regisss/math_qa huggingface dataset:
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Problem: angelina walked 720 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 24
Rationale: "let the speed be x . . . so time taken from home to grocery = 720 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 720 / x - 240 / x = 40 . . 480 / x = 40 . . x = 12 m / secs . . so grocery to gym = 2 * 12 = 24 m / s . . . e"
Answer: e
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is :
Options: a ) 11 , b ) 14 , c ) 15 , d ) 13 , e ) 18
Rationale: "age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer a"
Answer: a
Problem: john and peter are among the 9 players a volleyball coach can choose from to field a 6 - player team . if all 6 players are chosen at random , what is the probability of choosing a team that includes john and peter ?
Options: a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15
Rationale: the total possible ways of selecting a 6 - member team is 9 c 6 = 84 the possible ways which include john and peter is 7 c 4 = 35 the probability of choosing both john and peter is 35 / 84 = 5 / 12 the answer is c .
Answer: c
Problem: a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.6 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 360
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.6 = 360 answer : e"
Answer: e
Problem: how many diagonals does a 62 - sided convex polygon have ?
Options: a ) 1829 , b ) 2356 , c ) 3458 , d ) 3843 , e ) 4820
Rationale: "a 62 - sided convex polygon has 62 vertices . if we examine a single vertex , we can see that we can connect it with 59 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be ( 62 ) ( 59 ) = 3658 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3658 by 2 to get 1829 . the answer is a ."
Answer: a
Problem: if y > 0 , ( 8 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 4 y / 10 + 3 y / 10 = 7 y / 10 = 70 % answer d"
Answer: d
Problem: how many kg of pure salt must be added to 30 kg of 2 % solution of salt and water to increase it to a 10 % solution ?
Options: a ) 8 / 3 , b ) 9 / 7 , c ) 7 / 4 , d ) 5 / 2 , e ) 6 / 7
Rationale: "amount salt in 30 kg solution = 2 * 30 / 100 = 0.6 kg let x kg of pure salt be added then ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x 90 x = 240 x = 8 / 3 answer is a"
Answer: a
Problem: on dividing 14698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 154 , c ) 852 , d ) 741 , e ) 165
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 14698 - 14 ) / 89 = 165 answer ( e )"
Answer: e
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 190 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 18.0 sec , e ) 72.0 sec
Rationale: "d = 110 + 190 = 300 m s = 60 * 5 / 18 = 50 / 3 t = 300 * 3 / 50 = 18.0 sec answer : d"
Answer: d
Problem: paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 60 %
Rationale: "let original income = $ 100 expenditure = $ 75 savings = $ 25 new income = $ 120 new expenditure = $ 110 / 100 * 75 = $ 165 / 2 new savings = 120 - 165 / 2 = $ 75 / 2 increase in savings = 75 / 2 - 25 = $ 25 / 2 increase % = 25 / 2 * 1 / 25 * 100 = 50 % answer is c"
Answer: c
Problem: rice weighing 33 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 27 , b ) 30 , c ) 33 , d ) 36 , e ) 39
Rationale: "33 / 4 ÷ 4 = 33 / 16 pounds in each container 33 / 16 pounds * 16 ounces / pound = 33 ounces in each container the answer is c ."
Answer: c
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 22 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 12
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 22 = > x = 4 so deepak age is = 3 ( 4 ) = 12 answer : e"
Answer: e
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 112 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 98 , c ) 105 , d ) 120 , e ) 210
Rationale: "set up equation : x = total number of workers 112 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 112 = 16 / 30 x x = 210 210 - 112 = 98 answer b"
Answer: b
Problem: if an object travels 70 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 15.95 , b ) 17.28 , c ) 19.54 , d ) 21.73 , e ) 23.86
Rationale: "70 feet / 2 seconds = 35 feet / second ( 35 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 23.86 miles / hour ( approximately ) the answer is e ."
