regisss/math_qa huggingface dataset:
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 14 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 77 , c ) 48 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 14 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 14 = 4 / 9 ( t - 14 ) 10 t = 1386 - 616 = > t = 77 . answer : b"
Answer: b
Problem: the population of a town increased from 1 , 75000 to 2 , 97500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) 7 %
Rationale: solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 ã — 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e
Answer: e
Problem: the workforce of company x is 40 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 50 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 480 , b ) 500 , c ) 520 , d ) 460 , e ) 440
Rationale: "let x be the total worker then 0.4 x = female worker and 0.6 x is male worker then 20 male worker added 04 x / ( 0.6 x + 20 ) = 50 / 100 or 40 x = 50 * ( 0.6 x + 100 ) = 30 x + 5000 or 10 x = 5000 , x = 500 total worker = 500 + 20 = 520 c"
Answer: c
Problem: the ratio of kamla and nisha is 6 : 5 and the sum of their ages is 44 . what will be the ratio of their ages after 8 years .
Options: a ) 5 : 6 , b ) 7 : 8 , c ) 8 : 7 , d ) 12 : 11 , e ) 14 : 13
Rationale: answer : let age of kamla is 6 x and age of nisha is 5 x . then , 6 x + 5 x = 4411 x = 44 , x = 4 after 8 year the ratio of their ages = 6 x + 8 / 5 x + 8 = 8 : 7 answer c
Answer: c
Problem: two identical cubes if one of them is painted pink on its 4 side and blue on the remaining two side then how many faces painted pink to other cube so that probability of getting cube is 1 / 3 when we roll both the cube .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: 0 faces should be painted pink i . e all faces blue answer : a
Answer: a
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 25 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 11.79 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 25 = 9 * 12 / 5 = 21.6 time difference = 11.79 ans : a"
Answer: a
Problem: the cost price of a radio is rs . 2400 and it was sold for rs . 1980 , find the loss % ?
Options: a ) 17 % , b ) 12 % , c ) 22 % , d ) 24 % , e ) 21
Rationale: "2400 - - - - 420 100 - - - - ? = > 17 % answer : a"
Answer: a
Problem: a couple spent $ 132 in total while dining out and paid this amount using a credit card . the $ 132 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 ) $ 100 , b ) $ 104 , c ) $ 108 , d ) $ 112 , e ) $ 116
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 = 132 x = 100 the correct answer is a ."
Answer: a
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 28 , b ) 19 , c ) 22 , d ) 20 , e ) 21
Rationale: "let the total number of workers be x . then , 8000 x = ( 14000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 56000 = x = 28 . answer : a"
Answer: a
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 52 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 10 , b ) 36 , c ) 38 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 6 ) ( b + 6 ) = m + 52 - - - - - - - - - > ( l + 6 ) ( b + 6 ) - 52 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 6 ) ( b + 6 ) - 52 lb + 2 l + 2 b + 4 = lb + 6 l + 6 b + 36 - 52 simplify 4 l + 4 b = 20 - - - - - - > 2 ( l + b ) = 10 ( check eq ( 1 ) ) answer is a"
Answer: a
Problem: uncle bruce is baking chocolate chip cookies . he has 50 ounces of dough ( with no chocolate ) and 40 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 30 % chocolate ?
Options: a ) 22.86 , b ) 23.86 , c ) 25 , d ) 26 , e ) 27
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 70 % * total = 40 = > ( 7 / 10 ) total = 40 = > total = 400 / 7 = > total = 57.14 oz , from there , you must find 30 % of the total 57.14 oz of the mixture . 30 % * total = > ( 3 / 10 ) ( 57.14 ) = 17.14 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 40 - 17.14 = 22.86 oz chocolate left over . answer : a"
Answer: a
Problem: in arun ' s opinion , his weight is greater than 61 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 64 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 62.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: let arun ' s weight be x kg . according to arun , 61 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 64 . the values satisfying all the above conditions are 62 and 63 . required average = ( 62 + 63 ) / 2 = 62.5 kg answer : b
Answer: b
Problem: a and b together have $ 1210 . if of a ' s amount is equal to of b ' s amount , how much amount does b have ?
