regisss/math_qa huggingface dataset:
Problem: a book is bought for $ 60 and sold for $ 75 . what is the profit in percentage ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "75 / 60 = 1.25 the answer is d ."
Answer: d
Problem: how many multiples of 5 are there between 5 to 85 ?
Options: a ) 15 , b ) 18 , c ) 17 , d ) none of these , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 . answer : a"
Answer: a
Problem: the difference between a number and its two - fifth is 510 . what is 10 % of that number ?
Options: a ) 12.75 , b ) 85 , c ) 204 , d ) 250 , e ) none of these
Rationale: "explanation : let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 10 % of 850 = 85 . answer is b"
Answer: b
Problem: in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 45 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 891 , e ) 1,001
Rationale: "james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 45 / 100 ) * total votes + 1 = ( 45 / 100 ) * 2000 + 1 = 901 remaining voted needed to win election = 901 - 10 = 891 answer : option d"
Answer: d
Problem: the value of a machine depreciates at 23 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 252935 , b ) $ 432935 , c ) $ 122935 , d ) $ 112935 , e ) $ 152935
Rationale: "the value of the machine after two years = 0.77 * 0.77 * 1 , 50,000 = $ 88,935 sp such that a profit of $ 24,000 is made = 88,935 + 24,000 = $ 1 , 12,935 d"
Answer: d
Problem: a train travels 240 km in 3 hours and 450 km in 5 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 86 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 240 + 450 = 690 km thus , total speed = 8 hrs or , average speed = 690 / 8 or , 86 kmph . answer : c"
Answer: c
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400
Rationale: in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 3,000 - $ 880 = $ 2,120 . answer : b .
Answer: b
Problem: a train running at the speed of 60 km / hr crosses a pole in 12 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 200 meter , c ) 156 meter , d ) 168 meter , e ) 154 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 12 = 200 meter answer : b"
Answer: b
Problem: two trains of equal lengths take 12 sec and 24 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 18 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 16 sec
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 24 = 5 m / sec . relative speed = 10 + 5 = 15 m / sec . required time = ( 120 + 120 ) / 15 = 16 sec . answer : e"
Answer: e
Problem: set a contains 4 different positive odd integers and 6 different positive even integers . set b contains two different positive odd integers and 3 different positive even integers . if one integer from set a and one integer from set b are chosen at random , what is the probability that the product of the chosen integers is even ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 17 / 25 , d ) 21 / 25 , e ) 43 / 50
Rationale: there can be an odd product only if both integers are odd . p ( odd product ) = 4 / 10 * 2 / 5 = 4 / 25 p ( even product ) = 1 - 4 / 25 = 21 / 25 the answer is d .
Answer: d
Problem: a and b can do a piece of work in 16 days , b and c in 24 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 16 days , b ) 55 days , c ) 24 days , d ) 32 days , e ) 22 days
Rationale: "2 c = 1 / 24 + 1 / 12 – 1 / 16 = 1 / 16 c = 1 / 32 = > 32 days answer : d"
Answer: d
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrement of 35 % and in 2007 there is an increment of 45 % , then find the population of city at theend of the year 2007
Options: a ) 2456789 , b ) 3458009 , c ) 3890043 , d ) 3455048 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1083875 e"
Answer: e
Problem: a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 5 seconds ) = 1 - 5 / 20 = 1 - 1 / 4 = 3 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 15 / 20 seconds = 3 / 4 ."
