 585
Rationale: "80 = ( 400 * 4 * r ) / 100 r = 8.75 % i = ( 400 * 6 * 8.75 ) / 100 = 210 400 + 210 = 610 answer : d"
Answer: d
Problem: whats the reminder when 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,985 is divided by 4
Options: a ) 1 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: "a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,985 = 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,900 + 85 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 4 . 85 / 4 gives remainder 1 . answer ( a )"
Answer: a
Problem: 400 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "26 trees have 25 gaps between them , required distance ( 400 / 25 ) = 16 d"
Answer: d
Problem: a car averages 30 miles per hour for the first 6 hours of a trip and averages 46 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 34 miles per hour , how many hours long is the trip ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let t be the total time of the trip . 30 * 6 + 46 ( t - 6 ) = 34 t 12 t = 276 - 180 t = 8 the answer is a ."
Answer: a
Problem: 5 / 8 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 41 % , c ) 45 % , d ) 72 % , e ) 68 %
Rationale: "total population = 80 ( assume ) . 5 / 8 * 80 = 50 people from montague . 3 / 8 * 80 = 30 people from capulet . 0.2 * 50 = 10 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 10 + 21 ) = ~ 68 . answer : e"
Answer: e
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 5 is
Options: a ) 3 , b ) 7 , c ) 21 , d ) 27 , e ) 189
Rationale: "a prime number greater than 5 can have only the following four units digits : 1 , 3 , 7 , or 9 . if the units digit of p is 1 then the units digit of 2 p + 1 would be 3 , which is a possible units digit for a prime . for example consider p = 11 = prime - - > 2 p + 1 = 23 = prime ; if the units digit of p is 3 then the units digit of 2 p + 1 would be 7 , which is a possible units digit for a prime . for example consider p = 23 = prime - - > 2 p + 1 = 47 = prime ; if the units digit of p is 7 then the units digit of 2 p + 1 would be 5 , which is not a possible units digit for a prime ; if the units digit of p is 9 then the units digit of 2 p + 1 would be 9 , which is a possible units digit for a prime . for example consider p = 29 = prime - - > 2 p + 1 = 59 = prime . the product of all the possible units digits of sophie germain primes greater than 5 is 1 * 3 * 9 = 27 . answer : d ."
Answer: d
Problem: 32 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.32 * 5 / 8 = 1.6 / 8 = 0.2 correct option : a"
Answer: a
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: in a class of 38 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15
Rationale: "total # of students = 38 avg # of books per student = 2 total # of books = 38 * 2 = 76 # of student borrowed at least 3 books = 38 - 2 - 12 - 10 = 14 # of books borrowed by above 14 students = 76 - ( 12 * 1 ) + ( 10 * 2 ) = 44 considering that 13 out of above 14 students borrowed only 3 books , # of books borrowed = 13 * 3 = 39 so maximum # of books borrowed by any single student = 44 - 39 = 5 option b"
Answer: b
Problem: in a hostel there were 100 students . to accommodate 25 more students the average is decreased by some rupees . but total expenditure increased by rs . 500 . if the total expenditure of the hostel now 8500 , find decrease of average budget ?
Options: a ) 20 , b ) 15 , c ) 12 , d ) 18 , e ) 24
Rationale: "let average is x 100 x + 500 = 8500 x = 80 let decrease = y 125 ( 80 – y ) = 8500 y = 12 answer : c"
Answer: c
Problem: 8 men , working 7 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 7 * 18 = 1008 12 × 12 × ( x ) = 1008 x = 7 the answer is b ."
Answer: b
Problem: of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 6048 , b ) 3648 , c ) 7248 , d ) 1448 , e ) 2168
Rationale: "of the four - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; # of permutations of 3 digits in ppqr - 4 ! / 2 ! total : 9 * 8 * 7 * 4 ! / 2 ! = 6048 . answer : a ."
Answer: a
Problem: ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ?