Options: a ) $ 400 , b ) $ 489 , c ) $ 484 , d ) $ 365 , e ) % 342
Rationale: ( 4 / 15 ) a = ( 2 / 5 ) b = > a = ( ( 2 / 5 ) * ( 15 / 4 ) ) b = > a = ( 3 / 2 ) b = > a / b = 3 / 2 a : b = 3 : 2 b ' s share = rs . ( 1210 * ( 2 / 5 ) ) = $ 484 option c
Answer: c
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 28 % , c ) 60 % , d ) 26 % , e ) 30 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 80 2 / 3 sp 1 = 80 sp 1 = 120 100 - - - 20 = > 20 % answer : a"
Answer: a
Problem: what is the minimum value of | x - 4 | + | x + 6 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 6 | > = 0 - - > minimum occurs at x = - 6 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 6 - - > result = 10 + 0 + 11 = 21 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 10 + 1 = 11 x = 5 - - > result = 1 + 11 + 0 = 12 x = 6 - - > result = 2 + 12 + 1 = 15 so minimum value of the expression occurs at x = 4 and the resultant value = 11 answer : e
Answer: e
Problem: how many five - digit numbers that do not contain the digits 4 or 7 are there ?
Options: a ) 44648 , b ) 27844 , c ) 28642 , d ) 16864 , e ) 32458
Rationale: "we can have 7 digits ( 1 , 2,3 , 5,6 , 8,9 ) for the first place ( ten thousand ' s place ) . and similarly 8 digits for thousand ' s , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 5,6 , 8,9 ) so in total 7 * 8 * 8 * 8 * 8 = 28672 hence c"
Answer: c
Problem: the larger interior angle of a parallelogram is 90 ° more than its smaller interior angle . what is the measure of the smaller interior angle of the parallelogram ?
Options: a ) 90 ° , b ) 75 ° , c ) 60 ° , d ) 45 ° , e ) 30 °
Rationale: let smaller be x , larger becomes x + 90 . . . total of all angles = 360 so 4 x + 180 = 360 and x = 45 answer : d
Answer: d
Problem: a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a bridge of 800 meter length ?
Options: a ) 72 seconds , b ) 27 seconds , c ) 40 seconds , d ) 128 seconds , e ) 18 seconds
Rationale: "speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 + 800 = 1200 meter time = distance / speed = 1200 * ( 9 / 150 ) = 72 seconds answer : a"
Answer: a
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 200 per month . what is his monthly salary ?
Options: a ) rs . 5000 , b ) rs . 25000 , c ) rs . 7500 , d ) rs . 8500 , e ) rs . 9500
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 – 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 200 = > 5000 answer : a"
Answer: a
Problem: the average height of 20 students is 20 cm and the average height of 11 students is 20 cm . what is the average height of the 31 students ?
Options: a ) 40 cm , b ) 20 cm , c ) 30 cm , d ) 25 cm , e ) 35 cm
Rationale: the total height of the 31 students = ( 20 * 20 ) + ( 11 * 20 ) = 400 + 220 = 620 cm the required average height = 620 / 31 = 20 cm answer : b
Answer: b
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , two - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were left - handed - - > 6 * 2 / 3 = 4 were left - handed and 2 right - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : d
Answer: d
Problem: excluding the stoppages , the speed of a bus is 64 km / hr and including the stoppages the speed o the bus is 48 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 28 , e ) 91
Rationale: answer : b ) 15 minutes
Answer: b
Problem: what amount does an investor receive if the investor invests $ 3000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 3420 , b ) $ 3630 , c ) $ 3870 , d ) $ 4040 , e ) $ 4220
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 3630 the answer is b ."
