regisss/math_qa huggingface dataset:
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity w of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Problem: if n = 2 ^ 0.15 and n ^ b = 1 , b must equal
Options: a ) 3 / 80 , b ) 20 / 3 , c ) 4 , d ) 5 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 1 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 1 b = 20 / 3 answer : b"
Answer: b
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 300 km , b ) 320 km , c ) 360 km , d ) 390 km , e ) 400 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 4 h is 90 × 4 = 360 km ans . ( c )"
Answer: c
Problem: find the sum of first 89 odd numbers
Options: a ) 7921 , b ) 4800 , c ) 7900 , d ) 4980 , e ) 4960
Rationale: "explanation : n 2 = 892 = 7921 answer : option a"
Answer: a
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 5 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 960 , b ) 980 , c ) 900 , d ) 970 , e ) 1000
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 1 = > x = 1000 answer : e ) rs 1000"
Answer: e
Problem: the difference between a number and its 3 - fourth is 100 . what is 25 % of that number ?
Options: a ) 120 , b ) 100 , c ) 125 , d ) 150 , e ) none of these
Rationale: explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b
Answer: b
Problem: i chose a number and divide it by 4 . then i subtracted 175 from the result and got 10 . what was the number i chose ?
Options: a ) 200 , b ) 740 , c ) 780 , d ) 500 , e ) 100
Rationale: "let x be the number i chose , then x / 4 − 175 = 10 x / 4 = 185 x = 740 answer is b ."
Answer: b
Problem: ramu bought an old car for rs . 42000 . he spent rs . 15000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 13.8 , b ) 77 , c ) 18 , d ) 99 , e ) 88
Rationale: "total cp = rs . 42000 + rs . 15000 = rs . 57000 and sp = rs . 64900 profit ( % ) = ( 64900 - 57000 ) / 57000 * 100 = 13.8 % answer : a"
Answer: a
Problem: how many 3 digit numbers n are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b
Answer: b
Problem: the length and breadth of a rectangle is increased by 3 % and 6 % respectively . what is the increase in the area ?
Options: a ) 9.18 , b ) 9.25 , c ) 9.5 , d ) 8.98 , e ) 8.88
Rationale: "100 * 100 = 10000 103 * 106 = 10918 - - - - - - - - - - - 918 10000 - - - - - - - 918 100 - - - - - - - - - - 9.18 ans a"
Answer: a
Problem: a sells a bicycle to b and makes a profit of 60 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 112.5
Rationale: "explanation : let cp be 100 a sells at 60 % profit so sp = 160 b sells at 25 % profit = 160 x ( 1 + 25 / 100 ) = 200 cp sp 100 - - - 200 x - - - 225 cp = 225 x 100 / 200 = 112.5 answer : e"
Answer: e
Problem: a shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 2 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 30 % , c ) 50 % , d ) 150 % , e ) 33 %
Rationale: "the total number of mangoes bought by the shopkeeper be 10 . if he buys 5 a rupee , his cp = 2 he selling at 2 a rupee , his sp = 5 profit = sp - cp = 5 - 2 = 3 profit percent = 3 / 2 * 100 = 150 % answer : d"
Answer: d
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 14 cm .
Options: a ) 335 cm 2 , b ) 885 cm 2 , c ) 285 cm 2 , d ) 825 cm 2 , e ) 266 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : e"
Answer: e
Problem: if x is 50 percent greater than 88 , then x =
Options: a ) 68 , b ) 132 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x = 88 * 1.5 = 132 so the answer is b ."
Answer: b
Problem: if x represents the product of the first 15 positive integers , then x is not a multiple of :
Options: a ) a ) 99 , b ) b ) 84 , c ) c ) 72 , d ) d ) 57 , e ) e ) 67
Rationale: a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 72 = 9 * 11 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 19 is not there in first 15 positive numbers it is the only possibility d )
Answer: d
Problem: a can complete a project in 20 days and b can complete the same project in 40 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 20 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 40 ) . ( 1 / 20 ) * ( x - 10 ) + ( 1 / 40 ) * ( x ) = 1 ( x / 20 ) + ( x / 40 ) - ( 10 / 20 ) = 1 3 x / 40 = 3 / 2 x = 20 therefore , the answer is b : 20 ."
