Cheukting/mathqa huggingface dataset:
Question (geometry): find the circumference and area of radius 8 cm .
Options: a ) 124 cm ² , b ) 201 cm ² , c ) 210 cm ² , d ) 184 cm ² , e ) 194 cm ²
Rationale: "area of circle = π r ² = 22 / 7 × 8 × 8 cm ² = 201 cm ² answer : b"
Answer: b
Question (general): if a - b = 10 and a 2 + b 2 = 210 , find the value of ab .
Options: a ) 68 , b ) 42 , c ) 55 , d ) 18 , e ) 44
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 210 - 100 = 110 ab = 55 . answer : c"
Answer: c
Question (general): in a 150 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 22 , b ) 21 , c ) 20 , d ) 19 , e ) 18
Rationale: solution simple out of 150 10 % are male i . e 15 and 20 % are female i . e 30 , so total homeowner is 45 . now min number homeowner is 15 and max is 30 so question ask us to find least and 18 has least value among all option . so ans is 18 . ans : e
Answer: e
Question (physics): the length of the longest rod that can fit in a cubical room of 4 m side is ?
Options: a ) 6.978 m
b ) 6.928 m
c ) 6.829 m
d ) 6.248 m
e ) 6.982 m
Rationale: the length of the longest rod = 4 sq . root of 3 = 6.928 m answer : b
Answer: b
Question (gain): if $ 5,000 is invested in an account that earns 16 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.16 / 2 ) ^ 2 = 5416 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 16 / 100 ) = 5400 difference = 5416 - 5400 = 16 $ d"
Answer: d
Question (geometry): a rectangular paper , when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides . what is the area of the paper ?
Options: a ) 140 cm
b ) 240 cm 2
c ) 560 cm 2
d ) none of these
e ) can not be determined
Rationale: solution when folded along breadth , we have : 2 ( l / 2 + b ) = 34 or l + 2 b = 34 when folded along length , we have : 2 ( l / 2 + b ) = 38 or 2 l + b = 38 solving ( i ) and ( ii ) , we get : l = 14 and b = 10 . ∴ area of the paper = ( 1410 ) cm 2 = 140 cm 2 answer a
Answer: a
Question (gain): after giving a discount of rs . 50 the shopkeeper still gets a profit of 20 % , if the cost price is rs . 180 . find the markup % ?
Options: a ) 0.5 , b ) 0.6 , c ) 0.48 , d ) 0.65 , e ) 0.45
Rationale: "cost price = 180 s . p = 180 * 120 / 100 = 216 disc = 50 so . . . mark price = 216 + 50 = 266 . . . . . . mark up % = 266 - 180 / 180 = 86 / 180 = . 48 or 48 % answer : c"
Answer: c
Question (geometry): the water level in a rectangular swimming pool measuring 60 feet by 10 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 2250 , c ) 750 , d ) 1200 , e ) 5625
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 10 * 1 / 2 = 300 feet ^ 3 of water must be removed , which equals to 300 * 7.5 = 2250 gallons . answer : b"
Answer: b
Question (gain): a leak in the bottom of a tank can empty the tank in 6 hrs . an pipe fills water atthe rate of 4 ltrs / min . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs . the capacity of the tank is ?
Options: a ) 4670 , b ) 4546 , c ) 4556 , d ) 4675 , e ) 5760
Rationale: 1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 e
Answer: e
Question (physics): what is the least number of squares tiles required to pave the floor of a room 2 m 25 cm long and 1 m 35 cm broad ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 44 , e ) 48
Rationale: "length of largest tile = h . c . f . of 225 cm and 135 cm = 45 cm . area of each tile = ( 45 x 45 ) cm 2 . required number of tiles = 225 x 135 / ( 45 ^ 2 ) = 15 . answer : a"
Answer: a
Question (general): 7 people average age is 30 . youngest person age is 8 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 22 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 56 = 154 so average age would be 154 / 7 = 22 answer : d"
Answer: d
Question (physics): 24 people can write 48 book in 6 days working 8 hour a day . then in how many day 192 can be written by 50 people ?
