regisss/math_qa huggingface dataset:
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 61.50 , his capital is ?
Options: a ) 24,607 , b ) 24,609 , c ) 24,600 , d ) 24,602 , e ) 24,604
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 61.50 32 x - 31 x = 6150 * 4 x = 24,600 . answer : c"
Answer: c
Problem: a 210 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 290 , b ) 280 , c ) 270 , d ) 260 , e ) 250
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 210 ) / 9 = 500 / 9 = > x = 290 . answer : option a"
Answer: a
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 6 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 24 min , e ) 12 min
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 5 1 - - - - - - - - 6 4 - - - - - - - - - ? è 24 answer : d"
Answer: d
Problem: the age of father 8 years ago was thrice the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
Options: a ) 47 : 11 , b ) 37 : 21 , c ) 27 : 21 , d ) 47 : 21 , e ) 47 : 31
Rationale: let the ages of father and son 8 years ago be 3 x and x years respectively . then , ( 3 x + 8 ) + 5 = 2 [ ( x + 8 ) + 5 ] 3 x + 13 = 2 x + 26 x = 13 . required ratio = ( 3 x + 8 ) : ( x + 8 ) = 47 : 21 . answer : option d
Answer: d
Problem: if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 69 , what is the value of a ?
Options: a ) 26 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: ( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 69 a = 26 the answer is a .
Answer: a
Problem: what is the remainder when 43 ^ 89 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 89 has the form 4 k + 1 so the units digit of 43 ^ 89 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Problem: the value of 99 ^ ( 91 / 99 ) x 99 is :
Options: a ) 9989 , b ) 9896 , c ) 9892 , d ) 9809 , e ) 9810
Rationale: ( 100 â € “ 8 / 99 ) x 99 = 9900 â € “ 8 = 9892 . answer : c
Answer: c
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 3 * / 5 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 5 / 3 b"
Answer: b
Problem: the length of the bridge , which a train 130 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 288 , b ) 269 , c ) 245 , d ) 888 , e ) 121
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 130 + x ) / 30 = 25 / 2 x = 245 m . answer : c"
Answer: c
Problem: if the average of 55 , 48 , 507 , 2 , 684 and y is 223 , then what is y ?
Options: a ) 701 , b ) 120 , c ) 42 , d ) 868 , e ) 1
Rationale: y = 42 , because : ( 55 + 48 + 507 + 2 + 684 + y ) / 6 = 223 ( 55 + 48 + 507 + 2 + 684 + y ) / 6 * 6 = 223 * 6 ( 55 + 48 + 507 + 2 + 684 + y ) - 1296 = 1338 - 1296 y = 42 so the correct answer is c , 42 .
Answer: c
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 5 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 5 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k - - - > 5 = 2 k - - - > k = 5 / 2 . the answer is , therefore , ( d ) ."
Answer: d
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area r of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Problem: the sum of the first 70 positive even integers is 4970 . what is the sum of the first 70 odd integers ?
Options: a ) 4500 , b ) 4600 , c ) 4300 , d ) 4900 , e ) 5000
Rationale: sum of first n even numbers = n ( n + 1 ) = 4970 sum of first n odd numbers = n ^ 2 = 70 * 70 = 4900 ( here n = 70 ) answer : d
Answer: d
Problem: a train crosses a platform of 150 m in 10 sec , same train crosses another platform of length 250 m in 15 sec . then find the length of the train ?
Options: a ) 150 m , b ) 180 m , c ) 159 m , d ) 250 m , e ) 50 m
Rationale: "length of the train be ‘ x ’ x + 150 / 10 = x + 250 / 15 3 x + 450 = 2 x + 500 x = 50 m answer : e"
Answer: e
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 5 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 7 th year ?
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 7 th year : 6 - 7 ( age ) , we take age = 6 thus for the 5 th year = 50 , 6 th year = 50 - 5 = 45 7 th year = 45 - 6 = 39 the correct answer is d ."