Answer: b
Problem: . 005 / ? = . 01
Options: a ) . 5 , b ) . 05 , c ) . 005 , d ) . 0005 , e ) none of them
Rationale: "let . 005 / x = . 01 ; then x = . 005 / . 01 = . 5 / 1 = . 5 answer is a"
Answer: a
Problem: the sum of two consecutive integers is 51 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 5 , 6 , d ) 1 , 2 , e ) 25,26
Rationale: "n + ( n + 1 ) = 51 2 n + 1 = 51 2 n = 50 n = 25 answer : e"
Answer: e
Problem: a can finish a work in 12 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 12 b ' s 1 day work = 1 / 6 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 12 + 1 / 6 ) = 1 / 4 so in one day 1 / 4 work will be done answer : a"
Answer: a
Problem: a train speeds past a pole in 25 seconds and a platform 150 m long in 30 seconds . its length is ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 30 , e ) 19
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 ( x + 150 ) / 30 = x / 25 x = 30 m . answer : d"
Answer: d
Problem: the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum e of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just e = 900 : the answer is c .
Answer: c
Problem: if m is the average ( arithmetic mean ) of the first 10 positive multiples of 3 and if m is the median of the first 10 positive multiples of 3 , what is the value of m – m ?
Options: a ) – 5 , b ) 5 , c ) 0 , d ) 25 , e ) 27.5
Rationale: the first 10 positive multiples of 3 is an evenly spaced set . one of the most important properties of evenly spaced set ( aka arithmetic progression ) is : in any evenly spaced set the arithmetic mean ( average ) is equal to the median . hence m = m - - > m - m = 0 . answer : c .
Answer: c
Problem: subtracting 3 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.97 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 3 % of a = ab . ⇒ ( 97 x a ) / 100 = ab ∴ b = 0.97 correct option : a"
Answer: a
Problem: sachin is older than rahul by 7 years . if the ratio of their ages is 11 : 9 , find the age of sachin
Options: a ) 24.5 , b ) 24.8 , c ) 38.5 , d ) 24.88 , e ) 24.19
Rationale: explanation : if rahul age is x , then sachin age is x + 7 , so , 9 x + 63 = 11 x 2 x = 63 x = 31.5 so sachin age is 31.5 + 7 = 38.5 answer : c ) 38.5
Answer: c
Problem: when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ? putting a value say x = 24 we get remainder as 24 when divided by 61 . when 24 divided by 5 we get 4 as remainder . c is the answer ."
Answer: c
Problem: solve below question 2 x + 1 = - 19
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 10
Rationale: "2 x + 1 = - 19 x = - 10 e"
Answer: e
Problem: a train 150 m long can cross an electric pole in 3 sec and then find the speed of the train ?
Options: a ) 180 , b ) 120 , c ) 72 , d ) 27 , e ) 28
Rationale: "length = speed * time speed = l / t s = 150 / 3 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : a"
Answer: a
Problem: approximately how many revolutions will be made by a car tire with a 10 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 120 , b ) 180 , c ) 1003 , d ) 1000 , e ) 1,440
Rationale: "diameter of car tire = 10 inches radius of car tire = 5 inches = 5 * 2.54 cm = 12.7 cm circumference of the car tire = 2 * pi * 12.7 = 2 * 3.14 * 12.7 = 79.76 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 79.76 = 1003 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"
Answer: c
Problem: calculate the share of z , if rs . 3720 is divided among x , y and z in the ratio 7 : 8 : 11 ?
Options: a ) 1564.1 , b ) 1214.1 , c ) 1574.1 , d ) 1271.1 , e ) 1044.1
Rationale: 7 + 8 + 11 = 26 3720 / 26 = 143.1 so z ' s share = 11 * 143.1 answer : c
Answer: c
Problem: the area of a triangle is with base 18 m and height 6 m ?
Options: a ) 88 m 2 , b ) 10 m 2 , c ) 66 m 2 , d ) 54 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 18 * 6 = 54 m 2 answer : d"
Answer: d
Problem: if a population of women in a town is 50 % of men . what is the population of men as a % of population of women ?
