Cheukting/mathqa huggingface dataset:
Question (physics): two men are walking towards each other alongside a railway track . a freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction . the train passes this man is 18 seconds . assume the velocities are constant throughout . how long after the train has passed the second man will the two men meet ?
Options: a ) 89.7 minutes , b ) 90 minutes , c ) 90.3 seconds , d ) 91 seconds , e ) none of these
Rationale: explanation : let ‘ l ’ be the length of train , ‘ x ’ be the speed of the first man , ‘ y ’ be the speed of the second man and ‘ z ’ be the speed of the train . = > 20 = 1 / ( z − x ) and = > 18 = 1 / ( z + x ) = > z = 10 x + 9 y . distance between the two men = 600 ( z + y ) . time = ( 600 ( z + y ) - 600 ( x + y ) ) / ( x + y ) . = > 600 ( 9 x + 9 y ) / ( x + y ) . = > 90 minutes . answer : b
Answer: b
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 16 % , then the cost price of the article is :
Options: a ) 500 , b ) 334 , c ) 531 , d ) 664 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 116 = rs . 531 answer : option c"
Answer: c
Question (general): a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is :
Options: a ) 2 , b ) 5 , c ) 9 , d ) 7 , e ) 6
Rationale: let the number be x x - 4 = 21 / x x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 correct answer d
Answer: d
Question (physics): a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3520 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 420 , d ) s . 440 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3520 × ( 1 / 8 ) = 440 answer : option d"
Answer: d
Question (physics): a is half good a work man as b and together they finish a job in 15 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 45 / 2 , d ) 36 , e ) 48
Rationale: "c 45 / 2 wc = 1 : 2 2 x + x = 1 / 15 = > x = 1 / 45 2 x = 2 / 45 = > 45 / 2 days"
Answer: c
Question (general): bookman purchased 30 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 240 , how many paperback copies were sold ?
Options: a ) 8 , b ) 12 , c ) 6 , d ) 4 , e ) 5
Rationale: "the bookman had 10 hardback ad 30 - 10 = 20 paperback copies ; 14 copies were sold , hence 30 - 14 = 16 copies were left . let # of paperback copies left be p then 10 p + 20 ( 16 - p ) = 240 - - > 10 p = 80 - - > p = 8 # of paperback copies sold is 20 - 8 = 12 answer : b"
Answer: b
Question (geometry): what is the perimeter , in meters , of a rectangular garden 4 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48
b ) 56
c ) 60
d ) 76
e ) 104
Rationale: say length of garden is l meters . then ( l * 4 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 48 meters . perimeter of garden = 2 * ( 48 + 4 ) = 104 meter . answer is e
Answer: e
Question (physics): a train running at the speed of 80 km / hr crosses a pole in 10 seconds . what is the length of the train ?
Options: a ) 450 m , b ) 350 m , c ) 150 m , d ) 250 m , e ) 240 m
Rationale: speed = ( 90 * 5 / 18 ) m / sec = 25 m / sec length of the train = ( speed x time ) = ( 25 * 10 ) m = 250 m . answer : d
Answer: d
Question (general): a sum of rs . 1360 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ' s share is :
Options: a ) 240 , b ) 120 , c ) 280 , d ) 160 , e ) 200
Rationale: "let c ' s share = rs . x then , b ' s share = rs . x / 4 , a ' s share = rs . ( 2 / 3 x ( x / 4 ) ) = rs . x / 6 therefore , x / 6 + x / 4 + x = 1360 = 17 x / 12 = 1360 x = 1360 x 12 / 17 = rs . 960 hence , b ' s share = rs . ( 960 / 4 ) = rs . 240 . answer is a ."