Answer: e
Problem: 85 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 85 = 113.33 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 113.33 = 170 litres . answer d"
Answer: d
Problem: evaluate 28 % of 650 + 45 % of 280
Options: a ) 232 , b ) 308 , c ) 252 , d ) 262 , e ) 282
Rationale: "explanation : = ( 28 / 100 ) * 650 + ( 45 / 100 ) * 280 = 182 + 126 = 308 answer : option b"
Answer: b
Problem: a can give b 300 meters start and c 600 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 111.67 , c ) 428.57 , d ) 111.11 , e ) 101.12
Rationale: "a runs 1000 m while b runs 700 m and c runs 400 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 400 ) / 700 = 571.43 m . b can give c = 1000 - 571.43 = 428.57 m . answer : c"
Answer: c
Problem: there are 2000 students in a school and among them 10 % of them attends chess class . 50 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 50 , e ) 20
Rationale: "10 % of 2000 gives 200 . so 200 attends chess and 50 % of 200 gives 100 so 100 enrolled for swimming answer : c"
Answer: c
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 6 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "i think e - 11 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 6 x so old = x , new = 5 x now 1 / 3 of x are occupied and 1 / 5 of 5 x are occupied which simplifies to ( 5 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 5 / 5 of x occupied in the new ward . add them up to get 4 / 3 of x there are 5 x beds in new tower so ratio is : ( 4 / 3 ) x / 5 x = 4 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new tower = 11 / 15 . e"
Answer: e
Problem: the sum of two numbers is 40 and their difference is 4 . the ratio of the numbers is
Options: a ) 11 : 9 , b ) 11 : 18 , c ) 21 : 19 , d ) 21 : 19 , e ) none
Rationale: sol . let the numbers be x and y . then , x + y / x - y = 40 / 4 = 10 ⇔ ( x + y ) = 10 ( x - y ) ⇔ 9 x = 11 y ⇔ x / y = 11 / 9 . answer a
Answer: a
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number q of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: q = 7 is the correct answer . good solution buneul . b
Answer: b
Problem: the ages of 2 persons differ by 21 years . if 15 years ago the elder one be 8 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 48.5 , c ) 50.4 , d ) 62.6 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 21 8 ( x - 15 ) = x + 21 - 15 x = 18 age of elder person = 18 + 21 = 39 answer is e"
Answer: e
Problem: in a 100 m race , a covers the distance in 30 seconds and b in 45 second . in this race a beats b by :
Options: a ) 33.33 m , b ) 25 m , c ) 45 m , d ) 30 m , e ) none of these
Rationale: solution distance covered by b in 15 sec . = ( 100 / 45 x 15 ) m = 33.33 m . ∴ a beats b by 33.33 metres . answer a
Answer: a
Problem: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 12 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 14
Rationale: i am guessing the question is : ( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 12 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 12 hence x = 14 . answer is e
Answer: e
Problem: a , b , c can do a work in 15 , 20,45 days respectively . they get rs 500 for their work . what is the share of a ?
Options: a ) rs . 240 , b ) rs . 340 , c ) rs . 260 , d ) rs . 280 , e ) rs . 440
Rationale: lcm = 180 share of a = ( lcm / a x total amount ) / lcm / a + lcm / b + lcm / c = ( 180 / 15 ) / ( 180 / 15 + 180 / 20 + 180 / 45 ) = ( 12 / 25 ) * 500 = rs . 240 answer : a
Answer: a
Problem: express a speed of 252 kmph in meters per second ?
Options: a ) 10 mps , b ) 05 mps , c ) 09 mps , d ) 12 mps , e ) 70 mps
Rationale: "e 70 mps 252 * 5 / 18 = 70 mps"
Answer: e
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 40 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 67.5 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 40 minutes after it was poured is : f = 120 ( 2 ^ - 40 / 10 ) + 60 f = 120 * 1 / 16 + 60 f = 15 / 2 + 60 f = 135 / 2 = 67.5 a"
Answer: a
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 3 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 6 , b ) 2 , c ) 4 , d ) 8 , e ) 16
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 3 ( pir ^ 2 ) pir ^ 2 = 6 pir r = 6 answer : a"
Answer: a
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 49 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 2 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 49 = ( 5 / 7 ) * ( 5 / 7 ) therefore probability that the next one she draws is pink = 2 / 7 option ( b )"
Answer: b
Problem: the areas of the two spheres are in the ratio 1 : 4 . the ratio of their volume is ?