Options: a ) 200 % , b ) 100 % , c ) 50 % , d ) 65 % , e ) 110 %
Rationale: "we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . if . . . . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 5 = 2 = 200 % answer is a"
Answer: a
Problem: 225 mtrs long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 a
Answer: a
Problem: in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3,200 circuit boards where 64 fail inspection ?
Options: a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264
Rationale: total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c
Answer: c
Problem: the rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 400 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 2 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 6 times . 2 ^ 6 * x = 400 x = ( 2 ^ 4 * 25 ) / 2 ^ 6 = 25 / 4 the answer is b ."
Answer: b
Problem: the area of a parallelogram is 288 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 12 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "2 x * x = 288 = > x = 12 answer : a"
Answer: a
Problem: robert ' s salary was increased by 50 % and subsequently decreased by 10 % . how much percentage does he gain ?
Options: a ) 15 % , b ) 20 % , c ) 10 % , d ) 25 % , e ) 30 %
Rationale: let original salary be $ 100 increased salary = 10 % of ( 150 % of $ 100 ) = ( 10 / 100 ) * ( 150 / 100 ) * 100 = $ 15 increase = 15 % correct option is a
Answer: a
Problem: the average ( arithmetic mean ) of 7 , 8 , 10 and 11 equals the average of 2 , 9 , 13 , and
Options: a ) 7 , b ) 9 , c ) 10 , d ) 12 , e ) 13
Rationale: "7 + 8 + 10 + 11 = 2 + 9 + 13 + x 36 = 24 + x or , x = 12 hence , answer will be ( d ) 12"
Answer: d
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 29.16 , the number of the member is the group is :
Options: a ) 57 , b ) 54 , c ) 77 , d ) 87 , e ) 97
Rationale: money collected = ( 29.16 x 100 ) paise = 29.16 paise numbers of members = 2916 squareroot = 54 answer b
Answer: b
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 25 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "800 - - - 200 100 - - - ? = > 25 % answer : b"
Answer: b
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 66 kg . what might be the weight of the new person ?
Options: a ) 56 kg , b ) 90 kg , c ) 86 kg , d ) data inadequate , e ) none of these
Rationale: "c 86 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 66 + 20 ) kg = 86 kg ."
Answer: c
Problem: if ( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) = > 5 ^ 9 * 3 ^ 10 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 9 * 3 ^ 10 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 9 answer b"
Answer: b
Problem: a boat having a length 8 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 160 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 8 x 2 x 0.01 ) m 3 = 0.16 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.16 x 1000 ) kg = 160 kg . answer : d"
Answer: d
Problem: what is the sum between the place values of two 3 ' s in the numeral 63130
Options: a ) 3111 , b ) 300 , c ) 3029 , d ) 3030 , e ) 3003
Rationale: required sum = 3000 + 30 = 3030 answer is d
Answer: d
Problem: lloyd normally works 7.5 hours per day and earns $ 4.00 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 48.00 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 70.00
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.0 + 3 * 4.0 * 1.5 = 48 answer b"
Answer: b
Problem: the average weight of 20 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 48.79286 , b ) 42.25 , c ) 50.87364 , d ) 51.25 , e ) 52.25474
Rationale: "explanation : average weight of 20 boys = 50.25 total weight of 20 boys = 50.25 × 20 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 20 ) + ( 45.15 × 8 ) total boys = 20 + 8 = 28 average weight of all the boys = ( 50.25 × 20 ) + ( 45.15 × 8 ) / 28 = answer : option a"
Answer: a
Problem: what is the difference between the c . i . on rs . 9000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 3.67 , d ) s . 2.83 , e ) s . 2.42
Rationale: c . i . when interest is compounded yearly = [ 9000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 9000 * 26 / 25 * 51 / 50 = rs . 9547.2 c . i . when interest is compounded half - yearly = [ 9000 * ( 1 + 2 / 100 ) 2 ] = ( 9000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 9550.87 difference = ( 9550.87 - 9547.2 ) = rs . 3.67 . answer : c
Answer: c
Problem: a tank is filled by 3 pipes a , b , c in 3 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 20 hr , e ) 21 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 3 7 / x = 1 / 3 x = 21 hours answer is e"
Answer: e
Problem: a girl multiplies 987 by a certain number and obtains 559981 as her answer . if in the answer , both 9 ’ s are wrong but the other digits are correct , then the correct answer will be
Options: a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) none of these
Rationale: 987 = 3 x 7 x 47 . so , required number must be divisible by each one of 3 , 7 , 47 . none of the numbers in 553681 and 555181 are divisible by 3 . while 556581 is not divisible by 7 . correct answer is 555681 . answer : c
Answer: c
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 20 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 20 page ' s copy = ( 20 / 2.5 ) = 8 hrs answer : a"
Answer: a
Problem: a couple spent $ 198 in total while dining out and paid this amount using a credit card . the $ 198 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 130 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 170
Rationale: let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 198 x = $ 150 the correct answer is c .