Options: a ) 223 / 26 , b ) 288 / 27 , c ) 309 / 22 , d ) 288 / 26 , e ) 288 / 25
Rationale: work per day epr hour per person = 48 / ( 6 * 8 * 24 ) / / eq - 1 people = 50 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 192 / ( p * 8 * 50 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 288 / 25 answer : e
Answer: e
Question (gain): john makes $ 60 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 25 % , c ) 16.56 % , d ) 17.66 % , e ) 18.1 %
Rationale: "increase = ( 15 / 60 ) * 100 = ( 1 / 4 ) * 100 = 25 % . b"
Answer: b
Question (general): at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 5 on candy , how much did john spend at the supermarket ?
Options: a ) $ 75 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 5 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 5 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 150 = 30 t 28 t + 150 = 30 t 150 = 2 t t = 75 john spent $ 7 at the supermarket . answer : a"
Answer: a
Question (general): a bus started its journey from chennai and reached mumbai in 50 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 6 km / hr , how much time will it take to cover the same distance ?
Options: a ) 45 min . , b ) 55 min . , c ) 65 min . , d ) 60 min . , e ) 50 min .
Rationale: sol . distance between mumbai and pune = ( 60 * 50 ) / 60 = 50 average speed of the bus is increased by 6 km / hr then the speed of the bus = 66 km / hr required time = 50 * 66 / 60 = 55 min . b
Answer: b
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 sec , b ) 88 sec , c ) 48 sec , d ) 18 sec , e ) 9 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 6 / 125 = 48 sec . answer : c"
Answer: c
Question (other): the ratio between the present ages of a and b is 4.5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 7 : 3 , e ) 3 : 7
Rationale: "let the present ages of a and b be 4.5 x and 3 x years respectively . then , ( 4.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1.5 x = 8 = > x = 5.33 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 28 : 12 = 7 : 3 . answer : d"
Answer: d
Question (general): the average weight of a , b and c is 46 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 17 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 22 kg
Rationale: "let d sum of a , b , c is 3 * 46 = 144 and sum of a and b s 2 * 40 = 80 sum of b and c is 3 * 43 = 86 hence 80 + 86 - 144 = 22 ans = 22 answer : e"
Answer: e
Question (physics): the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 6400 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 2 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 6400 x = ( 2 ^ 8 * 25 ) / 2 ^ 9 = 25 / 2 the answer is a ."
Answer: a
Question (general): if two integers x , y ( x > y ) are selected from - 5 to 6 ( inclusive ) , how many cases are there ?
Options: a ) 62 , b ) 66 , c ) 70 , d ) 74 , e ) 78
Rationale: "there are 12 integers from - 5 to 6 inclusive . 12 c 2 = 66 . the answer is b ."
Answer: b
Question (general): what is the remainder when 2 ^ 20 is divided by 10 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "2 ^ 20 = 2 ^ 10 x 2 ^ 10 and 2 ^ 10 = 1024 4 * 4 = 16 , so the unit digit of this multiplication is 6 the remainder is 6 answer : d"
Answer: d
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 56 ?
Options: a ) s . 3944 , b ) s . 3948 , c ) s . 3942 , d ) s . 3808 , e ) s . 3929
Rationale: "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 56 = rs . 3808 . answer : d"
Answer: d
Question (general): the average weight of a group of boys is 20 kg . after a boy of weight 34 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 13 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 34 kg joins the group , total weight of boys = 20 x + 34 so 20 x + 34 = 21 ( x + 1 ) = > x = 13 . answer : d"
Answer: d
Question (general): in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 12 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 25 , d ) 150 , e ) 100
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 12 + 2 / 3 of 12 80 / 100 x = 20 x = 25 . answer : option c"
Answer: c
Question (general): if w is a positive integer and 10 ^ w – 74 in decimal notation has digits whose sum is 440 , what is the value of w ?