Answer: e
Problem: in the first 10 overs of a cricket game , the run rate was only 4.8 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 4.25 , b ) 5.85 , c ) 6.25 , d ) 7 , e ) 7.5
Rationale: "required run rate = 282 - ( 4.8 x 10 ) = 234 234 / 40 = 5.85 b )"
Answer: b
Problem: the timing of a college is from 12 p . m to 4.20 p . m . six lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 39 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 20 minutes = 260 minutes as there are 6 lectures , the number of breaks between lectures is 5 . total time of the break = 25 minutes hence , the duration of each lecture is = ( 260 â € “ 25 ) / 6 = 39 minutes answer d"
Answer: d
Problem: a man rows his boat 75 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9
Rationale: "speed downstream = d / t = 75 / ( 2 1 / 2 ) = 30 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 30 - 18 ) / 2 = 6 kmph answer : a"
Answer: a
Problem: in the land of oz only one or two - letter words are used . the local language has 66 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 132
Rationale: "the seventh letter ( let it be @ ) can be used with other 65 in two type of arrangents one when seventh letter is in 1 st slot @ _ ( 65 ways ) another , when seventh letter is in 2 nd slot _ @ ( 65 ways ) seventh letter ( @ ) itself lost words = 1 + 65 + 65 = 131 answer : d"
Answer: d
Problem: the sum of the first 100 numbers , 1 to 100 is always divisible by
Options: a ) 2 , b ) 2 and 4 , c ) 2 , 4 and 8 , d ) 2 , 4 and 9 , e ) none of these
Rationale: explanation : the sum of the first 100 natural numbers = ( 100 x 101 ) / 2 = ( 50 x 101 ) as 101 is an odd number and 50 is divisible by 2 , so the sum is always divisible by 2 . answer : option a
Answer: a
Problem: a horse is tethered to one corner of a rectangular grassy field 45 m by 25 m with a rope 22 m long . over how much area of the field can it graze ?
Options: a ) 354 cm 2 , b ) 380 m 2 , c ) 350 m 2 , d ) 407 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 22 ) 2 = 380 m 2 answer b"
Answer: b
Problem: p and q started a business investing rs . 85,000 and rs . 35,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 7 , d ) 17 : 2 , e ) 17 : 3
Rationale: p : q = 85000 : 35000 = 17 : 7 . answer : c
Answer: c
Problem: a can complete a project in 30 days and b can complete the same project in 30 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 ) 27 days , c ) 26.67 days , d ) 5 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 / 30 ) . ( 1 / 30 ) * ( x - 10 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 30 ) + ( x / 30 ) - ( 10 / 30 ) = 1 2 x / 30 = 1 / 3 x = 5 therefore , the answer is d : 5 ."
Answer: d
Problem: express a speed of 42 kmph in meters per second ?
Options: a ) 10 mps , b ) 18 mps , c ) 19 mps , d ) 17 mps , e ) 12 mps
Rationale: "42 * 5 / 18 = 12 mps answer : e"
Answer: e
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 5 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 5 more blue balls than white balls . . . equation # 2 : y = 5 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 5 ) = 100 5 y - 5 = 100 5 y = 105 y = 21 there are 21 blue balls . this is 5 more than the number of white balls , so z = 16 . that ' s the answer . just as a check , x = 63 , and 63 + 21 + 16 = 100 . answer = 16 , ( e )"
Answer: e
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 459 ?
Options: a ) 18 % , b ) 21 % , c ) 20 % , d ) 26.1 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 459 , discount = 621 - 459 = 162 discount % = 162 / 621 * 100 = 26.1 % answer : d"
Answer: d
Problem: income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 21000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3000 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 21000 = > x = 3000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 3000 answer : d"
Answer: d
Problem: a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn
Options: a ) 8223 , b ) 8123 , c ) 8323 , d ) 8423 , e ) 8523
Rationale: let total salary be x a / q = > x = ( x / 3 ) + ( x / 4 ) + ( x / 5 ) + 1760 = > x - 47 x / 60 = 1760 = > 13 x / 60 = 1760 = > x = 1760 * 60 / 13 = > x = 8123 ( approax ) answer : b
Answer: b
Problem: what is the largest 4 digit number exactly divisible by 48 ?
Options: a ) 4676 , b ) 4678 , c ) 9984 , d ) 9504 , e ) 9936
Rationale: largest 4 digit number = 9999 9999 ÷ 48 = 208 , remainder = 15 hence largest 4 digit number exactly divisible by 48 = 9999 - 15 = 9984 answer : c
Answer: c
Problem: the ratio of length of two refill is 9 : 8.2 nd refill got damaged when only half length of 2 nd refill get used . the ratio of total no . of pages written by both refill .