Answer: b
Problem: a fruit seller sells mangoes at the rate of rs . 12 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.82 , b ) rs 9.82 , c ) rs 10.82 , d ) rs 14.82 , e ) none of these
Rationale: "explanation : 85 : 12 = 105 : x x = ( 12 × 105 / 85 ) = rs 14.82 option d"
Answer: d
Problem: a sells a bicycle to b and makes a profit of 35 % . b sells the same bicycle to c at a profit of 45 % . 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 ) 115
Rationale: "explanation : let cp be 100 a sells at 35 % profit so sp = 135 b sells at 45 % profit = 135 x ( 1 + 45 / 100 ) = 195.75 cp sp 100 - - - 195.75 x - - - 225 cp = 225 x 100 / 195.75 = 114.94 answer : e"
Answer: e
Problem: how many zeros does 10 ! end with ?
Options: a ) 10 , b ) 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "according to above 10 ! has 10 / 5 = 2 = 2 trailing zeros . answer : e"
Answer: e
Problem: find the value of y from ( 12 ) ^ 2 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 432
Rationale: 432 e
Answer: e
Problem: find the simple interest on rs . 5000 at 6 % per annum for the period from 5 th feb to 19 th april , 2015 .
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 60 , d ) rs . 70 , e ) none of these
Rationale: "explanation : given : 1 ) principal = rs . 5000 2 ) rate of interest = 6 % 3 ) time = 5 th feb to 19 th april , 2015 first find the time period 5 th feb to 19 th april , 2015 feb = 28 – 5 = 23 days march = 31 days april = 19 days total days = 23 + 31 + 19 = 73 days convert days into years , by dividing it by 365 time = 73 / 365 = 1 / 5 simple interest = ( p × r × t ) / 100 = [ 5000 × 6 × ( 1 / 5 ) ] / 100 = rs . 60 simple interest = rs . 60 answer is c"
Answer: c
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 36 km / hr . what is the length of the platform ?
Options: a ) 160 , b ) 240 , c ) 288 , d ) 277 , e ) 221
Rationale: "speed = 36 * 5 / 18 = 10 m / sec . length of the train = 10 * 20 = 200 m . let the length of the platform be x m . then , ( x + 200 ) / 36 = 10 = > x = 160 m . answer : a"
Answer: a
Problem: car a runs at the speed of 42 km / hr & reaches its destination in 6 hr . car b runs at the speed of 52 km / h & reaches its destination in 9 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 7 : 13 , c ) 13 : 7 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 42 × 6 = 252 km distance travelled by car b = 52 × 9 = 468 km ratio = 252 / 468 = 7 : 13 b"
Answer: b
Problem: the speed of a car is 90 km in the first hour and 55 km in the second hour . what is the average speed of the car ?
Options: a ) 72.5 kmph , b ) 75 kmph , c ) 87 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 90 + 55 ) / 2 = 72.5 kmph answer : a"
Answer: a
Problem: by selling 15 pencils for a rupee a man loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "75 % - - - 15 125 % - - - ? 75 / 125 * 15 = 9 answer : b"
Answer: b
Problem: find the remainder of the division ( 3 ^ 14 ) / 4 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "find the pattern of the remainders after each power : ( 3 ^ 1 ) / 4 remainder 3 ( 3 ^ 2 ) / 4 remainder 1 - - > this is where the cycle ends ( 3 ^ 3 ) / 4 remainder 3 - - > this is where the cycle begins again ( 3 ^ 4 ) / 4 remainder 1 continuing the pattern to ( 3 ^ 14 ) / 4 gives us a remainder of 1 final answer : a ) 1"
Answer: a
Problem: a certain machine produces 850 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 7 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 142,800 , e ) 168,000
Rationale: "since 7 days consist of 24 * 7 hours the total hours of a week is 168 hours . since every hour the machine produces 850 units of product p the total product during 168 hours is 850 * 168 = 142,800 . correct option : d"
Answer: d
Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 5 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 7429
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 5 ) = rs . 7429 . answer : option e"
Answer: e
Problem: a contractor undertakes to built a walls in 50 days . he employs 70 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 105 , b ) 30 , c ) 35 , d ) 20 , e ) none of these
Rationale: "70 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 70 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 70 × 25 × 0.6 / 25 × 0.4 = 105 men answera"
Answer: a
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 answer , e ) 95
Rationale: "the square roots of all numbers from answer choices are between 9 and 10 , so the product of primes of the number we are looking should be less then 9 , so this number should have only 2 - s , only 3 - s , only 5 - s , or only 2 - s and 3 - s as its primes . only 96 satisfies this . answer : d ."