Options: a ) 40 , b ) 44 , c ) 45 , d ) 46 , e ) 50
Rationale: answer e = 50 we have ( 10 ^ w ) - 74 , where the sum of the digits is 440 . 100 - 74 = 26 , so we already have 2 + 6 = 8 from the 440 . because we have a power of 10 , we will have numbers like 100 , 1000 , 10000 and so on . this minus 74 rests 26 and a lot of 9 s . e . g : 1000 - 74 = 9926 . so dividing the 432 / 9 = 48 , that ` s the number of 9 s . and we have 2 other numbers ( 2 and 6 ) wich were 00 before the subtraction . so we have 48 + 2 as an w = 50
Answer: e
Question (general): the average age of 30 students of a class is 20 years . out of these , the average age of 10 students is 16 years and that of the other 19 students is 22 years . the age of the 30 th student is :
Options: a ) 22 years , b ) 24 years , c ) 15 years , d ) 16 years , e ) none of these
Rationale: "explanation : age of the 30 th student = [ 30 x 20 - ( 10 x 16 + 19 x 22 ) ] = ( 600 - 278 ) = 22 years . answer : a"
Answer: a
Question (physics): roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 4 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 28 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 4 + 3 ) * 4 = 28 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : a"
Answer: a
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 176 votes . find the total number of valid votes ?
Options: a ) 440 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 176 = > 4 x / 10 = 176 = > 4 x = 1760 = > x = 440 . answer : a"
Answer: a
Question (general): ( 17 ) 5.25 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 5.25 * ( 17 ) x = 178 . then , ( 17 ) 5.25 + x = ( 17 ) 8 . ∴ 5.25 + x = 8 ⇔ x = ( 8 - 5.25 ) ⇔ x = 2.75 answer b"
Answer: b
Question (geometry): in measuring the sides of a rectangle , one side is taken 20 % in excess and the other 10 % in deficit . find the error per cent in area calculated from the measurement ?
Options: a ) 12 % deficit
b ) 10 % excess
c ) 8 % excess
d ) 9 % excess
e ) none of these
Rationale: since side 1 x side 2 = area therefore , error % in area = ( x + y + xy / 100 ) % = [ 20 - 10 + ( - 10 x 20 ) / 100 ] % or 8 % i . e . , 8 % excess answer : c
Answer: c
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 54 kmph , find the speed of the stream ?
Options: a ) 77 , b ) 18 , c ) 14 , d ) 12 , e ) 17
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 54 / 3 = 18 kmph . answer : b"
Answer: b
Question (physics): some ladies can do a piece of work in 12 days . two times the number of such ladies will do half of that work in :
Options: a ) 6 days , b ) 4 days , c ) 12 days , d ) 3 days , e ) 8 days
Rationale: expl : let x ladies can do the work in 12 days . more ladies , less days ( indirect ) less work , less days ( direct ) ladies 2 x : x work 1 : ½ 2 x : x , 1 : ½ : : 12 : y : . 2 x * 1 * y = x * ½ * 12 or y = 3 hence the required number of days = 3 answer : d
Answer: d
Question (general): think of a number , divide it by 5 and add 6 to it . the result is 65 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 295 , d ) 267 , e ) 29
Rationale: "explanation : 65 - 6 = 59 59 x 5 = 295 answer : c"
Answer: c
Question (gain): sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 200 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.56 , b ) $ 1.88 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25
Rationale: "6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 200 - - > x = 1.25 . 1.25 x = ~ 1.56 . answer : a ."
Answer: a
Question (gain): a candidate got 32 % of the votes polled and he lost to his rival by 1908 votes . how many votes were cast ?
Options: a ) 5100 , b ) 5200 , c ) 5300 , d ) 5400 , e ) 5500
Rationale: "let x be the total number of votes . 0.32 x + 1908 = 0.68 x 0.36 x = 1908 x = 1908 / 0.36 = 5300 the answer is c ."
Answer: c
Question (other): the sub - duplicate ratio of 1 : 9 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 1 : 4 , e ) 2 : 3
Rationale: "root ( 1 ) : root ( 9 ) = 1 : 3 answer : c"
Answer: c
Question (general): a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 482 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 3377 , b ) 6886 , c ) 2788 , d ) 2000 , e ) 28712
Rationale: "p ( 11 / 10 ) 4 - p ( 6 / 5 ) 2 = 482 p = 2000 answer : d"
Answer: d
Question (general): what is the value of 10 ^ 8 - 6 ^ 4 ?
Options: a ) 9,99 , 98,623 , b ) 9,99 , 98,704 , c ) 9,99 , 98,800 , d ) 9,99 , 99,521 , e ) 9,99 , 99,932
Rationale: "as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer b"
Answer: b
Question (geometry): what is the area of a square field whose diagonal of length 14 m ?