Options: a ) 8 : 3 , b ) 6 : 5 , c ) 9 : 8 , d ) 9 : 4 , e ) 5 : 4
Rationale: the no . of page written is directly proportional to length of refill . so , initial no . of page to be write = 9 x , 8 x . now , 2 nd refill only can write 4 x page so new ratio of page written = 9 x / 4 x = 9 : 4 . answer d
Answer: d
Problem: a train running at the speed of 45 km / hr crosses a pole in 16 seconds . find the length of the train .
Options: a ) 200 , b ) 188 , c ) 204 , d ) 288 , e ) 500
Rationale: "speed = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec length of train ( distance ) = speed * time ( 25 / 2 ) * 16 = 200 meter answer : a"
Answer: a
Problem: he number of times a bucket of capacity 4 liters to be used to fill up a tank is less than number of ties another bucket of capacity 3 liters used for the same purpose by 4 . what is the capacity of the tank ?
Options: a ) 360 liters , b ) 256 , c ) 48 , d ) 525 , e ) 425
Rationale: 4 x = 3 ( x + 4 ) , where x may be number of times 4 l bucket is used . 4 x = 3 ( x + 4 ) - - > 1 . x = 12 , substitute x to lhs or rhs of 1 , which gets you the capacity , and it is 48 . answer : c
Answer: c
Problem: a and b start a business , with a investing the total capital of rs . 5000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 2500 , b ) b ) 3500 , c ) c ) 5000 , d ) d ) 6000 , e ) e ) 8000
Rationale: interest received by a from b = 10 % of half of rs . 5000 = 10 % * 2500 = 250 . amount received by a per annum for being a working partner = 500 * 12 = rs . 1000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 250 + 1000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 250 + 1000 + p ) = 2 ( p ) p = 1250 total profit = 2 p + 1000 = 2 * 1250 + 1000 = 3500 answer : b
Answer: b
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability w that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability w = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Problem: how many plants will be there in a circular bed whose outer edge measure 35 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 19 , e ) none of these
Rationale: "circumference of circular bed = 35 cm area of circular bed = ( 35 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 35 ) 2 â  „ 4 ï € ã · 4 = 24.36 = 24 ( approx ) answer c"
Answer: c
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 700 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.28 , d ) 2.72 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 700 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 700 * 2 * ( 4 / 5 ) = 1120 2160 + 1120 = 3280 solving for units gives us 3.28 so the answer is c"
Answer: c
Problem: find the last 3 digit of 443 ^ 443 .
Options: a ) 306 , b ) 307 , c ) 308 , d ) 309 , e ) 310
Rationale: power is 443 = > 443 / 4 rem = 3 so , 443 ^ 3 = 86938307 last 3 digit = 307 answer : b
Answer: b
Problem: the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 78 , and last 6 numbers is 75 then find 6 th number ?
Options: a ) a ) 258 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 78 + 6 * 75 - 11 * 60 = 258 answer is a"
Answer: a
Problem: a train running at the speed of 120 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 100 meter , b ) 150 meter , c ) 200 meter , d ) 250 meter , e ) 300 meter
Rationale: "speed = 120 * ( 5 / 18 ) m / sec = 200 / 6 m / sec length of train ( distance ) = speed * time ( 200 / 6 ) * 9 = 300 meter answer : e"
Answer: e
Problem: marts income is 60 percent more than tims income and tims income is 50 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %
Rationale: "m = ( 160 / 100 ) t t = ( 50 / 100 ) j = > m = ( 80 / 100 ) j answer d ."
Answer: d
Problem: 155 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 62 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
Rationale: milk = 3 / 5 * 155 = 93 liters water = 62 liters 93 : ( 62 + p ) = 3 : 4 186 + 3 p = 372 = > p = 62 62 liters of water are to be added for the ratio become 3 : 4 . answer : b
Answer: b
Problem: the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > 0 and y > x ?
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points above the x - axis satisfy the condition that y > 0 . the intersection of these two areas is 3 / 8 of the circle . the answer is c .
Answer: c
Problem: how many different positive integers are factors of 196 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 49 , e ) 36
Rationale: "15 , 14 × 15 , 14 = 7 ^ 2 × 2 ^ 2 so total factors = ( 6 + 1 ) ( 6 + 1 ) = 49 answer : d"
Answer: d
Problem: the product of two numbers is 266 and their difference is 5 . what is the bigger number ?