Answer: d
Problem: in how many no . between 10 and 40 exactly two of the digits is 4 ?
Options: a ) 10 , b ) 15 , c ) 35 , d ) 1 , e ) 45
Rationale: "it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even ae are large to have correct choice . ans : d"
Answer: d
Problem: 10 people went to a hotel for combine dinner party 8 of them spent rs . 10 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 110 , c ) 1492 , d ) 1496 , e ) none of these
Rationale: "solution : let average expenditure of 10 people be x . then , 10 x = 8 * 10 + 2 * ( x + 4 ) ; or , 10 x = 10 * 10 + 2 x + 8 ; or , x = 11 ; so , total money spent = 11 * 10 = rs . 110 . answer : option b"
Answer: b
Problem: a carpenter worked alone for 1 day on a job that would take him 6 more days to finish . he and another carpenter completed the job in 5 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 4.5 , b ) 7.5 , c ) 9.5 , d ) 17.5 , e ) 24.5
Rationale: a carpenter worked only 1 day on something that takes him 6 more days . means ; carpenter finishes his work in 7 days . let his buddy finish the same task in x days . respective rates per day : 1 / 7 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 7 per day . second one worked for 5 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 7 + 5 * 1 / x = 1 5 x + 35 = 7 x 2 x = 35 x = 17.5 days . ans : d
Answer: d
Problem: find the least number of five digits which is exactly divisible by 12 and 18 ?
Options: a ) a ) 1080 , b ) b ) 10080 , c ) c ) 10025 , d ) d ) 11080 , e ) e ) 12080
Rationale: "the smallest five digit numbers are 10025 , 10080,11080 10025 is not divisible by 12 10080 is divisible by both 12 and 18 answer : b"
Answer: b
Problem: how many odd prime numbers are there less than 75 ?
Options: a ) 20 , b ) 1 , c ) 2 , d ) 16 , e ) 17
Rationale: "odd prime number less than 75 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 there is 20 the odd prime number answer is a"
Answer: a
Problem: a is twice as good a workman as b and they took 7 days together to do the work b alone can do it in .
Options: a ) 23 days , b ) 25 days , c ) 21 days , d ) 26 days , e ) 29 days
Rationale: "c 21 days wc = 2 : 1 2 x + x = 1 / 7 x = 1 / 21 = > 21 days"
Answer: c
Problem: if x is a positive integer with fewer than 3 digits , what is the probability that c x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability c that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Problem: if the cost price of 65 chocolates is equal to the selling price of 50 chocolates , the gain percent is :
Options: a ) 35 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 33 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 50 chocolates = rs . 50 ; s . p . of 50 chocolates = rs . 65 . . ' . gain % = 15 * 100 / 50 = 30 % answer : d"
Answer: d
Problem: a train , 155 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 155 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 155 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 155 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 155 + x = > 45 ã — 10 ã — 10 / 12 = 155 + x = > 15 ã — 10 ã — 10 / 4 = 155 + x = > 15 ã — 25 = 155 + x = 375 = > x = 375 - 155 = 220 answer : option d"
Answer: d
Problem: sachin is younger than rahul by 7 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 24.1
Rationale: "if rahul age is x , then sachin age is x - 7 , so ( x - 7 ) / x = 7 / 9 = > 9 x - 63 = 7 x = > 2 x = 63 = > x = 31.5 so sachin age is 31.5 - 7 = 24.5 answer : b"
Answer: b
Problem: the present population of a town is 500 . population increase rate is 10 % p . a . find the population of town before 2 years ?
Options: a ) 512 , b ) 615 , c ) 810 , d ) 413 , e ) 123
Rationale: "p = 500 r = 10 % required population of town = p / ( 1 + r / 100 ) ^ t = 500 / ( 1 + 10 / 100 ) ^ 2 = 500 / ( 11 / 10 ) ^ 2 = 413 ( approximately ) answer is d"
Answer: d
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 5,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 . the answer is c ."