Options: a ) 1 : 4
b ) 1 : 16
c ) 1 : 8
d ) 1 : 64
e ) 2 : 3
Rationale: 4 π r 12 : 4 π r 22 = 1 : 4 r 1 : r 2 = 1 : 2 4 / 3 π r 13 : 4 / 3 π r 23 r 13 : r 23 = 1 : 8 answer : c
Answer: c
Problem: a hostel had provisions for 250 men for 40 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 40 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 40 250 × 40 = 200 x 5 × 40 = 4 x x = 5 × 10 = 50 answer c"
Answer: c
Problem: the distance between parallel sides of the hexagon is 9 . determine the length of the hexagon
Options: a ) 18 * sqrt 3
b ) 18 * sqrt 2
c ) 18 * sqrt 4
d ) 19 * sqrt 3
e ) 17 * sqrt 3
Rationale: length of each side of regular hexagon will be 3 * sqrt 3 . total length ( perimeter ) of regular hexagon will be 18 * sqrt 3 answer : a
Answer: a
Problem: a train covers a distance of 12 km in 10 min . if it takes 3 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 70 m , b ) 16 m , c ) 60 m , d ) 80 m , e ) 88 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 3 = 60 m . answer : c"
Answer: c
Problem: if g and f are both odd prime numbers andg < f , then how many different positive integer factors does 2 gfhave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: g and f are both odd prime numbers - it means either g or f is not 2 and since prime numbers have only two factors - 1 and the number itself g and f each will have ( 1 + 1 ) = 2 factors hence 2 gf will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer
Answer: d
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 30 kmph and 60 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 176 sec , c ) 178 sec , d ) 72 sec , e ) 189 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 30 * 5 / 18 ) , 600 / ( 60 * 5 / 18 ) } = 72 sec . answer : d"
Answer: d
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 18,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 850 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 18,000 * 5 % = 900 . thus , e is the answer ."
Answer: e
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 18 ) both lie on the line defined by the equation x = ( y / 6 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 6 ) - ( 2 / 5 ) , and so y = 6 x + 12 / 5 . the slope is 6 . ( n + 18 - n ) / ( m + p - m ) = 6 p = 3 the answer is c ."
Answer: c
Problem: if w is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of w ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: w = 30 ! 8 w = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 out of these 30 , 27 , 24 , 21 , 18 , 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2 , 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 so we have a total of 14 three ' s . . . therefore the maximum value of k can be 14 ( c )
Answer: c
Problem: a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . what will be b ' s share in the total profit of rs . 25000 earned at the end of 2 years from the starting of the business ?
Options: a ) rs . 7500 , b ) rs . 9000 , c ) rs . 9500 , d ) rs . 10,000 , e ) none
Rationale: solution a : b : c = ( 20000 × 24 ) : ( 15000 × 24 ) : ( 20000 × 18 ) = 4 : 3 : 3 b ' s share = rs . ( 25000 × 3 / 10 ) = rs . 7500 . answer a
Answer: a
Problem: length of a rectangular plot is 14 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 50 m , b ) 57 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 14 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 14 ) + x ] = 200 2 x + 14 = 100 2 x = 86 x = 43 . hence , length = x + 14 = 57 m b"
Answer: b
Problem: 9 log 9 ( 7 ) = ?
Options: a ) 1 , b ) 2 , c ) 7 , d ) 4 , e ) 5
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 7 ) = 7 correct answer c"
Answer: c
Problem: if ( a + b ) = 4 , ( b + c ) = 5 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 4 b + c = 5 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 5 + 3 = 2 . option d . . ."