Options: a ) 13 , b ) 15 , c ) 19 , d ) 24 , e ) none of these
Rationale: "explanation : let the two numbers be a and b , here a > b ab = 266 b = 266 / a - - - - - - - - - - - - - - - - - ( i ) given , a – b = 5 - - - - - - - - - - - ( ii ) substitute from ( i ) in ( ii ) , we get a – 266 / a = 5 a 2 – 5 a + 266 = 0 ( a – 19 ) ( a – 14 ) = 0 therefore , a = 19 or a = 14 hence , bigger number = a = 19 answer : c"
Answer: c
Problem: if 821562 is to be divisible by 5 , what is the least whole number that should be added to it ?
Options: a ) 6 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: a number is divisible by 8 if the number formed by the last three digits is divisible by 8 . here , 821562 = 562 , the next multiple of 9 is 568 . 6 must be added to 821562 to make it divisible by 8 a
Answer: a
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 16 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 128 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,16 = 16 / 100 x = 80 * 16 / 100 x = 12.8 12.8 / 10 = 1,28 = 128 % , answer e"
Answer: e
Problem: the difference between the place values of 8 and 3 in the number 587435 is
Options: a ) 75200 , b ) 79970 , c ) 75460 , d ) 24580 , e ) none
Rationale: sol . = ( place value of 8 ) – ( place value of 3 ) = ( 80000 - 30 ) = 79970 answer b
Answer: b
Problem: what is the unit digit of 3 ^ 58 ?
Options: a ) 0 , b ) 5 , c ) 7 , d ) 1 , e ) 9
Rationale: "unit digit in 3 ^ 58 = unit digit in [ ( 3 ^ 4 ) ^ 14 ] * 3 ^ 2 = 1 * 9 = 9 answer is e"
Answer: e
Problem: if the average ( arithmetic mean ) of a and b is 35 and the average of b and c is 80 , what is the value of c − a ?
Options: a ) 25 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 70 ) b + c = 160 c - a = 90 c . 90"
Answer: c
Problem: a group of men decided to do a work in 17 days , but 8 of them became absent . if the rest of the group did the work in 21 days , find the original number of men ?
Options: a ) 15 , b ) 20 , c ) 42 , d ) 25 , e ) 18
Rationale: "original number of men = 8 * 21 / ( 21 - 17 ) = 42 answer is c"
Answer: c
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 10 % profit ?
Options: a ) 13.86 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 110 % of rs . 630 = 110 / 100 * 630 = rs . 693 s . p . per kg = 693 / 50 = rs . 13.86 answer : a"
Answer: a
Problem: in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 6 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 50 , b ) 70 , c ) 10 , d ) 105 , e ) 140
Rationale: rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 5 of all one - bedroom : 1 / 6 * { all one bedroom } = 40 - - > { all one - bedroom } = 240 . { all two - bedroom } = 490 - 240 = 250 . two - bedroom not rented = 250 - 240 = 10 . answer : c .
Answer: c
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 51 , b ) 52 , c ) 59 , d ) 55 , e ) 56
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 976 - 640 = 336 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 336 / 28 = 12 total hrs = 40 + 12 = 52 answer b"
Answer: b
Problem: a works twice as fast as b . if b can complete a work in 18 days independently , the number of days in which a and b can together finish the work is :
Options: a ) 4 days , b ) 6 days , c ) 8 days , d ) 10 days , e ) 12 days
Rationale: "explanation : ratio of rates of working of a and b = 2 : 1 . so , ratio of times taken = 1 : 2 a ' s 1 day ' s work = 1 / 9 b ' s 1 day ' s work = 1 / 18 ( a + b ) ' s 1 day ' s work = ( 1 / 9 + 1 / 18 ) = 3 / 18 = 1 / 6 so , a and b together can finish the work in 6 days answer is b"
Answer: b
Problem: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg
Rationale: explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : d
Answer: d
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 8800 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) 1600
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 8800 x ( 2 / 11 ) ) = rs . 1600 . answer is e"
Answer: e
Problem: how many numbers are divisible by 4 between 1 and 100 ?