Answer: d
Problem: two trains 170 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 sec , b ) 18.8 sec , c ) 14.8 sec , d ) 10.88 sec , e ) 11.88 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 170 + 160 = 330 m . required time = 330 * 9 / 250 = 297 / 25 = 11.88 sec . answer : e"
Answer: e
Problem: on a certain road 12 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 12 % + 0,2 x id est x = 15 %"
Answer: c
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 2.5 liters of alcohol and 7.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 9 % , b ) 12 % , c ) 15 % , d ) 18 % , e ) 21 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 2.5 ) / 50 = 4.5 / 50 = 9 % the answer is a ."
Answer: a
Problem: in a consumer survey , 80 % of those surveyed liked at least one of 3 products : 1 , 2 , and 3 . 50 % of those asked liked product 1 , 30 % liked product 2 , and 20 % liked product 3 . if 5 % of the people in the survey liked all 3 of the products , what percentage of the survey participants liked more than one of the 3 products ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: pick 100 and x = all set with exactly two items 80 = 30 + 50 + 20 - ( x ) - 10 x = 10 so the answer is 10 + 5 / 100 = 15 % answer c
Answer: c
Problem: in township k each property is taxed at 8 percent of its assessed value . if the assessed value of a property in township k is increased from $ 180,000 to $ 24,000 , by how much will the property tax increase ?
Options: a ) $ 32 , b ) $ 50 , c ) $ 480 , d ) $ 400 , e ) $ 500
Rationale: "increase in house value = $ 24,000 - $ 18,000 = $ 8000 so , tax increase = 8 % of $ 6000 = $ 480 answer : c"
Answer: c
Problem: find the greatest number which on dividing 1255 and 1490 , leaves a reminder of 8 and 11 respectively
Options: a ) 27 , b ) 29 , c ) 33 , d ) 39 , e ) 41
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1255 - 8 ) and ( 1490 - 11 ) = hcf ( 1247 , 1479 ) = 29 option b"
Answer: b
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2.5 % more . she would get how much ?
Options: a ) 9800 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 2.5 ) / 100 = 600 9200 - - - - - - - - 9800 answer : a"
Answer: a
Problem: 8 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 84 , e ) 45
Rationale: "there are 8 business exec and in each handshake 2 business execs are involved . hence 8 c 2 = 28 also , each of 8 exec will shake hand with every 7 other chairmen for total of 56 handshake . total = 28 + 56 = 84 ans : d"
Answer: d
Problem: there are 2 positive integers x and y . what is the probability that x + y is odd ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 5 , e ) 1 / 9
Rationale: explanation : the addition of two integer results in an odd number only if any one of the integers is an odd number . the probability of an odd among the two integer is 1 / 2 . hence , the required probability is 1 / 2 . answer : b
Answer: b
Problem: solution x contains 20 % of material a and 80 % of material b . solution y contains 30 % of material a and 70 % of material b . a mixture of both these solutions contains 22 % of material a in the final product . how much solution x is present in the mixture ?
Options: a ) 40 % , b ) 60 % , c ) 80 % , d ) 100 % , e ) 110 %
Rationale: we can assume the total weight of the mixture = 100 conc of a in the final mixture = 22 let weight of a in the mixture be x . conc given = 20 % = . 2 therefore , weight of b = 100 - x . conc given = 30 % = . 3 now , acc to the problem , . 2 x + . 3 ( 100 - x ) = 22 solving , we get x = 80 . since we assumed the weight of the mixture = 100 , therefore presence of a in the mixture = 80 % . answer : c
Answer: c
Problem: set a consists of the integers from 4 to 17 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "a = { 4 , 5,6 , 7,8 , 9,10 , 11,12 , . . . 17 } b = { 6 , 7,8 , 9,10 , 11,12 . . . , 20 } thus we see that there are 12 distinct integers that are common to both . e is the correct answer ."
Answer: e
Problem: a student travels from his house to school at 10 km / hr and reaches school 2 hours late . the next day he travels 16 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
Options: a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "let x be the distance from his house to the school . x / 10 = x / 16 + 3 8 x = 5 x + 240 3 x = 240 x = 80 km the answer is c ."