Answer: c
Problem: in an election , candidate douglas won 58 percent of the total vote in counties x and y . he won 64 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 15 % , b ) 18 % , c ) 25 % , d ) 36 % , e ) 46 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 64 % voted means 64 * 200 = 128 votes combined for xy has 300 voters and voted 58 % so total votes = 174 balance votes = 174 - 128 = 46 as y has 100 voters so 46 votes means 46 % of votes required ans e"
Answer: e
Problem: if x is an integer and 2.134 × 10 ^ x is less than 21,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 21,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 21,000 to remain true , the greatest number is 2,134 , which makes x = 3 e . 3"
Answer: e
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ? a . 480 liters
Options: a ) 480 , b ) 489 , c ) 486 , d ) 482 , e ) 483
Rationale: 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a
Answer: a
Problem: what is the units digit of ( 147 ^ 17 ) ^ 48 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 17 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 48 has the form 4 n , so the units digit is 1 . the answer is a .
Answer: a
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 8 kilometers per hour , while ferry q takes a route that is two times longer . if ferry p is slower than ferry q by 4 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the distance traveled by ferry p is 24 km . then the distance traveled by ferry q is 48 km . ferry q travels at a speed of 12 kph . the time of the journey for ferry q is 48 / 12 = 4 hours , which is 1 hour more than ferry p . the answer is a ."
Answer: a
Problem: find the cost of fencing around a circular field of diameter 39 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 132 , c ) 156 , d ) 158 , e ) 128.73
Rationale: "2 * 22 / 7 * 19.5 = 122.6 122.6 * 1 1 / 2 = rs . 128.73 answer : e"
Answer: e
Problem: the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 78 kg and 93 kg join the group . find the initial number of members in the group ?
Options: a ) 87 , b ) 67 , c ) 23 , d ) 75 , e ) 25
Rationale: let the initial number of members in the group be n . initial total weight of all the members in the group = n ( 48 ) from the data , 48 n + 78 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 69 = > n = 23 therefore there were 23 members in the group initially . answer : c
Answer: c
Problem: in δ pqs above , if pq = 4 and ps = 5 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 16 / 5 , d ) 15 / 4 , e ) 10 / 3
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 4 * 5 / 2 = pr * 6 / 2 pr = 10 / 3 e"
Answer: e
Problem: convert 0.34 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none
Rationale: "answer 0.34 = 34 / 100 = 17 / 50 correct option : c"
Answer: c
Problem: dhoni bought 5 toys with the average cost of $ 10 . if david also buys the sixth toy with the price of $ 16 , what is the average ( arithmetic mean ) price of those 6 toys ?
Options: a ) $ 10 , b ) $ 7 , c ) $ 8.5 , d ) $ 9 , e ) $ 11
Rationale: 5 toys - > total cost = 5 * avg cost = 5 * 10 = 50 sixth toy cost = 16 total cost for 6 toys = 50 + 16 = 66 am = 66 / 6 = 11 hence e
Answer: e
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 1777 meters , d ) 1822 meters , e ) none of these
Rationale: "relative speed of the train with respect to the motorbike should be the speed with which the length of the train is covered in 40 secs . calculate the relative speed = > 100 - 64 = 36 kmph and time is 40 sec = 40 / 3600 hrs distance ( in this case the length of the train ) = s * t = 36 * 40 / 3600 . 4 km or 400 meters . so answer ( a )"
Answer: a
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 350 m long platform ?
