Cheukting/mathqa huggingface dataset:
Question (general): if 5 a + 7 b = g , where a and b are positive integers , what is the largest possible value of g for which exactly one pair of integers ( a , b ) makes the equation true ?
Options: a ) 35 , b ) 48 , c ) 69 , d ) 70 , e ) 74
Rationale: 5 * a 1 + 7 * b 1 = g 5 * a 2 + 7 * b 2 = g 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 to a we will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 from a , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer
Answer: d
Question (physics): a worker earns $ 24 on the first day and spends $ 18 on the second day . the worker earns $ 24 on the third day and spends $ 18 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 48 ?
Options: a ) 6 , b ) 7 , c ) 9 , d ) 12 , e ) 16
Rationale: every two days , the net total is $ 6 . after 8 days , the worker will have $ 24 . on day 9 , the worker will receive $ 24 for a net total of $ 48 . the answer is c .
Answer: c
Question (physics): the length of the bridge , which a train 200 metres long and travelling at 60 km / hr can cross in 30 seconds , is ?
Options: a ) 720 , b ) 470 , c ) 270 , d ) 370 m . , e ) 570
Rationale: "speed = [ 60 x 5 / 18 ] m / sec = [ 50 / 3 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 50 / 3 = > ( 130 + x ) / 30 = 370 = > x = 370 m . answer : d"
Answer: d
Question (general): the average monthly income of p and q is rs . 2050 . the average monthly income of q and r is rs . 5250 and the average monthly income of p and r is rs . 6200 . the monthly income ofq is :
Options: a ) 1100 , b ) 2100 , c ) 1200 , d ) 3100 , e ) 1300
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 2050 x 2 ) = 4100 . . . . ( i ) q + r = ( 5250 x 2 ) = 10500 . . . . ( ii ) p + r = ( 6200 x 2 ) = 12400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 27000 or p + q + r = 13500 . . . . ( iv ) subtracting ( iii ) from ( iv ) , we get p = 1100 . p ' s monthly income = rs . 1100 . answer : a"
Answer: a
Question (physics): riya and priya set on a journey . riya moves eastward at a speed of 24 kmph and priya moves westward at a speed of 35 kmph . how far will be priya from riya after 45 minutes
Options: a ) 25 kms , b ) 10 kms , c ) 50 kms , d ) 30 kms , e ) 44 kms
Rationale: "total eastward distance = 24 kmph * 3 / 4 hr = 18 km total westward distance = 35 kmph * 3 / 4 hr = 26 km total distn betn them = 18 + 26 = 44 km ans 44 km answer : e"
Answer: e
Question (general): 0.009 / x = 0.01 . find the value of x
Options: a ) 0.0009 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90
Rationale: "x = 0.009 / 0.01 = 0.9 answer : c"
Answer: c
Question (general): if the mean of numbers 28 , x , 70 , 88 and 104 is 67 , what is the mean of 50 , 62 , 97 , 124 and x ?
Options: a ) 76.5 , b ) 75.6 , c ) 73.5 , d ) 79 , e ) 77
Rationale: "mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 67 = ( x + 28 + 70 + 88 + 104 ) / ( 5 ) 67 x 5 = 290 + x x = 45 therefore mean of 2 nd series m 2 = ( x + 50 + 62 + 97 + 124 ) / 5 m 2 = 75.6 answer = b"
Answer: b
Question (general): elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 10 of these pens for $ 42.00 , how many brand x pens did she purchase ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 5 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : b ."
Answer: b
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 16 : √ 9 = 4 : 3 . answer b"
Answer: b
Question (physics): if the speed of a man is 45 km per hour , then what is the distance traveled by him in 30 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 375 m , d ) 420 m , e ) 480 m
Rationale: "the distance traveled in 30 sec = 45 * ( 5 / 18 ) * 30 = 375 m answer : c"
Answer: c
Question (physics): a participated in cycling contest and he drove the lap at the rate of 6 kmph , 12 kmph , 18 kmph , 24 kmph . . what is his average speed ?