Answer: d
Problem: indu gave bindu rs . 6500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 12.8 , b ) 20 , c ) 10.4 , d ) 11.6 , e ) 15
Rationale: "6500 = d ( 100 / 4 ) 2 d = 10.4 answer : c"
Answer: c
Problem: if the product of two numbers is 84942 and their h . c . f . is 33 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 1365 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 84942 , because we know product of two numbers = product of hcf and lcm lcm = 84942 / 33 = 2574 option a"
Answer: a
Problem: if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by
Options: a ) 6 only , b ) 6 and 12 both , c ) 12 only , d ) 18 only , e ) 12 and 18 both
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is divisible by both 6 and 12 , since n ( n + 1 ) is always even . answer b ."
Answer: b
Problem: express the ratio 3 2 / 3 : 7 1 / 3 in its simplest form .
Options: a ) 1 : 21 , b ) 1 : 1 , c ) 2 : 1 , d ) 1 : 2 , e ) 2 : 11
Rationale: solution we first convert the mixed numbers 3 2 / 3 and 7 1 / 3 into fractions 3 2 / 3 = 3 * 3 / 3 + 2 / 3 = 11 / 3 7 1 / 3 = 7 * 3 / 3 + 1 / 3 = 22 / 3 the ratio 3 2 / 3 : 7 1 / 3 can be expressed as 11 / 3 ÷ 22 / 3 = 11 / 3 × 3 / 22 simplify = 11 / 22 = 1 / 2 the ratio is 1 / 2 or 1 : 2 answer is d
Answer: d
Problem: a runs twice as fast as b and gives b a start of 64 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 128 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 64 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 64 m is 64 / 1 = 64 m so the total time taken by a and b to reach = 2 * 64 = 128 m answer : b"
Answer: b
Problem: on a map , 2.5 inches represent 25 miles . how many miles approximately is the distance if you measured 55 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 212.5 , b ) 213.5 , c ) 214.5 , d ) 215.5 , e ) 216.5
Rationale: "1 inch = 2.54 cm 2.5 inch = 2.54 * 2.5 cm 6.35 cm = 25 miles 55 cms = 25 / 6.35 * 55 = 216.5 miles answer : e"
Answer: e
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 920 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 50 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 920 - 640 = 280 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 280 / 28 = 70 / 7 = 10 total hrs = 40 + 10 = 50 answer d 50"
Answer: d
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 2 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005
b ) 0.002
c ) 0.001
d ) 0.0005
e ) 0.0002
Rationale: it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 2 then x = 2 / 1000 = 0.002 . the answer is b
Answer: b
Problem: the average age of a class of 20 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 42 , d ) 45 , e ) 43
Rationale: "total age of all students = 20 ã — 21 total age of all students + age of the teacher = 21 ã — 22 age of the teacher = 21 ã — 22 â ˆ ’ 21 ã — 20 = 21 ( 22 â ˆ ’ 20 ) = 21 ã — 2 = 42 answer is c ."
Answer: c
Problem: when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 71.2 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 80
Rationale: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e"
Answer: e
Problem: if a and b are integers and ( a * b ) ^ 5 = 128 y , y could be :
Options: a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 16
Rationale: distribute the exponent . a ^ 5 * b ^ 5 = 128 y find the prime factorization of 96 . this is 2 ^ 5 * 2 ^ 2 . we need 2 ^ 3 ( or some other power of 2 that will give us a multiple of 2 ^ 5 as our second term ) . 2 ^ 3 = 8 the answer is d .