Answer: c
Problem: the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 90 cents more than the commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 90 = $ 1.10 cents on commodity y , which will take 11 years . the answer is c .
Answer: c
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 650 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 725 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 1000 , b ) 1,250 , c ) 2,250 , d ) 3,250 , e ) 4,250
Rationale: so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 325 , thus 0.2 x = $ 325 - - > x = $ 1625 since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,625 = $ 3,250 answer d
Answer: d
Problem: at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 70 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 29 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 3
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 70 % of 60 = 42 total new books = 58 fraction = 16 / 58 = 8 / 29 ans : b"
Answer: b
Problem: 10 years ago , the age of anand was one - third the age of bala at that time . the present age of bala is 10 years more than the present age of anand . find the present age of anand ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: let the present ages of anand and bala be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 10 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 0 ) = > 3 a - 30 = a = > 2 a = 30 = > a = 15 . answer : d
Answer: d
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 17 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.3 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 17 = 403 hence , new average = 403 ⁄ 10 = 40.3 answer a"
Answer: a
Problem: nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 4 screws and 2 nails ?
Options: a ) 4 , b ) 5 / 2 , c ) 2 , d ) 3 / 2 , e ) 5 / 4
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 4 s and 2 n = 4 s + 2 * 4 s = 12 s . . ratio = 15 s / 12 s = 15 / 12 = 5 / 4 answer : e"
Answer: e
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1200 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 24750 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1200 × 20.625 ) = 24750 . answer c"
Answer: c
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 6 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 6 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 6 * ( 2 / 3 ) ) days = > 30 days answer : a
Answer: a
Problem: 4 brothers adam , bill , charles and david together contributed certain amount of money and purchased a car . the contribution made by adam is half that of the total contribution made by the other 3 brothers , contribution made by bill is one - fourth of the total contribution made by the other 3 brothers and the contribution made by charles is two - third of the total contribution made by the other 3 brothers . if the total price of the car is $ 9750 , find the contribution made by david .
Options: a ) $ 540 , b ) $ 580 , c ) $ 600 , d ) $ 650 , e ) $ 680
Rationale: given that a : ( b + c + d ) = 1 : 2 . hence a contributed 1 / 3 rd of the total price . given b : ( a + c + d ) = 1 : 4 hence b contributed 1 / 5 th of the total price . given c : ( a + b + d ) = 2 : 3 hence c contributed 2 / 5 th of the total price . thus the contribution made by a , b and c = 1 / 3 + 1 / 5 + 2 / 5 = 14 / 15 so , the remaining 1 / 15 th of the price is contributed by david . hence david ' s contribution = 1 / 15 × 9750 = $ 650 . the answer is d .
Answer: d
Problem: share rs . 6000 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 2000
Rationale: "amount received by sanjay . 4 / 12 x 6000 = 2000 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 2000 . e"
Answer: e
Problem: a worker makes a toy in every 2 h . if he works for 120 h , then how many toys will he make ?
Options: a ) 40 , b ) 60 , c ) 45 , d ) 39 , e ) none
Rationale: "no . of toys = 120 / 2 = 60 answer : b"
Answer: b
Problem: find the sum of all odd numbers up to 100 .
Options: a ) 2500 , b ) 2400 , c ) 2300 , d ) 2200 , e ) 2100
Rationale: "the given numbers are 1 , 3 , 5 , 7 , . . . , 99 . this is an a . p . with a = 1 and d = 2 . let it contain n terms . then , 1 + ( n - 1 ) x 2 = 99 or n = 50 . required sum = n / 2 ( first term + last term ) = 50 / 2 ( 1 + 99 ) = 2500 . answer is a ."
Answer: a
Problem: there are , in a certain league , 20 teams , and each team face another team for a total of 4 times . how many games are played in the season ?
Options: a ) 450 , b ) 760 , c ) 110 , d ) 180 , e ) 400
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 760 option b ."