Options: a ) 44 sec , b ) 49 sec , c ) 42 sec , d ) 47 sec , e ) none of these
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 350 ) / 36 * 5 / 18 = 47 min . answer : d"
Answer: d
Problem: gold is 10 times as heavy as water and copper is 6 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 10 w c = 6 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 6 wx = x + 1 * 8 w 10 + 6 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b"
Answer: b
Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction q of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives q = 1 / 9 . a"
Answer: a
Problem: what will be the compound interest on a sum of rs . 20,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 8098.56 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 20000 * ( 1 + 12 / 100 ) ^ 3 ] = 20000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 28098.56 c . i . = ( 28098.56 - 20000 ) = rs . 8098.56 answer : a"
Answer: a
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 3 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 3 / 7 , d ) 4 / 9 , e ) 5 / 9
Rationale: "her tips were 3 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 3 / 4 ) ( $ 4 ) = $ 3 so , her total income = $ 4 + $ 3 = $ 7 what fraction of her income for the week came from tips $ 3 / $ 7 = 3 / 7 = c"
Answer: c
Problem: the height of a triangle is decreased by 5 % and its base increased by 10 % . its area will
Options: a ) decrease by 12.5 %
b ) increase by 12.5 %
c ) increase by 4.5 %
d ) increase by 25 %
e ) none of these
Rationale: explanation : let the initial height be 100 and the base be 200 units . â ˆ ´ area = 1 / 2 x 100 x 200 = 10000 sq units now , height = 95 units and base = 220 units â ˆ ´ new area = 1 / 2 x 95 x 220 = 10450 â ˆ ´ area is increased by ( 10450 - 10000 ) / 10000 x 10 = 4.5 % answer : option c
Answer: c
Problem: how many different positive integers exist between 10 ^ 5 and 10 ^ 6 , the sum of whose digits is equal to 2 ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 18
Rationale: "so , the numbers should be from 100,000 to 1 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 100,001 100,010 100,100 101,000 110,000 5 numbers . 2 . one 2 and the rest are 0 ' s : 200,000 1 number . total = 6 numbers . answer : a"
Answer: a
Problem: the average age of 20 students of a class is 20 years . out of these , the average age of 9 students is 11 years and that of the other 10 students is 24 years . the age of the 20 th student is ?
Options: a ) 65 , b ) 61 , c ) 59 , d ) 63 , e ) 64
Rationale: "age of the 20 th student = 20 * 20 - ( 9 * 11 + 10 * 24 ) = 400 - 339 = 61 years answer is b"
Answer: b
Problem: a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 300 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 300 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 500 = 375 300 - - - - - - - - - - - - - 75 1 / 4 - - - - - - - - 75 1 - - - - - - - - - ? = > rs . 300 answer : d"
Answer: d
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 800 sq . ft , how many feet of fencing will be required ?
Options: a ) 100 feet , b ) 120 feet , c ) 150 feet , d ) 180 feet , e ) 186 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 800 = > breadth = 40 feet area to be fenced = 2 b + l = 2 * 40 + 20 = 100 feet answer : option a"
Answer: a
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) rs . 1090 , b ) rs . 1160 , c ) rs . 1190 , d ) rs . 1202 , e ) none
Rationale: "solution s . p = 90 % of rs . 1400 = rs . ( 90 / 100 × 1400 ) rs . 1260 . answer ce"
Answer: e
Problem: every day daniel drives 60 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 60 miles at 4 miles / hour . d = ( r ) ( t ) 60 = ( 4 ) ( t ) 60 / 4 = 15 = t it takes 15 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 28 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 28 = ( 2 ) ( t ) 28 / 2 = 14 = t it takes 14 hours for the second part total time to drive home on monday = 4 + 14 = 18 hours we ' re asked by what percent 18 hours is greater than 15 hours . 18 / 15 = 1.2 , so it is 20 % greater . b"
Answer: b
Problem: the length of a rectangle is halved , while its breadth is tripled . watis the % change in area ?