Options: a ) 25 , b ) 24 , c ) 23 , d ) 22 , e ) 20
Rationale: "numbers divisible by 4 till 100 = ( 100 / 4 ) = 25 but we should not consider 100 as we are asked to find the numbers between 1 and 100 which are divisible by 4 . so answer is 24 numbers . answer is option b"
Answer: b
Problem: a certain city with a population of 120,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,000 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 120 k x = 10,000 answer : b"
Answer: b
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . after how much time will the trains meet ?
Options: a ) 20 / 8 sec , b ) 20 / 4 sec , c ) 20 / 7 sec , d ) 22 / 7 sec , e ) 60 / 7 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = 100 / 35 = 20 / 7 sec . answer : c"
Answer: c
Problem: an oil cylinder was 3 / 4 th full . when 4 bottles of oil is poured into it , it is 4 / 5 th full . how many bottles of oil can the full cylinder hold ?
Options: a ) 90 , b ) 75 , c ) 70 , d ) 80 , e ) 85
Rationale: ( 4 / 5 - 3 / 4 ) cylinder is filled by 4 bottles 0.8 - 0.75 = 0.05 cylinder is filled by 4 bottles 1 cylinder is filled by 4 / 0.05 = 80 bottles answer : d
Answer: d
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2013 ) = ?
Options: a ) 2014 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2013 ) = 2014 ans : a"
Answer: a
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 50 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 788 , e ) $ 775
Rationale: "= ( 750 * 6 + 800 * 20 ) / 26 = 788 answer is d . posted from my mobile device"
Answer: d
Problem: a certain no . when divided by 110 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : 110 + 25 = 135 / 15 = 9 ( remainder ) e"
Answer: e
Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 600 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 30 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 600 = 20 t 19 t + 600 = 20 t 600 = t there are a total of 600 students in the math class . answer is d ."
Answer: d
Problem: a man can row 3 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 2.9 , b ) 2.8 , c ) 2.4 , d ) 2.8 , e ) 2.2
Rationale: "m = 3 s = 1.2 ds = 3.6 us = 1.8 x / 3.6 + x / 1.8 = 1 x = 1.2 d = 1.2 * 2 = 2.4 answer : c"
Answer: c
Problem: lloyd normally works 7.5 hours per day and earns $ 4.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 2.5 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 ) $ 47.25 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 67.50
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.5 + 3 * 4.5 * 2.5 = 67.5 answer e"
Answer: e
Problem: if a large pizza has a radius that is 40 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 40 % , b ) 80 % , c ) 96 % , d ) 112 % , e ) 124 %
Rationale: let the radius of medium pizza be r . then the radius of large pizza is 1.4 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.4 * r ) ^ 2 = 1.96 * pi * r ^ 2 , an increase of 96 % . the answer is c .
Answer: c
Problem: if tim had lunch at $ 60.50 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 72.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 60.50 = ( 20 / 100 ) * 60.50 = $ 12.1 total spent 60.50 + 12.1 = $ 72.6 correct answer b"
Answer: b
Problem: the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 14000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8600 , d ) rs . 9000 , e ) none
Rationale: answer average salary = 8000 + 5000 + 14000 + 7000 + 9000 / 5 = rs . 8600 correct option : c
Answer: c
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 162 grams of water ?
Options: a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 144
Rationale: "solution : we are given that the ratio of hydrogen to oxygen in water , by mass , is 2 : 16 . using our ratio multiplier we can re - write this as 2 x : 16 x . we can now use these expressions to determine how much oxygen is in 162 grams of water . 2 x + 16 x = 162 18 x = 162 x = 9 since x is 9 , we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water . answer e ."
Answer: e
Problem: a can do a piece of work in 20 days and b can do it in 30 days and c can do it 10 days . they started the work together and a leaves after 2 days and c leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 13 , b ) 16 , c ) 25 , d ) 14 , e ) 15
Rationale: 2 / 20 + x / 30 + 4 / 10 = 1 x = 300 / 20 = 15 answer : e
Answer: e
Problem: find the least number which when divided by 18,32 , 48,52 leaves remainder 14,28 , 44,48 respectively .