Answer: b
Problem: if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 12 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 6
Rationale: "p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 12 / 15 ) / ( 2 / 15 ) = 6 . e"
Answer: e
Problem: the water level in a rectangular swimming pool measuring 20 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100
b ) 250
c ) 1875
d ) 1200
e ) 5625
Rationale: 6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 20 * 25 * 1 / 2 = 250 feet ^ 3 of water must be removed , which equals to 250 * 7.5 = 1875 gallons . answer : c .
Answer: c
Problem: a man buys rs . 20 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 18
Rationale: dividend on rs 20 = 9 / 100 * 20 = 9 / 5 is 12 income 100 9 / 5 is an income on rs ( 100 / 12 * 9 / 5 ) = rs 15 answer d
Answer: d
Problem: a car travels first 160 km at 75 km / hr and the next 160 km at 90 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 81.81
Rationale: "car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 90 km / hr time taken to travel next 160 km = distancespeed = 160 / 90 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 75 + 160 / 90 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 90 ) = 81.81 km / hr answer : e"
Answer: e
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 360 . how much does c have ?
Options: a ) 60 , b ) 78 , c ) 267 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 360 - - - - - - - - - - - - - - a + b + 2 c = 560 a + b + c = 500 - - - - - - - - - - - - - - - - c = 60 answer : a"
Answer: a
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 190 games will be played during the tournament . what is the number of participants ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 190 n * ( n - 1 ) = 380 = 20 * 19 ( trial and error ) the answer is d ."
Answer: d
Problem: a certain number of men can finish a piece of work in 10 days . however , if there were 10 less men it will take 10 days more for the work to be finished . how many men were there originally ?
Options: a ) 10 men , b ) 30 men , c ) 40 men , d ) 20 men , e ) none of these
Rationale: "let x be the number of men originally thus , 10 x = ( 10 + 10 ) ( x - 10 ) 10 x = 20 ( x - 10 ) x = 2 ( x - 10 ) x = 20 answer : d"
Answer: d
Problem: find the average of all numbers between 4 and 34 which are divisible by 5
Options: a ) 20 , b ) 21 , c ) 25 , d ) 30 , e ) 55
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 5 = 105 / 5 = 21 option b"
Answer: b
Problem: how can a cake ( circular ) be cut into 8 pieces by making just 3 cuts ?
Options: a ) 21
b ) 787
c ) 37
d ) 26
e ) 01
Rationale: explanation : cut the cake using three mutually perpendicular planes . it leaves 8 pieces , one each in each octant . answera
Answer: a
Problem: the bankers discount of a certain sum of money is rs . 72 and the true discount on the same sum for the same time is rs . 60 . the sum due is :
Options: a ) rs . 360 , b ) rs . 432 , c ) rs . 540 , d ) rs . 1080 , e ) rs . 1280
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 72 * 60 ) / 72 - 60 ; 360 answer : a"
Answer: a
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1000 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 15,600 , d ) rs . 20,625 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1000 x 20.625 ) = rs . 20625 . answer d"
Answer: d
Problem: find the value of x in [ ( 17.28 / x ) / ( 3.6 * 0.2 ) ] = 2
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: ( 17.28 / x ) = 2 * 3.6 * 0.2 x = ( 17.28 / 1.44 ) = ( 1728 / 14 ) = 12 . option b
Answer: b
Problem: set a contains all the even numbers between 22 and 70 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 1200 , e ) 1400
Rationale: "each term in set b is 40 more than the corresponding term in set a . the difference of the sums = 25 * 40 = 1000 . the answer is c ."
Answer: c
Problem: a person travels from p to q a speed of 40 km / hr and returns by increasing his speed by 50 % . what is his average speed for both the trips ?
Options: a ) 27 , b ) 87 , c ) 48 , d ) 77 , e ) 51
Rationale: "speed on return trip = 150 % of 40 = 60 km / hr . average speed = ( 2 * 40 * 60 ) / ( 40 + 60 ) = 48 km / hr . answer : c"
Answer: c
Problem: the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 2 , the average of the numbers increases to 9.2 . what number is multiplied by 2 ?
Options: a ) 12.0 , b ) 30.0 , c ) 30.9 , d ) 40.0 , e ) 60.0
Rationale: the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 2 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 2 be n then , 2 n = n + 12 or n = 12 answer : - a
Answer: a
Problem: the sale price sarees listed for rs . 345 after successive discount is 12 % and 25 % is ?