Answer: c
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 1 / 2 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 8 / 11 , d ) 7 / 12 , e ) 11 / 15
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( x / 2 ) ( 3 y / 4 ) = 3 xy / 8 the total number of boxes is xy + 3 xy / 8 = 11 xy / 8 the fraction loaded by the day crew is xy / ( 11 xy / 8 ) = 8 / 11 the answer is c ."
Answer: c
Problem: of the 200 employees at company x , 80 are full - time , and 150 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "200 employees 80 are full - time 150 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 200 - 80 = 120 employees not full time 120 - 20 = 100 employees not full time who worked over a year 150 employees have worked at company x for at least a year - 100 employees not full time who worked over a year = 50 full - time employees of company x have worked at the company for at least a year c . 50"
Answer: c
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 1 / 2 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 62.5 , e ) 50
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 1 x / 2 hence , number of buckets needed = 25 x / ( 1 x / 2 ) = ( 25 × 2 ) / 1 = 50 answer is e ."
Answer: e
Problem: how many of the positive divisors of 480 are also multiples of 4 not including 480 ?
Options: a ) 15 , b ) 16 , c ) 19 , d ) 20 , e ) 24
Rationale: "480 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 ^ 3 * 3 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 3 , 1 , and 1 . there are ( 3 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 480 . the answer is a ."
Answer: a
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 45 % on his income , while mindy pays a rate of only 20 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 22 % , b ) 25 % , c ) 28 % , d ) 31 % , e ) 34 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 0.8 x = 1.25 x 1.25 x / 5 x = 0.25 the answer is b ."
Answer: b
Problem: let p be a prime number greater than 2 , and let n = 32 p . how many odd divisors does n have ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the answer is a , there is exactly one . since is the largest ( and only ) even prime number , any p larger than 2 is odd . then since 32 = 2 * 2 * 2 * 2 , all of which are even , this means that p must be the only odd prime factor .
Answer: a
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 12 m wide at the top and 5 m wide at the bottom and the area of cross - section is 344 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 27 , d ) 40 , e ) 71
Rationale: "1 / 2 * d ( 12 + 5 ) = 344 d = 40 answer : d"
Answer: d
Problem: when the number 209 y 913 is exactly divisible by 11 , then the smallest whole number that can replace y ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 9
Rationale: "the given number = 209 y 913 sum of the odd places = 3 + 9 + 9 + 2 = 23 sum of the even places = 1 + y + 0 ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 23 - ( 1 + y ) = divisible by 11 22 � y = divisible by 11 . y must be 0 , to make given number divisible by 11 . a"
Answer: a
Problem: pipe p can drain the liquid from a tank in 3 / 4 the time that it takes pipe q to drain it and in 1 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 8 / 23 , c ) 9 / 25 , d ) 17 / 29 , e ) 3 / 4
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 3 / 4 ) rq ] = 4 / 3 also , rp = rr / ( 1 / 3 ) = > 4 / 3 = rr / ( 1 / 3 ) = > rr = 4 / 9 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 4 / 3 + 4 / 9 = 25 / 9 = 1 / ( 9 / 25 ) thus running simultaneously , pipe q will drain 9 / 25 of the liquid . thus answer = c ."
Answer: c
Problem: a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 5 t seconds , then what is the length of the platform ?
Options: a ) l , b ) 2 l , c ) 3 l , d ) 4 l , e ) 5 l
Rationale: the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 5 t ( l + p ) / ( l / t ) = 5 t p = 4 l the answer is d .
Answer: d
Problem: the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 21 and 23 . the larger of the two numbers is
Options: a ) 276 , b ) 299 , c ) 312 , d ) 460 , e ) none
Rationale: "solution clearly , the numbers are ( 20 x 21 ) and ( 20 x 23 ) . larger number = ( 20 x 23 ) = 460 . answer d"
Answer: d
Problem: two numbers are in the ratio of 5 : 9 . if 25 be subtracted from each , they are in the ratio of 35 : 59 . find the numbers ?