Options: a ) 43 % , b ) 47 % , c ) 50 % , d ) 65 % , e ) 68 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Problem: the number of sailors on a ship is 85 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 37 : 20 , b ) 47 : 20 , c ) 47 : 25 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.85 * officer sailor / officer = 1.85 / 1 = 185 / 100 = 37 / 20 answer will be a"
Answer: a
Problem: a goods train runs at the speed of 72 km / hr and crosses a 270 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 278 , b ) 166 , c ) 151 , d ) 250 , e ) 109
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 270 ) / 26 = 20 x = 250 m . answer : d"
Answer: d
Problem: the volume of water inside a swimming pool doubles every hour . if the pool is filled to its full capacity within 8 hours , in how many hours was it filled to one quarter of its capacity ?
Options: a ) 2
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: d
Answer: d
Problem: if pintu is coded as 79523 in a certain code language , how would you code mintu in the same language ?
Options: a ) 13426 , b ) 14236 , c ) 49523 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . mintu is 49523 . . . answer : c"
Answer: c
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 y 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 = y = 10 ans e ."
Answer: e
Problem: evaluate : 2.5 + 0.0005
Options: a ) 2000 , b ) 3000 , c ) 1000 , d ) 5000 , e ) 4000
Rationale: "25 / 0.0005 = ( 25 * 10000 ) / ( 0.0005 * 10000 ) = 25000 / 5 = 5000 answer is d ."
Answer: d
Problem: it costs $ 2 for the first 1 / 5 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 2 hours and 15 minutes , how much will it cost him ?
Options: a ) $ 25 . , b ) $ 26 . , c ) $ 29 . , d ) $ 30 . , e ) $ 31 .
Rationale: "2 hrs 15 min = 135 min first 12 min - - - - - - > $ 2 time left is 135 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 135 min costs $ 12 / 60 * 135 = > $ 27 so , total cost will be $ 27 + $ 2 = > $ 29 hence answer will be c"
Answer: c
Problem: a train 200 m long can cross an electric pole in 5 sec and then find the speed of the train ?
Options: a ) 114 , b ) 124 , c ) 134 , d ) 144 , e ) 154
Rationale: "length = speed * time speed = l / t s = 200 / 5 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : d"
Answer: d
Problem: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 1 / 9 meters . what is value of the radius in meters ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 1 / 9 ) which is about 9 r = 3 the answer is b ."
Answer: b
Problem: a person crosses a 800 m long street in 5 minutes . what is his speed in km per hour ?
Options: a ) 1.23 , b ) 2.86 , c ) 4.36 , d ) 9.25 , e ) 9.61
Rationale: "distance = 800 meter time = 5 minutes = 5 x 60 seconds = 300 seconds speed = distance / time = 800 / 300 = 2.67 m / s = 2.67 ã — 18 / 5 km / hr = 9.61 km / hr answer : e"
Answer: e
Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 20 : 50 : 80 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 520 , b ) 640 , c ) 700 , d ) 750 , e ) 800
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 20 : 50 : 80 initial soap : alcohol = 20 / 50 = 20 : 50 after doubled soap : alcohol = 2 * 20 / 50 = 40 : 50 initial soap : water = 20 / 80 = 20 : 80 after halved soap : water : 1 / 2 * 20 / 80 = 10 / 80 = 10 : 80 after soap : alcohol : water - - > 40 : 50 : 320 - - > 4 : 5 : 32 given alcohol 100 cubic centimeter . ratio is 80 : 100 : 640 ( 4 : 5 : 32 ) for 100 cubic centimeter of alcohol - - - 640 cubic cm water is required . answer - b"
Answer: b
Problem: in a 100 m race , sam beats john by 5 seconds . on the contrary , if sam allowed john to start 15 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 4 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 17 seconds
Rationale: "their difference is 5 second but this difference is 0 if john allows sam to start the race from 15 m ahead . that means jhon was 15 m away from finishing line when they started together . so he will cover 15 m in 5 seconds . so his speed = 15 / 5 = 3 metre / second . so time taken = 100 / 5 = 20 seconds . so sam took = 17 seconds . correct answer = e"
Answer: e
Problem: a 150 meter long train crosses a man standing on the platform in 3 sec . what is the speed of the train ?