Options: a ) 2845 , b ) 3250 , c ) 3740 , d ) 4150 , e ) 5140
Rationale: "the difference of 18 - 14 = 4 , 32 - 28 = 4 , 48 - 44 = 4 , 52 - 48 = 4 lcm of 18,32 , 48,52 = 3744 required number = 3744 - 4 = 3740 answer is c"
Answer: c
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Problem: if 0.75 : x : : 7 : 8 , then x is equal to :
Options: a ) a ) 1.12 , b ) b ) 1.2 , c ) c ) 0.95 , d ) d ) 0.85 , e ) e ) 0.9
Rationale: "( x * 7 ) = ( 0.75 * 8 ) x = 6 / 7 x = 0.85 answer = d"
Answer: d
Problem: tom drives from town r to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between r and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point r to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Problem: of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 3 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 3 is 1200 * 1 / 3 so it reduced 400 people , so there is 800 clerical people left but since 400 people left , it also reduced from the total of 3600 so there are 3200 people total since 800 clerical left / 3200 people total you get ( a ) 25 %"
Answer: a
Problem: calculate the circumference of a circular field whose radius is 2 centimeters .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "circumference c is given by c = 2 ï € r = 2 ï € * 2 = 4 ï € cm correct answer b"
Answer: b
Problem: a and b can do a piece of work in 6 days , b and c in 7 days , c and a in 8 days . how long will c take to do it ?
Options: a ) 12.6 days , b ) 14.4 days , c ) 15.2 days , d ) 16.8 days , e ) 18.2 days
Rationale: "2 c = 1 / 7 + 1 / 8 – 1 / 6 = 20 / 168 = 10 / 84 c = 5 / 84 = > 84 / 5 = 16.8 days the answer is d ."
Answer: d
Problem: two trains are moving in opposite directions with speed of 210 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 48 , c ) 47 , d ) 26 , e ) 24
Rationale: explanation : relative speed = 210 + 90 = 300 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 300 hr = 1 / 150 hr = 3600 / 150 seconds = 24 seconds answer : option e
Answer: e
Problem: pat , kate and mark charged a total of 216 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 120 , d ) 90 , e ) 108
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 216 - total hours charged for , x = 24 . mat charged 6 x - x or 5 x for more hours than kate , or for 120 hours . c is correct"
Answer: c
Problem: find the principle on a certain sum of money at 5 % per annum for 5 years if the amount being rs . 1120 ?
Options: a ) 896 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 5 ) / 100 ] p = 896 answer : a"
Answer: a
Problem: 10 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 45 % , b ) 55 % , c ) 65 % , d ) 75 % , e ) 85 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.1 * 0.6 = 0.06 of the class are female science majors . then 0.34 of the class are male science majors . 0.4 x = 0.34 x = 0.85 = 85 % the answer is e .
Answer: e
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 6.5 liters of alcohol and 3.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 6.5 ) / 50 = 8.5 / 50 = 17 % the answer is e ."
Answer: e
Problem: the area of a parallelogram is 243 sq m and its altitude is three times the corresponding base . what is the length of the base ?