Options: a ) 150,170 , b ) 150,270 , c ) 50,270 , d ) 180,270 , e ) 150,290
Rationale: "( 5 x - 25 ) : ( 9 x - 25 ) = 35 : 59 x = 30 = > 150,270 answer : b"
Answer: b
Problem: there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure e in inches of the width of the foil covered prism ?
Options: a ) 4
b ) 6
c ) 8
d ) 9
e ) 10
Rationale: if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = e = 10 ans e .
Answer: e
Problem: a train 110 m long is running with a speed of 24 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 14 sec , e ) 13.2 sec
Rationale: "speed of train relative to man = 24 + 6 = 30 km / hr . = 30 * 5 / 18 = 8.33 m / sec . time taken to pass the men = 110 / 8.33 = 13.2 sec . answer : e"
Answer: e
Problem: worker a takes 10 hours to do a job . worker b takes 12 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 40 days , b ) 40 / 9 days , c ) 60 / 11 days , d ) 30 / 9 days , e ) 60 / 9 days
Rationale: "a ' s one hour work = 1 / 10 . b ' s one hour work = 1 / 12 . ( a + b ) ' s one hour work = 1 / 10 + 1 / 12 = 11 / 60 . both a & b can finish the work in 60 / 11 days c"
Answer: c
Problem: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 160 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 160 = 1600 3 * 100 + 5 * 150 = 1050 1600 – 1050 = 550 d"
Answer: d
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 80 . how much was lent at 5 % ?
Options: a ) 228 , b ) 299 , c ) 266 , d ) 500 , e ) 1000
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 80 5 x / 100 + 90 â € “ 6 x / 100 = 80 x / 100 = 10 = > x = 1000 answer : e"
Answer: e
Problem: if a truck is traveling at a constant rate of 216 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 10 , b ) 24 , c ) 30 , d ) 36 , e ) 48
Rationale: "speed = 216 km / hr = > 216,000 m / hr in one minute = > 216000 / 60 = 3600 meters in one sec = > 3600 / 60 = 60 meters time = total distance need to be covered / avg . speed = > 600 / 60 = 10 and hence the answer : a"
Answer: a
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 4 : 3 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 4 x and 3 x . then , their l . c . m = 12 x . so , 12 x = 48 or x = 4 . the numbers are 16 and 12 . hence , required sum = ( 16 + 12 ) = 28 . answer : a"
Answer: a
Problem: a number a is squared and then multiplied by negative 6 . the result of this operation is equal to 3 times the sum of fourth times a and two . what is one possible value of a ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: - 6 * a ^ 2 = 3 ( 4 a + 2 ) a = - 1 or - 1 a = - 1 = b answer : d
Answer: d
Problem: if 20 typists can type 38 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 171 , e ) 400
Rationale: "20 typists can type 38 letters , so 30 typists can type = 38 * 30 / 20 38 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 38 * 30 * 60 / 20 * 20 = 171 d is the answer"
Answer: d
Problem: a fair 2 sided coin is flipped 6 times . what is the probability that tails will be the result at least twice , but not more than 4 times ?
Options: a ) 25 / 32 , b ) 13 / 4 , c ) 17 / 8 , d ) 57 / 64 , e ) 15 / 16
Rationale: "at least twice , but not more than 5 timesmeans exactly 2 times , 3 times , 4 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 6 c 2 / 2 ^ 6 + 6 c 3 / 2 ^ 6 + 6 c 4 / 2 ^ 6 = ( 20 + 15 + 15 ) / 2 ^ 6 = 25 / 32 option : a"
Answer: a
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 40 kmph . what time will they take to be 50 km apart ?
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: to be ( 10 + 40 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 50 * 50 = 1 hrs answer is a
Answer: a
Problem: if x is a sum of all even integers on the interval 13 . . . 55 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 21 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 54 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 54 ) / 2 * 21 = 34 * 21 . gcd of 21 and 34 * 21 is 21 answer : b ."