Answer: a
Question (gain): the present worth of rs . 242 due in 2 years at 10 % per annum compound interest is :
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 240 , d ) rs . 220 , e ) rs . 230
Rationale: "explanation : present worth of rs . x due t years hence is given by present worth ( pw ) = x / ( 1 + r / 100 ) t present worth ( pw ) = 242 / ( 1 + 10 / 100 ) 2 = 242 / ( 11 / 10 ) 2 = rs . 200 answer : option a"
Answer: a
Question (physics): beginning in town a , biker bob rides his bike 20 miles west , 6 miles north , 10 miles east , and then 18 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 28 miles , b ) 30 miles , c ) 26 miles , d ) 18 miles , e ) 22 miles
Rationale: using pythagoras we have one side i , e total distance traveled in north direction = 18 + 6 = 24 m other being the base ie distance traveled west - distance traveled eat = 20 - 10 = 10 m now this third side or the distance between town a and town b = 24 ^ 2 + 10 ^ 2 = sq root 676 = 26 m answer : c
Answer: c
Question (physics): a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 23 m * 2 m * 0.75 m ?
Options: a ) 22377 , b ) 27782 , c ) 27891 , d ) 25000 , e ) 23000
Rationale: "23 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 23 = 1 / 100 * x = > x = 23000 answer : e"
Answer: e
Question (general): 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 $ 1340 in total compensation , how many total hours did he work that week ?
Options: a ) 76 , b ) 60 , c ) 65 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1340 - 640 = 700 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 700 / 28 = 25 total hrs = 40 + 25 = 65 answer c 65"
Answer: c
Question (geometry): find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm .
Options: a ) 34 cm ²
b ) 38 cm ²
c ) 54 cm ²
d ) 56 cm ²
e ) 64 cm ²
Rationale: ab ² = ac ² - bc ² = 15 ² - 12 ² = 225 - 144 = 81 therefore , ab = 9 therefore , area of the triangle = ¹ / ₂ × base × height = ¹ / ₂ × 12 × 9 = 54 cm ² answer : c
Answer: c
Question (general): 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 24 / 60 oxen = 12 days the answer is b ."
Answer: b
Question (physics): the time it took car p to travel 300 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 34 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 300 / x ) - ( 300 / ( x + 10 ) ) = 2 solving for x = 34 miles \ hr . a"
Answer: a
Question (physics): a boat having a length 7 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 140 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 7 x 2 x 0.01 ) m 3 = 0.14 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.14 x 1000 ) kg = 140 kg . answer : a"
Answer: a
Question (physics): a certain car can travel 64 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 64 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 64 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : e ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 64 x 3.9 x 3.8 / 5.7 x 1.6 = 104 e"
Answer: e
Question (other): an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 9 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1800 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 9 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2700 . hence , ( r - p ) = ( 2700 - 900 ) = 1800 answer : a"
Answer: a
Question (general): a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6000 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6000 * 6 ) – 30,130 ] = rs . ( 36000 – 30,130 ) = rs . 5870 answer a"
Answer: a
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 10 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 4.8 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.4 tax on others = 2.4 percentage = 4.8 / 100 = 4.8 % answer : e"
Answer: e
Question (general): x ^ 2 + sx + 72 = 0 has two distinct integer roots ; how many values are possible for s ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 24
Rationale: for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know that total factors are ( 3 + 1 ) * ( 2 + 1 ) = 12 ( reason : with 2 ^ n , we have n + 1 possibilities . n ^ 0 to n ^ n . so n + 1 ) = d
Answer: d
Question (geometry): the sides of a square region , measured to the nearest centimeter , are 5 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 25.25 sq cm , b ) 20.25 sq cm , c ) 30.25 sq cm , d ) 36.25 sq cm , e ) 40.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 4.5 is equidistant from both 4 and 5 ) the answer still should be : 4.5 ^ 2 = 20.25 . answer : b"
Answer: b
Question (physics): an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets water in at the rate of 4 litres / min then outlet pipe would take 6 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 6400 litres , c ) 12800 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 4 litres / min , or 4 * 60 = 240 liters / hour ; net outflow rate when both pipes operate would be x - 240 liters / hour . capacity of the tank = x * 10 hours = ( x - 240 ) * ( 10 + 6 ) hours 10 x = ( x - 240 ) * 16 - - > x = 640 - - > capacity = 10 x = 6400 liters . answer : b ."