Options: a ) 15 kmph , b ) 18 kmph , c ) 14.25 kmph , d ) 11.52 kmph , e ) 16 kmph
Rationale: = 4 x / ( x / 6 + x / 12 + x / 18 + x / 24 ) = 11.52 answer : d
Answer: d
Question (gain): a watch was sold at a loss of 20 % . if it was sold for rs . 520 more , there would have been a gain of 6 % . what is the cost price ?
Options: a ) rs . 1500 , b ) rs . 2000 , c ) rs . 3000 , d ) rs . 4200 , e ) rs . 2500
Rationale: "80 % 106 % - - - - - - - - 26 % - - - - 520 100 % - - - - ? = > rs . 2000 answer : b"
Answer: b
Question (general): total dinning bill for 5 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 48.53 , c ) 34.66 , d ) 32.29 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 5 = 48.53 answer : b"
Answer: b
Question (physics): kathleen can paint a room in 2 hours , and anthony can paint an identical room in 5 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 20 / 7 , b ) 4 / 3 , c ) 15 / 8 , d ) 9 / 4 , e ) 15 / 4
Rationale: "( 1 / 2 + 1 / 5 ) t = 2 t = 20 / 7 answer : a"
Answer: a
Question (other): in a school of 320 students , 85 students are in the band , 200 students are on sports teams , and 60 students participate in both activities . how many students are involved in either band or sports ?
Options: a ) 220 , b ) 225 , c ) 230 , d ) 240 , e ) 245
Rationale: 25 + 60 + 140 = 225 there are 225 students involved in either band or sports . b )
Answer: b
Question (gain): if the cost price of 20 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 25 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 20 articles = rs . 20 . selling price of 16 articles = rs . 20 therefore , selling price of 20 articles is : - = > 20 / 16 × 20 = > 25 . therefore , profit = selling price - cost price . = > 25 − 20 = 5 . hence , the percentage of profit = profit x 100 / c . p . = > 5 / 20 × 100 . = > 25 % profit . answer : b"
Answer: b
Question (general): the positive numbers w , x , y , and z are such that x is 20 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: y = 100 ( start with yy , it makes getting x easier ) . x = y * 1.2 = 120 z = y / 1.2 = 83.33 w = x * 0.8 = 96 then for the answer : ( w - z ) / z = ( 96 - 83.33 ) / 83.33 = 15.2 % answer : a
Answer: a
Question (geometry): on the coordinate plane , points p and u are defined by the coordinates ( - 1,0 ) and ( 3,3 ) , respectively , and are connected to form a chord of a circle which also lies on the plane . if the area of the circle is ( 25 / 4 ) π , what are the coordinates of the center of the circle ?
Options: a ) ( 1.5 , 1 )
b ) ( 2 , - 5 )
c ) ( 0,0 )
d ) ( 1 , 1.5 )
e ) ( 2,2 )
Rationale: although it took me 3 mins to solve this question using all those equations , later i thought this question can be solved easily using options . one property to keep in mind - a line passing through the centre of the circle bisects the chord ( or passes from the mid point of the chord ) . now mid point of chord here is ( - 1 + 3 ) / 2 , ( 3 + 0 ) / 2 i . e . ( 1 , 1.5 ) now luckily we have this in our ans . choice . so definitely this is the ans . it also indictaes that pu is the diameter of the circle . there can be a case when pu is not a diameter but in that case also the y - coordinate will remain same as it is the midpoint of the chord and we are moving up in the st . line to locate the centre of the circle . if ans choices are all distinct ( y cordinates ) only check for y cordinate and mark the ans = d
Answer: d
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 12 , b ) 77 , c ) 48 , d ) 54 , e ) 11
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.25 = 2 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : d"
Answer: d
Question (physics): paul and jack are 2 mechanics who work 8 hours per day changing oil in cars at the oil spot . if paul can change oil in 2 cars per hour , and jack can change oil in 3 cars per hour . what is the least number of cars per work day the 2 men can finish ?