Answer: d
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed t of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = t ans = c"
Answer: c
Problem: jacob is now 12 years younger than michael . if 5 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 3 , b ) 7 , c ) 11 , d ) 21 , e ) 25
Rationale: "jacob = x years , mike = x + 12 years 5 years from now , 2 ( x + 5 ) = x + 17 2 x + 10 = x + 17 x = 7 x + 4 = 11 years answer c"
Answer: c
Problem: ( 1000 ) 7 ÷ ( 10 ) 19 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 19 = ( 10 ) 21 / ( 10 ) 19 = 10 ( 2 ) = 100 option b"
Answer: b
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 143 per kg , the price of the third variety per kg will be
Options: a ) rs . 165.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 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 - 143 / 22.50 = 1 = â € º x - 143 = 22.50 = â € º x = 165.50 . hence , price of the third variety = rs . 165.50 per kg . answer a"
Answer: a
Problem: 3 numbers are in the ratio 3 : 5 : 7 . the largest number is 56 . what is the difference between smallest and largest number ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: the three numbers are 3 x , 5 x , and 7 x . the largest number is 56 = 7 * 8 , so x = 8 . the smallest number is 3 * 8 = 24 . 56 - 24 = 32 the answer is d .
Answer: d
Problem: mixture a is 20 % oil and 80 % material b by weight . if 2 more kilograms of oil are added to the 8 kilograms mixture a , how many kilograms of mixture a must be added to make a 70 % material b in the new mixture ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: old mix has 20 % oil . you add 2 kgs of 100 % oil . you get new mix with 30 % oil ( 70 % material b ) . w 1 / w 2 = ( 100 - 30 ) / ( 30 - 20 ) = 70 / 10 = 7 / 1 for every 7 parts of mix a , you have added 1 part of oil . since you have added 2 kgs oil , mix a must be 7 * 2 = 14 kgs . you already had 8 kgs of mix a , so extra mix a added must be 14 - 8 = 6 kgs . answer ( a )
Answer: a
Problem: kanul spent $ 5000 in buying raw materials , $ 200 in buying machinery and 30 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 7456.00 , b ) $ 7500.55 , c ) $ 7428.57 , d ) $ 7852.56 , e ) $ 7864.00
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 5000 + 200 70 % of x = 5200 70 x / 100 = 5200 x = $ 52000 / 7 x = $ 7428.57 answer is c"
Answer: c
Problem: there is 60 % increase in an amount in 6 yrs at si . what will be the ci of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2354 , b ) 2450 , c ) 2540 , d ) 2650 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 12000 . t = 3 years and r = 10 % p . a . c . i . = rs . 12000 x 1 + 10 3 - 1 100 = rs . 12000 x 331 1000 = 3972 . e"
Answer: e
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.8 km ?
Options: a ) 660 m , b ) 650 m , c ) 570 m , d ) 670 m , e ) 680 m
Rationale: "distance covered by amar = ( 18 / 48 ) * 1800 = 670 m answer : d"
Answer: d
Problem: find the value of x from the below equation : x ^ 2 − 7 x + 10 = 0
Options: a ) 5 , b ) 7 , c ) 6 , d ) 11 , e ) 12
Rationale: "here we need to find out a and b such that a + b = - 7 and ab = + 10 a = - 5 and b = - 2 satisfies the above condition . hence x ^ 2 − 7 x + 10 = ( x − 5 ) ( x − 2 ) x 2 − 7 x + 10 = ( x − 5 ) ( x − 2 ) x ^ 2 − 7 x + 10 = 0 ⇒ ( x − 5 ) ( x − 2 ) = 0 x 2 − 7 x + 10 = 0 ⇒ ( x − 5 ) ( x − 2 ) = 0 step 3 : equate each factor to 0 and solve the equations ( x − 5 ) ( x − 2 ) = 0 ⇒ ( x − 5 ) = 0 or ( x − 2 ) = 0 ⇒ x = 5 or 2 a"
Answer: a
Problem: find the largest 7 digit number which is exactly divisible by 88 ?
Options: a ) 9998765 , b ) 9998907 , c ) 9999944 , d ) 9999954 , e ) 9999968
Rationale: "largest 7 digit number is 9999999 after doing 9999999 ÷ 88 we get remainder 31 hence largest 7 digit number exactly divisible by 88 = 9999999 - 31 = 9999968 e"
Answer: e
Problem: in a theater , the first row has 15 seats and each row has 2 more seats than previous row . if the last row has 53 seats , what is the total number of seats in the theater ?