Answer: b
Question (general): a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 350 more than a :
Options: a ) 10150 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 350 total earning = \ inline \ frac { 58 xy } { 100 } = 10150 answer : a ) rs . 10150"
Answer: a
Question (physics): a train 50 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 3 sec . , b ) 7 sec . , c ) 9 sec . , d ) 11 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 50 m at ( 50 / 3 ) m / sec = ( 112 - 50 ) kmph = ( 50 x 3 / 50 ) sec = 3 sec . answer a"
Answer: a
Question (gain): indu gave bindu rs . 4375 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) s . 10 , b ) s . 7 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "4375 = d ( 100 / 4 ) 2 d = 7 answer : b"
Answer: b
Question (geometry): how many books each of volume 100 meter cube can be packed into a crate of volume 3000 meter cube ?
Options: a ) 50 , b ) can not be determined , c ) 150 , d ) 300 , e ) 350
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 3000 m 3 can be 300 * 10 or 30 * 100 or just 3000 * 1 we do n ' t know , so we cant calculate answer : b"
Answer: b
Question (gain): an article is bought for rs . 675 and sold for rs . 700 , find the gain percent ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "675 - - - - 25 100 - - - - ? = > = 4 % answer : c"
Answer: c
Question (general): having scored 98 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 98 = 19 ( n + 4 ) = > n = 22 so , average score after 19 th innings = x + 4 = 26 . answer : c"
Answer: c
Question (physics): p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 50 days to complete the same work . then q alone can do it in
Options: a ) 30 days , b ) 25 days , c ) 20 days , d ) 15 days , e ) 24 days
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 50 work done by p , q and r in 1 day = 1 / 10 + 1 / 50 = 6 / 50 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day × 2 = 6 / 50 = > work done by p in 1 day = 3 / 50 = > work done by q and r in 1 day = 3 / 50 hence work done by q in 1 day = 3 / 50 – 1 / 50 = 2 / 50 = 1 / 25 so q alone can do the work in 25 days option b"
Answer: b
Question (gain): dhoni spent 40 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 30 % , b ) 28 % , c ) 32 % , d ) 33 % , e ) 34 %
Rationale: "say dhoni ' s earning last month was $ 100 . dhoni spent 40 percent of his earning last month on rent - - > $ 40 on rent ; 20 percent less than what he spent on rent to purchase a new dishwasher - - > $ 40 * 0.8 = $ 32 on the dishwasher . left over amount 100 - ( 40 + 32 ) = $ 28 answer : b"
Answer: b
Question (general): a man whose bowling average is 12.4 , takes 7 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147
Rationale: 12.4 * x + 26 = ( 7 + x ) 12 solve equation x = 145 answer : c
Answer: c
Question (general): 137 + 276 = 435 how much is 731 + 672 ?
Options: a ) 534 , b ) 1403 , c ) 1623 , d ) 1513 , e ) 1613
Rationale: 137 - 731 and 276 - 672 similarly 435 - 534 answer : a
Answer: a
Question (general): a batsman scored 120 runs which included 6 boundaries and 4 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 60 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: number of runs made by running = 110 - ( 6 x 4 + 4 x 6 ) = 120 - ( 48 ) = 72 now , we need to calculate 60 is what percent of 120 . = > 72 / 120 * 100 = 60 % b
Answer: b
Question (other): a bag contains 3 red , 2 blue and 4 green balls . if 2 balls are picked at random , what is the probability that both are red ?