Options: a ) 50 , b ) 40 , c ) 35 , d ) 10 , e ) 90
Rationale: the proportion equation can be used . let x = number cars and c = least number of cars per day the 2 men can finish ( c = x / ( 8 hours ) , p = cars per hour paul can change , and j = cars per hour jack can change . note : 8 hours = a work day p + j = c ( 2 cars / hour ) + ( 3 cars / hour ) = x / ( 8 hours ) proportion : 2 / 1 + 3 / 1 / = x / 300 x = 8 ( 2 + 3 ) = 40 . at least 40 cars per work day . answer is b
Answer: b
Question (geometry): the edge of three cubes of metal is 3 dm , 4 dm and 5 dm . they are melted and formed into a single cube . find the edge of the new cube ?
Options: a ) 2
b ) 8
c ) 7
d ) 6
e ) 9
Rationale: 33 + 43 + 53 = a 3 = > a = 6 answer : d
Answer: d
Question (general): if a farmer sells 5 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 10 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 12 , b ) 24 , c ) 20 , d ) 55 , e ) 60
Rationale: "say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 5 ) * d + 4 = ( n + 10 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 10 d - 3 n = 30 4 n - 5 d = 20 = > n = 20 ans c it is !"
Answer: c
Question (geometry): if a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius , then surface area of each ball ( in cm 2 ) is ?
Options: a ) 100
b ) 272
c ) 287
d ) 189
e ) 289
Rationale: 4 / 3 π * 10 * 10 * 10 = 8 * 4 / 3 π r 3 r = 5 4 π * 5 * 5 = 100 π answer : a
Answer: a
Question (gain): at the end of the month , a certain ocean desalination plant ’ s reservoir contained 26 million gallons of water . this amount is eighth the normal level . if this amount represents 65 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 26 mg = 65 % of total . . total = 26 / . 65 = 40 mg . . normal level = 1 / 8 of 40 = 5 mg . . shortage of normal level = 40 - 5 = 35 mg . . c"
Answer: c
Question (general): if t = 5 / 9 * ( k - 32 ) , and if t = 20 , then what is the value of k ?
Options: a ) 68 , b ) 70 , c ) 72 , d ) 74 , e ) 76
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 20 ) / 5 + 32 = 68 the answer is a ."
Answer: a
Question (physics): someone on a skateboard is traveling 10 miles per hour . how many feet does she travel in 20 seconds ? ( 1 mile = 5280 feet )
Options: a ) 292 ft , b ) 293.4 ft , c ) 295 ft , d ) 296 ft , e ) 297 ft
Rationale: per second = > 10 * 5280 ft / 60 * 60 = 14.67 ft 20 seconds = > 14.67 * 20 = 293.4 ft answer : b
Answer: b
Question (geometry): a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 8 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 0.008 , b ) 0.08 , c ) 0.064 , d ) 0.64 , e ) 6.4
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 64 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 640 / 10,000 = 64 / 1000 = 0.064 ft the answer is c ."
Answer: c
Question (gain): at the end of the first quarter , the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 75 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 34.6 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 75 = 30 + b + 30 b / 100 b = 34.6 answer ( d )"
Answer: d
Question (general): solve : 18800 + 470 + 20
Options: a ) 2 , b ) 5 , c ) 4 , d ) 0 , e ) 1
Rationale: "18800 + 470 + 20 = ( 18800 / 470 ) + 20 = 40 / 20 = 2 . answer is a ."
Answer: a
Question (general): how many even integers n , such that 20 < = n < = 240 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 31 , b ) 33 , c ) 35 , d ) 37 , e ) 39
Rationale: "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 238 = 16 + 6 ( 37 ) there are 37 numbers in the list . the answer is d ."
Answer: d
Question (physics): a person crosses a 600 m long street in 2 minutes . what is his speed in km per hour ?
Options: a ) 12 , b ) 24 , c ) 18 , d ) 42 , e ) 64
Rationale: distance = 600 meter time = 2 minutes = 2 x 60 seconds = 120 seconds speed = distance / time = 600 / 120 = 5 m / s = 5 ã — 18 / 5 km / hr = 18 km / hr answer : c
Answer: c
Question (general): a train ride from two p to town q costs $ 2.35 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?