Options: a ) 176 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 180 kmph
Rationale: "s = 150 / 3 * 18 / 5 = 180 kmph answer : e"
Answer: e
Problem: in an examination , 300 students appeared . out of these students ; 29 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 51 , b ) 37 , c ) 54 , d ) 99 , e ) 01
Rationale: "the number of students with first division = 29 % of 300 = 29 / 100 × 300 = 8700 / 100 = 87 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 87 + 162 ) = 51 answer : a"
Answer: a
Problem: the length of rectangle is thrice its breadth and its perimeter is 104 m , find the area of the rectangle ?
Options: a ) 507 sq m , b ) 356 sq m , c ) 452 sq m , d ) 428 sq m , e ) 525 sq m
Rationale: "2 ( 3 x + x ) = 104 l = 39 b = 13 lb = 39 * 13 = 507 answer : a"
Answer: a
Problem: if x + y = 20 , x - y = 36 , for integers of x and y , x = ?
Options: a ) 20 , b ) 25 , c ) 28 , d ) 20 , e ) 42
Rationale: "x + y = 20 x - y = 36 2 x = 56 x = 28 answer is c"
Answer: c
Problem: if x , y is 20 % , 25 % greater than z then how much percentage is x smaller than y ?
Options: a ) 3 1 / 13 % , b ) 3 % , c ) 3 11 / 13 % , d ) 4 % , e ) none of these
Rationale: explanation : x = 125 % y = 130 % z = 100 % x - y / y * 100 = 5 / 130 * 100 = 500 / 130 % = 3 11 / 13 % smaller than y answer : option c
Answer: c
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 14 % , then the cost price of the article is :
Options: a ) 500 , b ) 540 , c ) 555 , d ) 664 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 114 = rs . 540 answer : option b"
Answer: b
Problem: the speed of a boat in still water is 14 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 8 minutes is
Options: a ) 1.6 km , b ) 2.5 km , c ) 3.6 km , d ) 4 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 14 + 5 ) kmph = 19 kmph . distance travelled = ( 19 x 8 / 60 ) km = 2.5 km option b"
Answer: b
Problem: what is the tens digit of 6 ^ 19 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 19 has the form 5 n + 4 , so the tens digit of 6 ^ 19 is 9 . the answer is e .
Answer: e
Problem: aa is two digit number then m times its cube of aa has 1 in its tens place then what is m .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when aa = 11 7 * ( 11 ) ^ 3 = 7 * 1331 = 9317 m = 7 answer : e
Answer: e
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability w that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability w = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Problem: the curved surface of a sphere is 64 π cm 2 . find its radius ?
Options: a ) 8
b ) 3
c ) 4
d ) 9
e ) 7
Rationale: explanation : 4 π r 2 = 64 = > r = 4 answer : option c
Answer: c
Problem: dhoni spent 25 percent of his earning last month on rent and 10 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 50 % , b ) 55 % , c ) 60 % , d ) 62 % , e ) 52.5 %
Rationale: "say dhoni ' s earning last month was $ 100 . dhoni spent 30 percent of his earning last month on rent - - > $ 25 on rent ; 10 percent less than what he spent on rent to purchase a new dishwasher - - > $ 25 * 0.9 = $ 22.5 on the dishwasher . left over amount 100 - ( 25 + 22.5 ) = $ 52.5 answer : e"
Answer: e
Problem: a present value of a machine is $ 800 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 648
Rationale: "p = $ 800 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 800 * 9 / 10 * 9 / 10 = $ 648 answer is e"
Answer: e
Problem: the effective annual rate of interest corresponding to a nominal rate of 16 % per annum payable half - yearly is ?
Options: a ) 16.64 % , b ) 16.07 % , c ) 16.08 % , d ) 16.09 % , e ) 16.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 8 / 100 ) 2 ] = rs . 116.64 effective rate = ( 116.64 - 100 ) = 116.64 % answer : a"
Answer: a
Problem: cost of 2 bats and 3 balls is rs . 1300 . the cost of 3 bats and 2 balls is rs . 1200 . the cost of each balls is more than that of each bat by ?