Options: a ) 4 , b ) 9 , c ) 10 , d ) 4 , e ) 12
Rationale: "3 x * x = 243 = > x = 9 answer : b"
Answer: b
Problem: rs . 730 were divided among punith , michael , suresh in such a way that if punith gets rs . 3 , then michael gets rs . 4 and if michael gets rs . 3.50 then suresh gets rs . 3 . the share of michael exceeds that of suresh by
Options: a ) rs 30 , b ) rs 40 , c ) rs 70 , d ) rs 210 , e ) rs 310
Rationale: explanation : let a = punith , b = michael , c = suresh . a : b = 3 : 4 and b : c = 7 / 2 : 3 = ( 8 / 7 ) * ( 7 / 2 ) * ( 8 / 7 ) * 3 = 4 : ( 24 / 7 ) a : b : c = 3 : 4 : 24 / 7 = 21 : 28 : 24 . bs share = rs . [ 730 * ( 28 / 73 ) ] = rs . 280 . cs share = rs . [ 730 * ( 24 / 73 ) ] = rs . 240 . difference of their shares = 40 answer : b
Answer: b
Problem: the value of log 5 ( 1 / 125 ) is :
Options: a ) 3 , b ) - 3 , c ) 1 / 3 , d ) - 1 / 3 , e ) none of these
Rationale: "log 5 ( 1 / 125 ) = log 5 ( 1 / 5 ) ^ 3 = 3 log 5 ( 1 / 5 ) = 3 ( log 5 1 - log 5 5 ) = 3 ( 0 - 1 ) = - 3 answer : b"
Answer: b
Problem: a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 222 for it , the cost price of the cricket bat for a is :
Options: a ) 150 , b ) 148 , c ) 130 , d ) 160 , e ) 210
Rationale: "125 % of 120 % of a = 222 125 / 100 * 120 / 100 * a = 222 a = 222 * 2 / 3 = 148 . answer b"
Answer: b
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 90 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 90 = 0.833 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 0.833 + t » 100 / 40 = 0.833 + t » 2.5 = 0.833 + t » t = 1.667 back to 2 nd part of the trip formula : 25 / s = 1.667 » s = 15 ans a"
Answer: a
Problem: there are 190 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 94 , d ) 105 , e ) 108
Rationale: "you had the answer almost right . the x = 82 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 82 + set ab = 82 + 23 = 105 d"
Answer: d
Problem: in a 240 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 23 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 240 m in 7 / 56 * 240 = 30 seconds since a beats b by 7 seconds , a runs 240 m in ( 30 - 7 ) = 23 seconds hence , a ' s time over the course = 23 seconds answer : a"
Answer: a
Problem: a man is 40 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is
Options: a ) 31 years , b ) 32 years , c ) 33 years , d ) 34 years , e ) 35 years
Rationale: "explanation : let ' s son age is x , then father age is x + 40 . = > 2 ( x + 6 ) = ( x + 40 + 6 ) = > 2 x + 12 = x + 46 = > x = 34 years answer : option d"
Answer: d
Problem: the perimeter of a semi circle is 198 cm then the radius is ?
Options: a ) 22 , b ) 28 , c ) 98 , d ) 38.5 , e ) 13
Rationale: "36 / 7 r = 198 = > r = 38.5 answer : d"
Answer: d
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.35 – 6.35 * ?
Options: a ) 0.35 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.35 * = 6 ( the greatest positive even integer less than or equal to 6.35 is 6 ) . hence , 6.35 – 6.35 * = 6.35 - 6 = 0.35 answer : a ."
Answer: a
Problem: joe drives 360 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 53 , c ) 50 , d ) 54 , e ) 56
Rationale: t 1 = 360 / 60 = 6 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 9 hours avg speed = total distance / t = 480 / 9 = 53 mph = b
Answer: b
Problem: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 8 .
Options: a ) 161 , b ) 152 , c ) 154 , d ) 158 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 8 d = 153 + 8 d = 161 answer a"
Answer: a
Problem: car a runs at the speed of 55 km / hr and reaches its destination in 8 hours . car b runs at the speed of 70 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 11 : 7 , d ) 5 : 7 , e ) 6 : 11
Rationale: "car a travels 55 × 8 = 440 km car b travels 70 × 4 = 280 km the ratio is 440 : 280 = 44 : 28 = 11 : 7 the answer is c ."
Answer: c
Problem: a train running at the speed of 70 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 700 , b ) 770 , c ) 707 , d ) 710 , e ) 720
Rationale: "speed = ( 70 * 5 / 18 ) m / sec = ( 175 / 9 ) m / sec length of the train = ( speed x time ) = ( 175 / 9 * 36 ) m = 700 m . answer : a"
Answer: a
Problem: a jeep takes 3 hours to cover a distance of 440 km . how much should the speed in kmph be maintained to cover the same direction in 1 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 252 kmph , c ) 293 kmph , d ) 263 kmph , e ) 265 kmph
Rationale: "time = 3 distance = 340 1 / 2 of 3 hours = 6 * 1 / 2 = 1.5 hours required speed = 440 / 1.5 = 293 kmph c )"
Answer: c
Problem: what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 4 , and 5 if each digit can be used only once in each number ?