Options: a ) $ 1.25 , b ) $ 2.50 , c ) $ 3.75 , d ) $ 4.70 , e ) $ 8.20
Rationale: let x be the cost of a bus ride . x + ( x + 235 ) = 985 2 x = 750 x = $ 3.75 the answer is c .
Answer: c
Question (general): in a can , there is a mixture of milk and water in the ratio 5 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: "let c be the capacity of the can . ( 5 / 8 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 15 c - 120 + 192 = 16 c c = 72 the answer is e ."
Answer: e
Question (physics): in what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 5 sec , b ) 4 sec , c ) 3 sec , d ) 6 sec , e ) 1 sec
Rationale: "t = 30 / 36 * 18 / 5 = 3 sec answer : c"
Answer: c
Question (physics): a 50 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 24.28 , b ) 14.28 , c ) 16.28 , d ) 18.28 , e ) 12.28
Rationale: 1 : 2 / 5 = 5 : 2 2 / 7 * 50 = 14.28 answer : b
Answer: b
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 46 meters . how many times did the ball bounce ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: division of total distance traveled will be 16 + 16 + 8 + 4 + 2 ans : a
Answer: a
Question (general): ( 786 × 74 ) ÷ ? = 1938.8
Options: a ) a ) 4.8 , b ) b ) 48 , c ) c ) 30 , d ) d ) 68 , e ) e ) 48
Rationale: explanation : 58164 / x = 1938.8 = > x = 58164 / 1938.8 = 30 answer : option c
Answer: c
Question (physics): in a 100 m race between rose and diane , rose lost to diane by 0.75 m . if diane was given a 7 m head start , how many meters more will it take before rose overtakes diane ?
Options: a ) 12.91 m , b ) 11.91 m , c ) 12.5 m , d ) 10.91 m , e ) 13.91 m
Rationale: distance rose ran before completion of race - - - 100 m - 0.75 m = 99.25 m distance gained on diane over 99.25 m - - - 7 m - 0.75 m = 6.25 then rose gains 99.25 / 6.25 m = 1 m on kelly every 15.88 meters . therefore 15.88 divided by 0.75 of 1 meter . answer : b . 11.91 m
Answer: b
Question (other): if ramola ranks 14 th in a class of 26 , what is her rank from the last ?
Options: a ) 11 th , b ) 13 th , c ) 12 th , d ) 14 th , e ) 15 th
Rationale: when considered from last , 12 ( i . e 26 - 14 ) students are ranked before her . so she is 13 th rank from last . answer : b
Answer: b
Question (other): the ratio of three numbers is 1 : 2 : 5 and the sum of their squares is 4320 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 2 x , 5 x then , x ^ 2 + 4 x ^ 2 + 25 x ^ 2 = 4320 30 x ^ 2 = 4320 x ^ 2 = 144 x = 12 answer is b"
Answer: b
Question (general): the average salary per head of the entire staff of an office including the officers and clerks is rs . 90 . the average salary of officers is rs . 600 and that of the clerks is rs . 84 . if the number of officers is 2 , find the number of officers in the office ?
Options: a ) 1 , b ) 8 , c ) 7 , d ) 6 , e ) 2
Rationale: 6 * 22 = 132 7 * 19 = 133 - - - - - - - - - - - - - - 1 . answer : a
Answer: a
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 28.28 cm , b ) 25.45 cm , c ) 26.45 cm , d ) 20.18 cm , e ) 32.14 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 20 + 16 ) = 72 cm parameter of the square = 72 cm i . e . 4 a = 72 a = 18 diameter of the semicircle = 18 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 18 ) = 1 / 2 ( 22 / 7 ) ( 18 ) = 396 / 14 = 28.28 cm to two decimal places answer : a"
Answer: a
Question (general): 100 × 10 – 100 + 2000 ÷ 100 = ?