Options: a ) 1 / 12 , b ) 1 / 13 , c ) 1 / 14 , d ) 1 / 15 , e ) 1 / 18
Rationale: "p ( both are red ) , = 3 c 2 / 9 c 2 = 1 / 12 a"
Answer: a
Question (physics): two pipes can separately fill a tank in 20 and 30 hours respectively . both the pipes are opened to fill the tank but when the tank is full , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 17 hrs , b ) 16 hrs , c ) 15 hrs , d ) 13 hrs , e ) 12 hrs
Rationale: 1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs answer : b
Answer: b
Question (physics): the area of playground is 5900 sq . meters . what will be the cost of covering it with grass sheet 1 cm deep , if cost of grass sheet is $ 2.80 per cubic meter .
Options: a ) a ) $ 144
b ) b ) $ 150.50
c ) c ) $ 165
d ) d ) $ 158.60
e ) e ) $ 160.70
Rationale: total volume * unit cost = total cost or , 5900 * 0.01 * 2.8 = total cost = 165 = c
Answer: c
Question (physics): hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 48 , then the other number is ?
Options: a ) 99 , b ) 66 , c ) 132 , d ) 264 , e ) 364
Rationale: "12 * 396 = 48 * x x = 99 answer : a"
Answer: a
Question (general): the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 4 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 36 , b ) 41 , c ) 38 , d ) 40 , e ) 42
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 4 th year = 50 , 5 th year = 50 - 4 = 46 6 th year = 46 - 5 = 41 the correct answer is b ."
Answer: b
Question (gain): a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 20 % ?
Options: a ) 600 , b ) 2877 , c ) 208 , d ) 1882 , e ) 191
Rationale: explanation : cost price = rs . 500 profit = 20 % of 500 = rs . 100 selling price = cost price + profit = 500 + 100 = 600 answer : a
Answer: a
Question (general): if x ^ 2 is divisible by 240 what is the least possible value of integer x ?
Options: a ) 120 , b ) 30 , c ) 90 , d ) 60 , e ) 12
Rationale: 240 can be written as ( 2 ^ 4 ) * 3 * 5 . for x ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option e because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option d is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : d
Answer: d
Question (general): machine t can produce x units in 3 / 4 of the time it takes machine n to produce x units . machine n can produce x units in 2 / 3 the time it takes machine o to produce x units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33
Rationale: let the following be true : t makes x in time t then the following follows : n makes x in 4 t / 3 o makes x in 3 / 2 ( 4 t / 3 ) = 2 t m : n : o = 1 : 4 / 3 : 2 = 3 : 4 : 6 so n = 4 / ( 3 + 4 + 6 ) = 4 / 13 = c
Answer: c
Question (general): ( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) what is m ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 31 , e ) 36
Rationale: ( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / ( 2 * ( 2 * 5 ) ^ 31 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ m = ( 1 / 5 ) ^ 31 ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / [ ( 2 ^ 32 ) * ( 5 ^ 31 ) ] so , m = 31 answer d
Answer: d
Question (general): in a recent head - to - head run - off election , 12000 absentee ballets were cast . 1 / 6 of the absentee ballets were thrown out and 3 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 4,000 , d ) 8,000 , e ) 9,000
Rationale: 5 / 6 * 2 / 5 ( total absentee votes ) = 1 / 3 ( total votes ) = 1 / 3 * 12000 = 4000 answer is c
Answer: c
Question (general): one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 00,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 40000 , c ) 50000 , d ) 75000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 100000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 100000 - x ) = x / 3 + x / 2 = 50000 = 5 x / 6 = 50000 = x = 50000 x 6 / 5 = 60000 savings in public provident fund = rs . ( 100000 - 60000 ) = rs . 40000 answer is b ."
Answer: b
Question (probability): what is the probability that company g ' s advertisement will be one of the first two be shown during the first commercial break ?
Options: a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15
Rationale: g 1 / 15 + ( 14 / 15 ) * 1 / 14 = 2 / 15 d
Answer: d
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 900 in 10 years ?
Options: a ) 6 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 10 * r ) / 100 r = 2 % answer : b"
Answer: b