Options: a ) 420 , b ) 260 , c ) 200 , d ) 300 , e ) 400
Rationale: explanation : ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 × 5 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 ) 0.75 × ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) × ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 × ( 12 ) 1 = 25 × 12 = 300 answer : option d
Answer: d
Problem: a computer factory produces 4200 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 , b ) 3.125 . , c ) 4.5 , d ) 5.225 , e ) 6.25
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 4200 / ( 28 * 24 * 2 ) = 3.125 answer b"
Answer: b
Problem: a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is 12 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 and 6 , d ) 4 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = 4 i . e x ^ 2 + 4 x - 12 = 0 is the quadratic equation which needs to be solved . ( x - 2 ) ( x + 6 ) = 0 hence x = 2 , x = - 6 imo c"
Answer: c
Problem: a bowl of fruit contains 14 apples and 20 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 14 number of oranges = 20 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 20 - x ) = 34 - x 14 / ( 34 - x ) = 7 / 10 = > 20 = 34 - x = > x = 14 answer c"
Answer: c
Problem: the area of a square field is 1225 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?
Options: a ) 7 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 1225 km 2 . then , each side of field = √ 1225 = 35 km distance covered by the horse = perimeter of square field = 35 × 4 = 140 km ∴ time taken by horse = distances / peed = 140 / 20 = 7 h answer a
Answer: a
Problem: xavier starts from p towards q at a speed of 50 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 52 km , then how much time does he take to cover the distance ?
Options: a ) 40 , b ) 60 , c ) 48 , d ) 70 , e ) 80
Rationale: first 12 min = 50 * 12 / 60 = 10 km 2 nd 12 min = 60 * 12 / 60 = 12 km 3 rd 12 min = 70 * 12 / 60 = 14 km 4 th 12 min = 80 * 12 / 60 = 16 km total time 12.4 = 48 min c
Answer: c
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 5 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 89.0 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 5 % of 400 = 20 therefore , total number of rotten fruits = 90 + 20 = 110 therefore number of fruits in good condition = 1000 - 110 = 890 therefore percentage of fruits in good condition = ( 890 / 1000 × 100 ) % = ( 89000 / 1000 ) % = 89.0 % answer : b"
Answer: b
Problem: if a rectangular room measures 8 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000
b ) 16 , 000,000
c ) 2 , 400,000
d ) 24 , 000,000
e ) 240 , 000,000
Rationale: b . 160 , 000,000 8 * 100 * 5 * 100 * 4 * 100 = 160 , 000,000
Answer: b
Problem: on a 20 mile course , pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break , ran the rest of the distance at an average rate of 8 miles per hour . how many minutes did pat take to cover the entire course ?
Options: a ) 75 , b ) 105 , c ) 117 , d ) 150 , e ) 162
Rationale: at an average rate of 30 miles per hour in 12 minute ( 1 / 5 hours ) pat covers ( distance ) = ( time ) * ( rate ) = 1 / 5 * 30 = 6 miles , thus she should cover the remaining distance of 20 - 6 = 14 miles at an average rate of 8 miles per hour . to cover 14 miles at an average rate of 8 miles per hour pat needs ( time ) = ( distance ) / ( rate ) = 14 / 8 = 1.75 hours = 105 minutes . therefore pat needs total of 12 + 105 = 117 minutes to cover the entire course . answer : c .
Answer: c
Problem: the sum of all the integers k such that – 25 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 47
Rationale: "- 24 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 24 - 23 sum of which is - 47 . hence option d . e"
Answer: e
Problem: sonika deposited rs . 14500 which amounted to rs . 12200 after 3 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 13505 , b ) 12004 , c ) 15003 , d ) 14500 , e ) 16400
Rationale: "( 14500 * 3 * 3 ) / 100 = 1305 12200 - - - - - - - - 13505 answer : a"
Answer: a
Problem: the sale price sarees listed for rs . 298 after successive discount is 12 % and 15 % is ?
Options: a ) 321 , b ) 223 , c ) 245 , d ) 265 , e ) 162
Rationale: "explanation : 298 * ( 88 / 100 ) * ( 85 / 100 ) = 223 answer : b"
Answer: b
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 170 kg then find the average weight of all the 7 rounds ?