Options: a ) 600 , b ) 640 , c ) 680 , d ) 720 , e ) 760
Rationale: "the number of seats in the theater is 15 + ( 15 + 2 ) + . . . + ( 15 + 38 ) = 20 ( 15 ) + 2 ( 1 + 2 + . . . + 19 ) = 20 ( 15 ) + 2 ( 19 ) ( 20 ) / 2 = 20 ( 15 + 19 ) = 20 ( 34 ) = 680 the answer is c ."
Answer: c
Problem: evaluate : 20 - 12 ÷ 12 × 2 =
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 12 , d ) d ) 16 , e ) e ) 20
Rationale: "according to order of operations , 12 ÷ 12 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 12 × 2 = 1 × 2 = 2 hence 20 - 12 ÷ 12 × 2 = 20 - 12 = 8 correct answer is b ) 8"
Answer: b
Problem: shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5,000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12,000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15,000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16,000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60,000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15
Rationale: for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e
Answer: e
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 276 . what is their h . c . f . ?
Options: a ) 18 , b ) 23 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 276 x = 23 hcf of 2 x , 3 x and 4 x = x = 23 the answer is b ."
Answer: b
Problem: if the length of a rectangle is increased by 10 % and the area is unchanged , then its corresponding breadth must be decreased by ?
Options: a ) 9 1 / 19
b ) 9 1 / 15
c ) 9 1 / 16
d ) 9 1 / 11
e ) 9 1 / 10
Rationale: suppose length = 100 m and breadth = x m area = 100 m new length = 110 m and breadth = ( x - y % of x ) then , \ inline 110 \ times ( x - \ frac { y } { 100 } x ) = 100 \ times x \ inline \ rightarrow \ inline 110 \ times ( 1 - \ frac { y } { 100 } ) = 100 \ inline \ rightarrow \ inline 1 - \ frac { y } { 100 } = \ frac { 100 } { 110 } \ inline \ rightarrow \ frac { y } { 100 } = 1 - \ frac { 100 } { 110 } = \ frac { 1 } { 11 } \ inline y = \ frac { 100 } { 11 } = 9 \ frac { 1 } { 10 } % answer : e
Answer: e
Problem: in a mayoral election , candidate x received 1 / 3 more votes than candidate y , and candidate y received 1 / 7 fewer votes than z . if z received 21,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: "z = 21 - - > y received 1 / 7 fewer votes than z - - > y = z - 1 / 7 * z = 18 ; x received 1 / 3 more votes than y - - > x = y + 1 / 3 * y = 24 . answer : c ."
Answer: c
Problem: each factor of 200 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 9
Rationale: 200 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 9 . answer : e .
Answer: e
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 18 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 32 , e ) 48
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 18 ) x solve for r , r = 66 66 - 18 = 48 mpg e"
Answer: e
Problem: can v and can в are both right circular cylinders . the radius of can v is twice the radius of can b , while the height of can v is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can v with the same brand of gasoline ?
Options: a ) $ 1
b ) $ 2
c ) $ 4
d ) $ 8
e ) $ 16
Rationale: let x be the radius of b and 2 h be the height of b . therefore , radius of v = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
Answer: e
Problem: x can give y 100 meters start and z 200 meters start in x kilometer race . how much start can y give z in x kilometer race ?
Options: a ) 112.2 m , b ) 216.3 m , c ) 111.12 m , d ) 213.27 m , e ) 222.40 m
Rationale: c 111.12 m x runs 1000 m while y runs 900 m and z runs 800 m . the number of meters that z runs when y runs 1000 m , = ( 1000 * 800 ) / 900 = 8000 / 9 = 888.88 m . y can give z = 1000 - 888.88 = 111.12 m .