Answer: b
Problem: how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 30 percent alcohol ?
Options: a ) 100 / 7 , b ) 5 , c ) 20 / 3 , d ) 8 , e ) 39 / 4
Rationale: 20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 30 % of ( 100 + x ) or 20 + x = ( 100 + x ) 3 / 10 200 + 10 x = 300 + 3 x 7 x = 100 x = 100 / 7 ans : a
Answer: a
Problem: the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . the present worth is
Options: a ) rs . 480 , b ) rs . 520 , c ) rs . 600 , d ) rs . 960 , e ) none
Rationale: solution t . d = ( b . g x 100 / rate x time ) = rs . ( 24 x 100 / 10 x 2 ) = rs . 120 . p . w = ( 100 x t . d / rate x time ) = rs . ( 100 x 120 / 10 x 2 ) = rs . 600 . answer c
Answer: c
Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 3000 , what is the area of the side face of the box ?
Options: a ) 300 , b ) 150 , c ) 180 , d ) 109 , e ) 200
Rationale: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 3000 l * 1.5 l * 2 l = 3000 l = 10 side face area = l * d = l * 2 l = 10 * 2 * 10 = 200 e is the answer"
Answer: e
Problem: the salary of a person was reduced by 20 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 50 % , b ) 32 % , c ) 25 % , d ) 43 % , e ) 29 %
Rationale: "let the original salary be $ 100 new salary = $ 80 increase on 80 = 20 increase on 100 = 20 / 80 * 100 = 25 % answer is c"
Answer: c
Problem: if 10 % of 30 % of 50 % of a number is 90 , then what is the number ?
Options: a ) 4000 , b ) 6000 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 10 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 1 / 10 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 6000 . answer : b"
Answer: b
Problem: the average of non - zero number and its square is 5 times the number . the number is ?
Options: a ) 9 , b ) 8 , c ) 6 , d ) 4 , e ) 3
Rationale: "let the number be x . then , ( x + x 2 ) / 2 = 5 x = > x 2 - 9 x = 0 = > x ( x - 9 ) = 0 = > x = 0 or x = 9 so , the number is 9 . answer : a"
Answer: a
Problem: preethi has 6 flavors of ice cream in his parlor . how many options are there for dorathy to pick a one - flavor , two - flavor , 3 - flavor , 4 - flavor , 5 flavor or 6 flavor order ?
Options: a ) 26 , b ) 36 , c ) 64 , d ) 67 , e ) 63
Rationale: 6 c 1 + 6 c 2 + 6 c 3 + 6 c 4 + 6 c 5 + 6 c 6 = 63 . answer : e
Answer: e
Problem: the average weight of 2 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 74 kg , b ) 76.5 kg , c ) 85 kg , d ) 78 , e ) none of these
Rationale: "explanation : total weight increased = ( 2 x 4.5 ) kg = 9 kg . weight of new person = ( 65 + 9 ) kg = 74 kg . answer : a"
Answer: a
Problem: john started a business , investing rs . 18000 . after 3 months and 4 months respectively , rose and tom joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 4070 . what is the difference between rose ’ s and tom ’ s share in the profit ?
Options: a ) s . 340 , b ) s . 362 , c ) s . 370 , d ) s . 382 , e ) s . 390
Rationale: john : rose : tom ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rose ’ s and tom ’ s share = 1 share : . i . e . = rs . 4070 × 1 / 11 = rs . 370 . c )
Answer: c
Problem: if each year the population of the country grows by 20 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "till year 2000 , population is 100 . year 2001 : population becomes 120 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 144 . . . . . . . . . . . . . 2 year elapsed year 2003 : population becomes 172 . . . . . . . . . . . . . 3 year elapsed year 2004 : population > 200 . . . . . . . . . . . . . . . . . . 4 year elapsed answer : b"
Answer: b
Problem: peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 664 , c ) 698 , d ) 744 , e ) 700
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 815 = 39 interest earned for 3 years = 39 * 3 = 117 amount invested = 815 - 117 = 698 answer : c"
Answer: c
Problem: andrew purchased 10 kg of grapes at the rate of 82 per kg and 6 kg of mangoes at the rate of 62 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1378 , d ) 1075 , e ) 1080
Rationale: "cost of 10 kg grapes = 82 × 10 = 820 . cost of 6 kg of mangoes = 62 × 6 = 558 . total cost he has to pay = 820 + 558 = 1378 c"
Answer: c
Problem: maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability r , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , r = 9 provide the desired outcome , making the answer e ."