Options: a ) 321 , b ) 276 , c ) 342 , d ) 228 , e ) 245
Rationale: "explanation : 345 * ( 88 / 100 ) * ( 75 / 100 ) = 228 answer : d"
Answer: d
Problem: the length and breadth of the floor of the room are 20 feet and 10 feet respectively . square tiles of 2 feet length of different colours are to be laid on the floor . black tiles are laid in the first row on all sides . if white tiles are laid in the one - third of the remaining and blue tiles in the rest , how many blue tiles will be there ?
Options: a ) 16
b ) 24
c ) 32
d ) 48
e ) none of these
Rationale: area left after laying black tiles = [ ( 20 – 4 ) × ( 10 – 4 ) ] sq . ft . = 96 sq . ft . area under white tiles = ( 1 ⁄ 3 × 96 ) sq . ft = 32 sq . ft . area under blue tiles = ( 96 – 32 ) sq . ft = 64 sq . ft . number of blue tiles = 64 / 2 × 2 = 16 . answer a
Answer: a
Problem: in a group of 89 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 27 , d ) 26 , e ) 31
Rationale: "number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 89 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 89 - 59 = 30 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 89 = 36 + 32 + 30 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - c"
Answer: c
Problem: the workforce of company x is 60 % female . the company hired 22 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 264 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 22 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 22 ) 0.05 x = 12.1 x = 242 - this is quantity of employees before adding 22 men so after adding it will be 264 answer is c"
Answer: c
Problem: a fruit seller sells mangoes at the rate of rs . 8 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.5 , b ) rs 9.5 , c ) rs 10.5 , d ) rs 11.5 , e ) none of these
Rationale: explanation : 80 : 8 = 105 : x x = ( 8 × 105 / 80 ) = rs 10.5 option c
Answer: c
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 21 seconds . the ratio of their speeds is ?
Options: a ) 3 / 6 , b ) 3 / 2 , c ) 2 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 21 = = > 27 x + 17 y = 21 x + 21 y = = > 6 x = 4 y = = > x / y = 2 / 3 . answer : c"
Answer: c
Problem: if n = 9 ^ 11 – 9 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 9 ^ 3 - 9 . now 9 ^ 3 has last digit 9 . , we subtract 9 from 9 , thus 9 - 9 = 0 is the answer . option a
Answer: a
Problem: two trains each 210 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 90 km / h while the other travels at 85 km / h . how long will it take for them to pass each other completely .
Options: a ) 3 sec , b ) 2.6 sec , c ) 3.6 sec , d ) 8.6 sec , e ) 7.6 sec
Rationale: "explanation : d = 210 m + 210 m = 420 m rs = 90 + 85 = 175 * 5 / 18 = 243 / 5 t = 420 * 5 / 243 = 8.6 sec answer : option d"
Answer: d
Problem: b completes a work in 8 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.44 days , c ) 5 days , d ) 6.44 days , e ) 7 days
Rationale: "1 / 8 + 1 / 10 = 9 / 40 40 / 9 = 4.44 days answer : b"
Answer: b
Problem: a sum fetched a total simple interest of rs . 1000 at the rate of 10 p . c . p . a . in 4 years . what is the sum ?
Options: a ) 2500 , b ) 2800 , c ) 3500 , d ) 1900 , e ) 1500
Rationale: sol . principal = rs . [ 100 * 1000 / 10 * 4 ] = rs . [ 100000 / 40 ] = rs . 2500 . answer a
Answer: a
Problem: p and q are the only two applicants qualified for a short - term research project that pays 360 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 3 , b ) $ 6 , c ) $ 9 , d ) $ 12 , e ) $ 15
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 360 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 360 / 30 = $ 12 p ' s hourly wage is 360 / ( t - 10 ) = $ 18 which is $ 6 per hour more . the answer is b ."