Answer: c
Problem: a sum of money deposited at c . i . amounts to rs . 1890 in 2 years and to rs . 2350 in 3 years . find the rate percent ?
Options: a ) 30 % , b ) 24 % , c ) 20 % , d ) 19 % , e ) 50 %
Rationale: "1890 - - - 460 100 - - - ? = > 24 % answer : b"
Answer: b
Problem: what is the least number that should be added to 1053 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1053 / 23 ) gives a remainder 18 so we need to add 5 . the answer is e ."
Answer: e
Problem: the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 16000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = rs . 9000 correct option : d"
Answer: d
Problem: find out the c . i on rs . 3000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 183.62 , b ) 106.07 , c ) 106.04 , d ) 106.03 , e ) 186.01
Rationale: "a = 3000 ( 51 / 50 ) 3 = 3183.62 3000 - - - - - - - - - - - 183.62 answer : a"
Answer: a
Problem: a number when divided by 20 leaves 6 as a remainder . what will be the remainder if the number is divided by 19 ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 11 , e ) 13
Rationale: let the minimum whole number be 20 + 6 = 26 where 6 is the remainder . 26 when divided by 19 then leaves 7 . correct answer a .
Answer: a
Problem: how many seconds will a 500 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 ) 65 , b ) 69 , c ) 30 , d ) 31 , e ) 32
Rationale: "let length of tunnel is x meter distance = 800 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 800 + x = ( 65 / 3 ) * 60 800 + x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters answer : option c"
Answer: c
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 5 % p . a . was rs . 492 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 4935 , b ) rs . 4925 , c ) rs . 5390 , d ) rs . 5290 , e ) rs . 5292
Rationale: "let the sum be rs . p p { [ 1 + 5 / 100 ] 2 - 1 } = 492 p ( 5 / 100 ) ( 2 + 5 / 100 ) = 492 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 492 / ( 0.05 ) ( 2.05 ) = 4800 . amount = 4800 + 492 = rs . 5292 answer : e"
Answer: e
Problem: a train 220 m long is running with a speed of 90 km / hr . in what time will it pass a bus that is running with a speed of 60 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.37 , b ) 5.28 , c ) 6.75 , d ) 8 , e ) 3.1
Rationale: "speed of train relative to bus = 90 + 60 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . time taken to pass the bus = 220 * 3 / 125 = 5.28 sec . answer : b"
Answer: b
Problem: a number is doubled and 9 is added . if resultant is trebled , it becomes 57 . what is that number
Options: a ) 5 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 57 = > 2 x + 9 = 19 = > x = 5 answer : option a"
Answer: a
Problem: tim and é lan are 30 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 20 miles . , b ) 35 miles . , c ) 45 miles . , d ) 60 miles . , e ) 65 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice a meet the 2 : 1 ( tim : elan = 20 : 10 ) ratio of maintaining total distance traveled 30 miles so correct answer a"
Answer: a
Problem: 2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened tofill the tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 10 hrs , b ) 12 hrs , c ) 16 hrs , d ) 18 hrs , e ) 20 hrs
Rationale: "1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c"
Answer: c
Problem: there are 99 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 69 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 99 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 99 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 69 answer : d"
Answer: d
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 252
Rationale: "ans : 252 7 c 1 * 9 c 2 answer e )"
Answer: e
Problem: the simple interest on rs . 8 for 12 months at the rate of 5 paise per rupeeper month is
Options: a ) 1.2 , b ) 4.8 , c ) 4.4 , d ) 3.21 , e ) none
Rationale: "sol . s . i . = rs . [ 8 * 5 / 100 * 12 ] = rs . 4.8 answer b"
Answer: b
Problem: an athlete runs 360 metres race in 24 seconds . what is his speed ?