Answer: e
Problem: tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 2 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 7 miles per hour . if both tom and linda travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes tom to cover half of the distance that linda has covered and the amount of time it takes tom to cover twice the distance that linda has covered ?
Options: a ) 60 , b ) 56 , c ) 84 , d ) 90 , e ) 108
Rationale: "b is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 2 t ) = 7 t = = > t = 2 / 5 = = > 24 minutes to travel double distance , 2 ( 2 + 2 t ) = 7 t = = > 2 = = > 80 minutes difference , 56 minutes b"
Answer: b
Problem: 64 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 26 , c ) 42 , d ) 28 , e ) 11
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 64 = 28 answer : d"
Answer: d
Problem: a man walking at the rate of 6 km / hr crosses a bridge in 15 minutes . the length of the bridge is ______ .
Options: a ) 1000 m , b ) 1250 m , c ) 1500 m , d ) 1800 m , e ) 2300 m
Rationale: "hint : to find the answer in meter , we will first convert distance from km / hour to meter / sec by multiplying it with 5 / 18 . also , change 15 minutes to seconds by multiplying it with 60 . distance = speed x time 1 . convert speed into m / sec : 6 x 5 / 18 m / s = 1.66 m / s 2 . convert time from minutes into seconds = 15 x 60 s = 900 sec 3 . calculate : distance = 1.66 x 900 = 1500 m answer is c"
Answer: c
Problem: if w = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x is between
Options: a ) 0 and 3 , b ) 3 and 6 , c ) 6 and 9 , d ) 9 and 12 , e ) 12 and 15
Rationale: my attempt : if w = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x would be when y is minimum . let y ^ 4 be 0 . now x ^ 4 = 100 . x should be definitely greater than 3 but less than 4 . the only option that fits this range is b hence answer is - - b ) 3 and 6 .
Answer: b
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 89 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 637
Rationale: "you need to integers which squared are equal 89 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 stop . the integers ca n ' t be greater than 8 or we will score above 89 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 the only pair that matches is 8 ^ 2 + 5 ^ 2 = 89 . so 8 ^ 3 + 5 ^ 3 = 637 . answer e . )"
Answer: e
Problem: the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 70 black cars in the lot , how many red cars are there in the lot ?
Options: a ) 11 , b ) 26 , c ) 24 , d ) 27 , e ) 32
Rationale: "b is correct r / b = 3 / 8 and b = 70 r = 70 * 3 / 8 = 26"
Answer: b
Problem: if the sum of a number and its square is 272 , what is the number ?
Options: a ) 14 , b ) 16 , c ) 19 , d ) 21 , e ) none of these
Rationale: "explanation : let the integer be x . then , x + x 2 = 272 x 2 + x - 272 = 0 ( x + 17 ) ( x – 16 ) = 0 x = 16 answer : b"
Answer: b
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2460 ?