Options: a ) 50 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: 2 bats + 3 ball = 1300 - - - ( 1 ) 3 bats + 3 ball = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - bats + ball = 100 = > ball - bats = 100 b
Answer: b
Problem: m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 2 , - 1 , 1 , 2 , 3 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: answer e . total # of outcomes : 5 * 5 = 25 # of outcomes where product is - ve : ( - 6,1 ) , ( - 6,2 ) , ( - 6,3 ) . . . hence , total : 15 probability : 15 / 25 = 3 / 5
Answer: e
Problem: what will be the vulgar fraction of 0.5
Options: a ) 3 / 5 , b ) 1 / 2 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.5 = 50 / 100 = 1 / 2 option b"
Answer: b
Problem: what is the total cost of 2 sandwiches at $ 2.45 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 8.38 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 11.85
Rationale: "answer = a 2 * 2.45 + 4 * 0.87 = 2 ( 2.50 - 0.05 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.1 - 0.52 = 9 - 0.62 = 8.38"
Answer: a
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 50 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 , b ) 27 , c ) 45 , d ) 99 , e ) 12
Rationale: "relative speed = 50 + 30 = 80 km / hr . 80 * 5 / 18 = 200 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 200 = 45 sec . answer : c"
Answer: c
Problem: set x consists of all two - digit primes and set y consists of all positive even multiples of 5 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 92 , e ) 95
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 10 , 20 , 30 , . . . . . . . . . . . . . . . , 70 , 80 , 90 } combining two sets , say set z set z = { 10,11 , 13 , 17 , 20,30 , . . . . . . . . . . . . . . . . . . . , 70 , 80 , 83 , 89 , 90 , 97 } range = max value - min value range ( z ) = 97 - 10 = 87 oa a is the answer ."
Answer: a
Problem: a woman complete a journey in 5 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 112 km . , d ) 224 km . , e ) 544 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 5 - - > x / 21 + x / 24 = 10 - - > x = 112 km . c"
Answer: c
Problem: a rectangular field is to be fenced on three sides leaving a side of 34 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 74 ft , b ) 88 ft , c ) 22 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 34 x breadth = 680 breadth = 20 feet area to be fenced = 2 b + l = 2 ( 20 ) + 34 = 88 feet answer : a ) 74 ft"
Answer: a
Problem: how many shots of 1 cm radius can be prepared from a sphere of 6 cm radius ?
Options: a ) 33 , b ) 88 , c ) 216 , d ) 288 , e ) 299
Rationale: "4 / 3 ï € * 6 * 6 * 6 = 4 / 3 ï € * 1 * 1 * 1 * x x = 216 answer : c"
Answer: c
Problem: a man can do a piece of work in 5 days , but with the help of his son , he can finish it in 4 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 7 1 / 2 , d ) 6 , e ) 20
Rationale: "son ' s 1 day work = 1 / 4 - 1 / 5 = 1 / 20 son alone can do the work in 20 days = 20 days answer is e"
Answer: e
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the standard deviation for the exam ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 0 , e ) 2
Rationale: "mean - 2 sd = 58 mean + 3 sd = 98 by solving above equation we get , sd ( absolute value ) = 8 ans . c"
Answer: c
Problem: a man & his wife appear in an interview for 2 vacancies in the same post . the probability of husband ' s selection is 1 / 7 & the probability of wife ' s selection is 1 / 5 . what is the probability that only 1 of them is selected ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 7 , d ) 3 / 11 , e ) 4 / 5
Rationale: let a = event that the husband is selected and b = event that the wife is selected . then , p ( a ) = 1 / 7 and p ( b ) = 1 / 5 ∴ p ( a ¯ ) = ( 1 - 17 / 5 ) = 6 / 7 and = ( 1 - 1 / 5 ) = 4 / 5 required probability = p [ ( a and not b ) or ( b and not a ) ] = p [ ( a and b ¯ ) or ( b and a ¯ ) ] = p ( a and b ¯ ) + p ( b and a ¯ ) = p ( a ) . p ( b ¯ ) + p ( b ) . p ( a ¯ ) = ( 1 / 7 * 4 / 5 ) + ( 1 / 5 * 6 / 7 ) = 10 / 35 = 2 / 7 c
Answer: c
Problem: find the length of the wire required to go 11 times round a square field containing 27889 m 2 .
Options: a ) 7348 , b ) 3388 , c ) 2667 , d ) 8766 , e ) 66711
Rationale: "a 2 = 27889 = > a = 167 4 a = 668 668 * 11 = 7348 answer : a"
Answer: a