Options: a ) 160 sq m , b ) 140 sq m , c ) 200 sq m , d ) 400 sq m , e ) 180 sq m
Rationale: "d 2 / 2 = ( 14 * 14 ) / 2 = 140 answer : b"
Answer: b
Question (physics): harish can paint a wall in just 3 hours . however it takes 6 hours for ganpat to complete the same job of painting the wall . how long would it take for both of them to paint the wall , if both work together ?
Options: a ) 3 hours , b ) 1 hours , c ) 3.20 hours , d ) 2 hours , e ) 1.35 hours
Rationale: d two hours . harish who could paint the wall in 3 hours could paint 2 / 3 of the wall in just two hours . ganpat who paint the wall in 6 hours could paint 1 / 3 of the wall in two hours . 2 / 3 + 1 / 3 = 1 .
Answer: d
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 38 years . what is deepak present age ?
Options: a ) 22 , b ) 24 , c ) 77 , d ) 266 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 38 = > x = 8 so deepak age is = 3 ( 8 ) = 24 answer : b"
Answer: b
Question (physics): two pipes a and b can fill a tank in 40 and 120 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 82 , e ) 22
Rationale: "part filled by a in 1 min . = 1 / 40 part filled by b in 1 min . = 1 / 120 part filled by ( a + b ) in 1 min . = 1 / 40 + 1 / 120 = 1 / 30 . both the pipes can fill the tank in 30 minutes . answer : a"
Answer: a
Question (gain): rs 70000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 70000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 70000 + y so y = 10000 then x = 70000 - 10000 = 60000 first part = 60000 answer : d"
Answer: d
Question (general): in a two digit number , the digit in the units place is 6 times the digit in 10 ' s place and sum of the digits is equal to 7 . what is the number ?
Options: a ) 16 , b ) 28 , c ) 32 , d ) 36 , e ) 38
Rationale: solution let the ten digits be x . then , units digit = 6 x therefore x + 6 x = 7 ‹ = › 7 x = 7 ‹ = › x = 1 . so , ten ' s digit = 1 , unit ' s digit = 6 . hence , the required number is 16 . answer a
Answer: a
Question (physics): shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 40 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 40 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 38 hence answer is c"
Answer: c
Question (physics): a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be b ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 780 , d ) $ 1170 , e ) $ 630
Rationale: explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , b ' s share will be 3 * 2340 / 9 = 780 correct choice is ( c )
Answer: c
Question (general): in an exam , amar scored 64 percent , bhavan scored 36 percent and chetan 44 percent . the maximum score awarded in the exam is 900 . find the average mark scored by all the 3 boys ?
Options: a ) 384 , b ) 432 , c ) 207 , d ) 269 , e ) 208
Rationale: average mark scored by all the three boys = [ 64 / 100 ( 900 ) + 36 / 100 ( 900 ) + 44 / 100 ( 900 ) ] / 3 = 432 answer : b
Answer: b
Question (physics): a 280 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 280 ) / 9 = 500 / 9 x + 280 = 500 x = 220 . a"
Answer: a
Question (general): find the average of first 5 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 ) / 5 = 15 answer is b"
Answer: b
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 108 km / hr . what is the length of the platform ?
Options: a ) 229 , b ) 240 , c ) 288 , d ) 480 , e ) 221
Rationale: "speed = 108 * 5 / 18 = 30 m / sec . length of the train = 30 * 20 = 600 m . let the length of the platform be x m . then , ( x + 600 ) / 36 = 30 = > x = 480 m . answer : d"
Answer: d
Question (physics): a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 2.9 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 1.6 , b ) 1.9 , c ) 2.2 , d ) 2.5 , e ) 2.8
Rationale: "72 km / hr = 1.2 km / min the total distance is 3 km . 3 / 1.2 = 2.5 minutes the answer is d ."
Answer: d
Question (physics): a train 120 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 7.2 sec , b ) 9.3 sec , c ) 12 sec , d ) 15.2 sec , e ) 18 sec
Rationale: speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 120 m at 50 / 3 m / sec = 120 * 3 / 50 sec = 7.2 sec answer : a .
Answer: a
Question (other): if exactly 7 guests drank only one of the two types of drinks , how many guests drank both types of drinks ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 4 , e ) 2
Rationale: say x guests drank both drinks . ( 7 - x ) + ( 4 - x ) = 7 - - > x = 2 . answer : e .
Answer: e