Options: a ) 28888 , b ) 27789 , c ) 2777 , d ) 14000 , e ) 2881
Rationale: "25 * 12 : 30 * 12 : 35 * 8 15 : 18 : 14 14 / 47 * 47000 = 14000 answer : d"
Answer: d
Problem: volume of a hemisphere is 19404 cu . cm . its radius is :
Options: a ) 19 cm
b ) 20 cm
c ) 21 cm
d ) 30 cm
e ) none
Rationale: sol . let the radius be r cm . then , 2 / 3 * 22 / 7 * r ³ = 19404 ⇔ r ³ = [ 19404 * 21 / 44 ] = ( 21 ) ³ ⇔ r = 21 cm . answer c
Answer: c
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 4 miles per hour for 5 hours . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 4 miles per hour and 5 hours - 20 miles total 18 + 20 + 20 = 58 answer : option c"
Answer: c
Problem: 2 corner most boxes of a chess board ( diagonally opposite ) haven been cut out there ' s a rectangular block = 2 sqaures of chess board , how many such blocks can be placed on the chess board ? ”
Options: a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 31
Rationale: chess board has 64 squares . so we can place 32 rectangular blocks , but 2 are cut off from the corner . hence 32 - 2 = 30 blocks answer : d
Answer: d
Problem: the perimeter of one square is 44 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 12.1 √ 2 , c ) 23 √ 2 , d ) 12 √ 4 , e ) 13 √ 9
Rationale: "4 a = 44 4 a = 20 a = 11 a = 5 a 2 = 121 a 2 = 25 combined area = a 2 = 146 = > a = 12.1 d = 12.1 √ 2 answer : b"
Answer: b
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 19,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 145 % , d ) 150 % , e ) 225 %
Rationale: "we can use approximation to get the answer quickly . like , 19,947 is approx 20000 8902 is approx 8900 so , total increase = 20000 - 8900 = 11100 hence , % increase = 11100 / 8900 = approx . 11 / 9 = 1.22 = approx . 1.25 so , choice is b ."
Answer: b
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 30 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 200 square feet and its length is 10 feet longer than its width . if the uniform width between the rug and room is 10 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 1360 , c ) 1000 , d ) 46 , e ) 104
Rationale: "rug ' s area = 200 which is ( x ) x ( 10 + x ) = 200 so x = 10 rug maintains a uniform distance of 10 feet so room has dimension 10 + 20 and 20 + 20 i . e . 30 and 40 area of room 30 x 40 = 1200 area covered is 200 so uncovered area is 1200 - 200 = 1000 ( answer c )"
Answer: c
Problem: the sum of money will be double itself in 20 years and simple interest find rate of interest ?
Options: a ) 10 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "t = 20 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 20 x = 5 % answer is b"
Answer: b
Problem: how many positive even integers less than 100 contain digits 3 or 7 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 10 , e ) 20
Rationale: "two digit numbers : 3 at tens place : 30 , 32,34 , 36,38 7 at tens place : 70 , 72,74 , 76,78 if 3 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer d"
Answer: d
Problem: if the simple interest on a sum of money for 4 years at 8 % per annum is rs . 560 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 640.86 , b ) rs . 430.86 , c ) rs . 330.86 , d ) rs . 630.86 , e ) rs . 130.86
Rationale: "sum = ( 50 * 100 ) / ( 2 * 5 ) = rs . 1 , 750.00 c . i . on rs . 1 , 750.00 for 4 years at 8 % = rs . 2 , 380.86 . = rs . 2 , 380.86 - 1 , 750.00 = rs . 630.86 answer : d"
Answer: d
Problem: bert left the house with n dollars . he spent 1 / 3 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 10.50 left in his pocket . what was the value of n ?
Options: a ) $ 42 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer a if he had 42 , then he spent 13 2 / 3 at hardware store now he was left with 27 1 / 3 $ he spent 7 dollars on cleaning , thus he remained with 20 1 / 3 $ he then spent 1 / 2 of 20 1 / 3 or 10.5 , hence , right option is a ."
Answer: a
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 44 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 14
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 44 + q = > q = 14 answer : e"
Answer: e
Problem: a train 360 m long is running at a speed of 42 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 27 sec , e ) 43 sec
Rationale: "speed = 42 * 5 / 18 = 35 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 35 = 43 sec answer : e"
Answer: e
Problem: pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed t ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this t we get x = 8 . b ."