Options: a ) 2442 , b ) 2552 , c ) 2662 , d ) 2772 , e ) 2882
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 444 ) + 2 ( 555 ) = 2442 the answer is a ."
Answer: a
Problem: the ratio between the length and the breadth of a rectangular park is 1 : 4 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 124545 m
b ) 134561 m
c ) 156787 m
d ) 15450 m
e ) 102400 m
Rationale: perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 4 x metres . then , 2 ( 1 x + 4 x ) = 1600 or x = 160 . length = 160 m and breadth = 640 m . area = ( 160 x 640 ) m 2 = 102400 m e
Answer: e
Problem: the difference between the ages of two persons is 20 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 28 , e ) 32
Rationale: let their ages be x years and ( x + 20 ) years then , ( x + 20 ) - 15 = 2 ( x - 15 ) x + 5 = 2 x - 30 x = 35 answer is b
Answer: b
Problem: if 70 percent of 600 is 40 percent of x , then x = ?
Options: a ) 105 , b ) 168 , c ) 342 , d ) 660 , e ) 1050
Rationale: "given : 0.7 * 600 = 0.4 x - - > 420 = 4 / 10 * x - - > x = 1,050 . answer : e ."
Answer: e
Problem: find the sum of divisors of 544 which are perfect squares
Options: a ) 21
b ) 22
c ) 23
d ) 24
e ) 25
Rationale: perfect squares divisiors are 1 , 2 ^ 2 & 2 ^ 4 only sum of divisors of 544 which are perfect squares = 1 + 2 ^ 2 + 2 ^ 4 = 21 answer : a
Answer: a
Problem: find compound interest on $ 6000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 2331.75 , b ) 2209.75 , c ) 2108.75 , d ) 2107.75 , e ) 2100.75
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 6000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 6000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 8331.75 . : . c . i . = rs . ( 8331.75 - 6000 ) = $ 2331.75 answer a ."
Answer: a
Problem: a towel , when bleached , lost 30 % of its length and 40 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 30 % , c ) 44 % , d ) 58 % , e ) 64 %
Rationale: "percentage change in area = ( − 30 − 40 + ( 30 × 40 ) / 100 ) % = − 58 % i . e . , area is decreased by 58 % answer : d"
Answer: d
Problem: in order to obtain an income of rs . 3800 from 70 % stock at rs . 280 , one must make an investment of
Options: a ) rs . 16000 , b ) rs . 15000 , c ) rs . 15250 , d ) rs . 15200 , e ) rs . 15300
Rationale: "explanation : market value = rs . 280 required income = rs . 3800 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 70 ( ie , 70 % of the face value 100 ) , investment = rs . 280 to obtain rs . 3800 , investment = 280 / 70 ã — 3800 = rs . 15200 answer : option d"
Answer: d
Problem: a train 300 m long can cross an electric pole in 15 sec and then find the speed of the train ?
Options: a ) 65 kmph , b ) 70 kmph , c ) 72 kmph , d ) 75 kmph , e ) 78 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 15 s = 20 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 72 kmph answer : c"
Answer: c
Problem: a pipe can empty 2 / 3 rd of a cistern in 12 mins . in 5 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 5 / 18 , c ) 4 / 9 , d ) 3 / 8 , e ) 4 / 7
Rationale: 2 / 3 - - - - 12 ? - - - - - 5 = = > 5 / 18 b
Answer: b
Problem: jane and thomas are among the 8 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "the total number of ways to choose 3 people from 8 is 8 c 3 = 56 . the number of committees without jane or thomas is 6 c 3 = 20 . there are 56 - 20 = 36 possible committees which include jane and / or thomas . the answer is d ."
Answer: d
Problem: find the surface area of a 10 cm x 4 cm x 3 cm brick
Options: a ) 84 , b ) 124 , c ) 164 , d ) 180 , e ) 120
Rationale: "explanation : surface area = [ 2 ( 10 x 4 + 4 x 3 + 10 x 3 ) ] cm 2 = 164 cm 2 answer : c"
Answer: c