Options: a ) 23 , b ) 64.8 , c ) 37 , d ) 30 , e ) 28
Rationale: "speed = distance / time = 360 / 20 = 18 m / s = 18 * 18 / 5 = 64.8 km / hr answer : b"
Answer: b
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 36 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 5 , d ) 3 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 36 : √ 4 = 6 : 2 = 3 : 1 answer : d"
Answer: d
Problem: a batsman scored 120 runs which included 10 boundaries and 6 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 36.67 % , d ) 70 % , e ) 75 %
Rationale: "number of runs made by running = 120 - ( 10 x 4 + 6 x 6 ) = 120 - ( 76 ) = 44 now , we need to calculate 60 is what percent of 120 . = > 44 / 120 * 100 = 36.67 % c"
Answer: c
Problem: the sum of the present ages of two persons a and b is 54 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 50 , b ) 64 , c ) 70 , d ) 80 , e ) 90
Rationale: "a + b = 54 , a = 2 b 2 b + b = 54 = > b = 18 then a = 36 . 5 years , their ages will be 41 and 23 . sum of their ages = 41 + 23 = 64 . answer : b"
Answer: b
Problem: if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ?
Options: a ) 7 % , b ) 9 % , c ) 11 % , d ) 12 % , e ) none of these
Rationale: we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > ( 2 x 9 ) % of x = ( 1 x 9 ) % of y thus , 18 % of x = 9 % of y . answer : b
Answer: b
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 80 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 10 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 80 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 10 liters . answer : e"
Answer: e
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 30 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 60 , b ) 65 , c ) 55 , d ) 50 , e ) 55
Rationale: round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 30 % of 50 % i . e 15 % . so he completed 50 + 15 = 65 % of total trip . b
Answer: b
Problem: on dividing 127 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 127 - 1 ) / 9 = 126 / 9 = 14 b )"
Answer: b
Problem: if x + | x | + y = 7 and x + | y | - y = 6 , then x + y =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "if x + | x | + y = 7 and x + | y | - y = 6 , then x + y = can be done in 2.3 mins : there are 4 cases to be tested : 1 ) x is - ve and y is - ve substituting in the equation , we get x - x + y = 7 and x - y - y = 6 solve for x and y we get x = 20 and y = 7 , so x + y = 27 reject 2 ) x is + ve and y is + ve substitute in the equation , we ger x + x + y = 7 and x + y - y = 6 solve for x and y we get x = 6 and y = - 5 , therefore x + y = 1 not on list so reject 3 ) x is - ve and y is + ve substitute , we get x - x = y = 7 and x + y - y = 6 solve fo x and y we get x = 6 and y = 7 , x + y = 13 not on list so reject 4 ) x is + ve and y is - ve substitute , we get x + x = y = 7 and x - y - y = 6 solve for x and y , we get x = 4 and y = - 1 , x + y = 3 , answer choice answer a"
Answer: a
Problem: a 300 meter long train crosses a platform in 45 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 450 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 45 = 50 / 3 3 ( x + 300 ) = 2250 è x = 450 m . answer : b"
Answer: b
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 3 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 60
Rationale: let the number of sheeps and horses be 3 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 3 x = 3 * 8 = 24 . hence a
Answer: a
Problem: one day a car rental agency rented 3 / 4 of its cars , including 4 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 23 / 40 , b ) 17 / 30 , c ) 12 / 25 , d ) 7 / 15 , e ) 3 / 10
Rationale: "the cars with cd players which were not rented is ( 1 / 5 ) ( 3 / 5 ) = 3 / 25 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 3 / 25 ) / ( 1 / 4 ) = 12 / 25 the answer is c ."
Answer: c
Problem: if a ( k ) = ( k + 1 ) ^ 2 , and k = 1 , what is the value of a ( a ( a ( a ( k ) ) ) ) ?
Options: a ) 328359 , b ) 557321 , c ) 258327 , d ) 458329 , e ) 4422
Rationale: a ( a ( a ( a ( 1 ) ) ) ) = a ( a ( a ( 4 ) ) ) = a ( a ( 25 ) ) = a ( 676 ) = 677 ^ 2 = 458329 thus , the answer is d .
Answer: d