Answer: b
Problem: a = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set a and one integer from set b . what is the probability q that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: rearrange the first set : a = { 5,4 , 3,2 } b = { 4,5 , 6,7 , 8 } as you can see numbers in each column ( the numbers of the same color ) give the sum of 9 . so there are 4 such pares possible , total # of pairs is 4 * 5 = 20 . q = favorable / total = 4 / 20 = 0.2 . answer : b . or : we can select any number from set a ( 4 / 4 = 1 ) but in this case we must select its matching pair from set b ( the number of the same color ) and since there are only one matching pair of this particular number in b then the probability of this is 1 / 5 . so , overall : q = 1 * 1 / 5 . answer : b .
Answer: b
Problem: a train 360 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 , b ) 99 , c ) 77 , d ) 66 , e ) 32
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 2 / 25 = 40 sec answer : a"
Answer: a
Problem: how many seconds will a 600 m long train take to cross a man walking with a speed of 2 km / hr in the direction of the moving train if the speed of the train is 56 km / hr ?
Options: a ) 30 , b ) 54 , c ) 40 , d ) 36 , e ) 31
Rationale: "speed of train relative to man = 56 - 2 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . time taken to pass the man = 600 * 1 / 15 = 40 sec . answer : c"
Answer: c
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 m 3 , b ) 4580 m 3 , c ) 9000 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 6000 * 2 * 45 ) / 60 = 9000 m 3 answer : option c"
Answer: c
Problem: how many times will the digit 3 be written when listing the integers from 1 to 1000 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 3 ) 3000 / 10 = 300 times . answer : c ."
Answer: c
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 9 cm and breadth 6 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 11.72 , b ) 11.52 , c ) 11.97 , d ) 10.91 , e ) 11.79
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 9 + 6 ) = 30 cm parameter of the square = 30 cm i . e . 4 a = 30 a = 7.5 diameter of the semicircle = 7.5 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 7.5 ) = 1 / 2 ( 22 / 7 ) ( 7.5 ) = 165 / 14 = 11.79 cm to two decimal places answer : e"
Answer: e
Problem: working alone , mary can pave a driveway in 3 hours and hillary can pave the same driveway in 6 hours . when they work together , mary thrives on teamwork so her rate increases by 10 % , but hillary becomes distracted and her rate decreases by 20 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 3 per hour hillary = 1 / 6 per hour rate when working together : mary = 1 / 3 + ( 1 / 10 * 1 / 3 ) = 3 / 8 per hour hillary = 1 / 6 - ( 1 / 5 * 1 / 6 ) = 2 / 15 per hour together they work 3 / 8 + 2 / 15 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Problem: if the remainder is 11 when the integer n is divided by 20 , what is the remainder when 2 n is divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 20 k + 11 2 n = 2 ( 20 k + 11 ) = 4 k * 10 + 22 = 4 k * 10 + 2 * 10 + 2 = 10 j + 2 the answer is c ."
Answer: c
Problem: a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points t that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points t for 12 th player is 100 - 77 = 23 . answer : e ."
Answer: e
Problem: a invested $ 400 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find b ' s shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 400 * 12 : 200 * 6 a : b = 4 : 1 b ' s share = 100 * 1 / 5 = $ 20 answer is c"
Answer: c
Problem: plot abcd is as shown in figure , where af = 30 m , ce = 40 m , ed = 50 m , ae = 120 m . find the area of the plot abcd ?
Options: a ) 7207 , b ) 7206 , c ) 7203 , d ) 7200 , e ) 7201
Rationale: "area of plot abcd = area of ade + area of afb + area of bcef = 1 / 2 * 50 * 120 + 1 / 2 * 40 * 30 + 40 * 90 = 3000 + 600 + 3600 = 7200 sq . m answer : d"
Answer: d
Problem: a and b can do a piece of work in 6 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 40 days , b ) 16 days , c ) 6 days , d ) 5 days , e ) 40 days
Rationale: "c 6 days c = 1 / 3 – 1 / 6 = 1 / 6 = > 6 days"
Answer: c
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 4 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.2 , d ) 5.5 , e ) 6.4
Rationale: "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 4 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 4 = 6.4 desks e is the correct answer ."
Answer: e