Options: a ) 29 , b ) 780 , c ) 920 , d ) 979 , e ) none of these
Rationale: "solution given exp . = 100 × 10 - 100 + 20 = 1000 - 100 + 20 = 1020 - 100 = 920 . answer c"
Answer: c
Question (gain): what percent is 1 gm of 1 kg ?
Options: a ) 0.1 % , b ) 1 % , c ) 1.5 % , d ) 2 % , e ) 3 %
Rationale: "1 kg = 1000 gm 1 / 1000 × 100 = 100 / 1000 = 1 / 10 = 0.1 % a )"
Answer: a
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8700 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 3700 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8700 = 34800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2800 salary of may is rs . 6500 salary of january = rs . 3700 answer : a"
Answer: a
Question (physics): one pump drains one - half of a pond in 5 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.2 hour , c ) 3 hours , d ) 5 hours , e ) 1.1 hours
Rationale: "the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 5 = 1 / 10 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 10 = 9 / 10 - - > time taken for the 2 nd pump to finish : 1 : 9 / 10 = 10 / 9 = 1.1 hours . e"
Answer: e
Question (general): if a jogger jogs 16 km / hr instead of 12 km / hr , he would have jogged 10 km more . the actual distance he jogged is
Options: a ) 50 km , b ) 40 km , c ) 30 km , d ) 20 km , e ) none of these
Rationale: explanation : the actual distance jogged be d . = > d / 12 = ( d + 10 ) / 16 = > 16 d = 12 d + 120 = > 4 d = 120 = > d = 30 answer : c
Answer: c
Question (general): when a certain number x is divided by 84 , the remainder is 25 . what is the remainder when x is divided by 14 ?
Options: a ) 10 , b ) 8 , c ) 9 , d ) 5 , e ) 11
Rationale: "let possible value of x is 109 least possible value of x / 14 is 109 / 14 = > 7 quotient with remainder 11 thus answer is ( e ) 11"
Answer: e
Question (other): how many multiples of 100 are there between 100 and 1000 ( both are inclusive ) ?
Options: a ) 2 , b ) 8 , c ) 4 , d ) 5 , e ) 10
Rationale: "the answer is ( 1000 - 100 ) / 100 + 1 = 10 answer is e"
Answer: e
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 50 % ?
Options: a ) 750 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 50 % of 500 = rs . 250 selling price = cost price + profit = 500 + 250 = 750 answer : a"
Answer: a
Question (gain): in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7500 , what was the number of valid votes that the other candidate got ?
Options: a ) 2800 , b ) 2700 , c ) 2100 , d ) 2500 , e ) none of these
Rationale: "explanation : total number of votes = 7500 given that 20 % of percentage votes were invalid = > valid votes = 80 % total valid votes = 7500 × ( 80 / 100 ) 1 st candidate got 55 % of the total valid votes . hence the 2 nd candidate should have got 45 % of the total valid votes = > valid votes that 2 nd candidate got = total valid votes × ( 45 / 100 ) = 7500 × ( 80 / 100 ) × ( 45 / 100 ) = 75 × 45 × 45 = 75 × 4 × 9 = 300 × 9 = 2700 answer : option b"
Answer: b
Question (physics): a and b can do a piece of work in 30 days , while b and c can do the same work in 24 days and c and a in 20 days . they all work together for 10 days when b and c leave . how many days more will a take to finish the work ?
Options: a ) 18 days , b ) 24 days , c ) 30 days , d ) 36 days , e ) 35 days
Rationale: explanation : 2 ( a + b + c ) ' s 1 day ' s work = ( 1 / 30 + 1 / 24 + 1 / 20 ) = 15 / 120 = 1 / 8 work done by a , b , c in 10 days = 10 / 6 = 5 / 8 . a ' s 1 day ' s work = ( 1 / 16 - 1 / 24 ) = 1 / 48 now , 1 / 48 work is done by a in 1 day so , 3 / 8 work will be done by a in ( 48 x 3 / 8 ) = 18 days . answer is a
Answer: a