Answer: b
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 17 cm
Options: a ) 178 cm 2 , b ) 323 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 17 ) = 323 cm 2 answer : b"
Answer: b
Problem: a cylinder of height h is 7 / 8 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 69 % , d ) 80 % , e ) 100 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 7 / 8 new cylinder 3 / 5 so 3 / 5 / 7 / 8 = 3 / 5 * 8 / 7 = 0.69 or 69 % . answer c"
Answer: c
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 1000
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 250 . so 1 / 4 of her savings is $ 250 . so her original savings are 4 times $ 250 = $ 1000 correct answer e"
Answer: e
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 7 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 39.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.93 * 150 x = 139.5 x hence total profit = 39.5 % option d"
Answer: d
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 56 more . what was his original selling price ?
Options: a ) $ 880 , b ) $ 950 , c ) $ 1100 , d ) $ 1240 , e ) $ 1360
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 56 0.07 = 56 p = 800 the original selling price was 800 * 1.1 = 880 . the correct answer is a ."
Answer: a
Problem: a train speeds past a pole in 10 seconds and a platform 100 m long in 30 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 50 m , e ) 45 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 100 / 30 = x / 10 x = 50 m . answer : d"
Answer: d
Problem: suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 112 runs thereby increasing his average by 6 runs . what is his average after the 17 th innings ?
Options: a ) 18 , b ) 25 , c ) 16 , d ) 72 , e ) 27
Rationale: "to improve his average by 6 runs per innings he has to contribute 16 x 6 = 96 runs for the previous 16 innings . thus , the average after the 17 th innings = 112 - 96 = 16 . answer : c"
Answer: c
Problem: a man can row downstream at the rate of 16 km / hr and upstream at 8 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 12,4 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 16 + 8 ) = 12 km / hr rate of current = 1 / 2 ( 16 - 8 ) = 4 km / hr answer : option a"
Answer: a
Problem: the average of squares of first 11 consecutive even numbers is :
Options: a ) 164 , b ) 174 , c ) 184 , d ) 194 , e ) 204
Rationale: 2 ( n + 1 ) ( 2 n + 1 ) / 3 ( 2 * 12 * 23 ) / 3 = 2 * 4 * 23 = 184 answer : c
Answer: c
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1430 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 190 , d ) 321 , e ) 220
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1430 x = 50 required perimeter = 2 ( 50 + 60 ) = 220 e"
Answer: e
Problem: rahul played weel in this season . his current batting averagge is 51 . if he score 69 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: 51 x + 69 = 54 ( x + 1 ) = > 3 x = 15 = > x = 5 answer : e
Answer: e
Problem: 1852 - 1230 ÷ 10.00 = ?
Options: a ) 62.2 , b ) 2000 , c ) 1700 , d ) 1729 , e ) none
Rationale: "answer given expression = 1852 - 1230 ÷ 10.00 = 1852 - 123 = 1729 correct option : d"
Answer: d
Problem: last year a certain bond price with a face value of 5000 yielded 8 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: "interest = 0.08 * 5000 = 0.065 * selling price - - > selling price = 0.08 * 5000 / 0.065 - - > selling price = ~ 6,154 answer : e ."
Answer: e
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 8 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 27 , d ) 4 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 32 x = 4 ( 3 x + 5 ) 20 x = 20 x = 1 quantity of alcohol = ( 4 x 1 ) litres = 4 litres . answer : d"
Answer: d
Problem: mary ' s income is 60 % more than tim ' s income and tim ' s income is 50 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 124 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.5 = 50 m = 50 * 1.6 = 80 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 80 * 100 / 100 = 80 ans : d"
Answer: d
Problem: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 40 kmph and prasanna moves southward at a speed of 38 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 78 , d ) 27 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 40 kmph x 1 hr = 40 km total southward prasanna ' s distance = 38 kmph x 1 hr = 38 km total distance between prasanna and laxmi is = 40 + 38 = 78 km . answer : c"
Answer: c
Problem: a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 70 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 36 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 70 % of 100 = 70 pounds of decaffeinated coffee 3 . wt have 150 pounds of decaffeinated out of 500 pounds , that means 150 / 500 * 100 % = 30 % . the correct answer is b ."
Answer: b