Options: a ) 97.1 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 170 / 7 = 97.1 kgs answer : a"
Answer: a
Problem: if the area of the equilateral triangle above is 0.75 , what is the area of the adjacent square ?
Options: a ) ( √ 3 ) / 2
b ) √ 3
c ) √ 6
d ) 3
e ) 2 √ 3
Rationale: area of equilateral triangle : a ^ 2 * ( square root of 3 ) / 4 = 0.75 hence , area of square = a ^ 2 = 0.75 * 4 / ( square root of 3 ) = 3 / ( square root of 3 ) = square root of 3 answer : b
Answer: b
Problem: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 20 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 45
Rationale: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 20 % of 50 % i . e 10 % . so he completed 50 + 10 = 60 % of total trip a"
Answer: a
Problem: it has been raining at the rate of 5 centimeters per hour . if the rain filled a cylindrical drum with a depth of 15 centimeters , and area 300 square centimeters , how long did it take to fill the drum completely ?
Options: a ) 3 hours
b ) 4 hours 15 minutes
c ) 6 hours
d ) 2 hours 5 minutes
e ) 8 hours
Rationale: answer is : a , 3 hours the volume of the drum is irrelevant and only height matters since rain fell all over the city . thus , it takes only 15 / 5 = 3 hours of rain to fill the drum
Answer: a
Problem: in digging a pond 28 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1000 , c ) 2866 , d ) 2787 , e ) 1400
Rationale: "28 * 10 * 5 = 1400 answer : e"
Answer: e
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour and $ . 16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 800 ( before payroll deductions ) ?
Options: a ) 1800 , b ) 1825 , c ) 1850 , d ) 1855 , e ) 1875
Rationale: "hourly = $ 12.50 / hour totalhours = 40 piecework = $ 0.16 / widget totalpieces = ? ? ? ? total pay = ( hourly * totalhours ) + ( piecework * totalpieces ) so , put it all together : $ 800 = ( $ 12.50 * 40 ) + ( $ 0.16 * total pieces ) totalpieces = ( $ 800 - ( $ 12.50 * 40 ) ) / $ 0.16 = 1875 widgets e . 1875"
Answer: e
Problem: the diameter of a cylindrical tin is 10 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 125 , b ) 155 , c ) 130 , d ) 120 , e ) 100
Rationale: "r = 5 h = 5 π * 5 * 5 * 5 = 125 π cc answer : a"
Answer: a
Problem: if 8 spiders make 4 webs in 9 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 10 , b ) 20 , c ) 12 , d ) 16 , e ) 18
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 8 : 1 ( webs ) 1 : 9 } : : x : 4 â ‡ ’ 8 ã — 1 ã — 9 = 1 ã — 4 ã — x â ‡ ’ x = 18 answer : option e"
Answer: e
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 9 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 79
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 9 ^ 2 - 2 = 79 . thus , the answer is e ."
Answer: e
Problem: ( 150 % of 1265 ) ÷ 7 = ?
Options: a ) a ) 125 , b ) b ) 175 , c ) c ) 271 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 150 x 1265 / 100 ) ÷ 7 = 189750 / 700 = 271 answer : option c"
Answer: c
Problem: two vessels contains equal number of mixtures milk and water in the ratio 7 : 2 and 8 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 1 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 7 / 9 + 8 / 9 ) : ( 2 / 9 + 1 / 9 ) = 15 / 9 : 3 / 9 = 5 : 1 answer is c"
Answer: c
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 12 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 477 , b ) 396 , c ) 279 , d ) 276 , e ) 291
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 12 + 21 = 33 t = 12 d = 33 * 12 = 396 . answer : b"
Answer: b
Problem: a part of certain sum of money is invested at 9 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 7 , b ) 4 : 0 , c ) 4 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: "12 : 9 = 4 : 3 answer : c"
Answer: c
Problem: the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 58 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 2 / 35 , e ) none
Rationale: "answer we have , m x n = 6 x 210 = 1260 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 58 / 1260 = 17 / 620 correct option : e"
Answer: e