Cheukting/mathqa huggingface dataset:
Question (physics): renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 4 days . in what time suma can do it alone ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 8 suma â € ™ s one day â € ™ s work = 1 / 4 - 1 / 8 = 1 / 8 suma can do it alone in 8 days . answer : a"
Answer: a
Question (gain): 90 percent of the members of a study group are women , and 60 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.34 , b ) 0.44 , c ) 0.54 , d ) 0.64 , e ) 0.74
Rationale: "say there are 100 people in that group , then there would be 0.9 * 0.60 * 100 = 54 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 54 / 100 . answer : c"
Answer: c
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 12 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 m , b ) 188 m , c ) 240 m , d ) 178 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 12 = 240 m . answer : c"
Answer: c
Question (general): a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 310000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,292 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 12,917 , e ) $ 20,796
Rationale: 0.04 x + 0.09 y = 310000 [ 1 ] 0.04 x = 0.80 * 310000 = 248000 [ 2 ] 248000 + 0.09 y = 310000 - - > 0.09 y = 62000 [ 3 ] 248000 / 12 = 258333.3333 [ 4 ] 62000 / 12 = 5166.67 [ 5 ] adding [ 4,5 ] we get : 25833 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.292 , ans a
Answer: a
Question (general): x and y started a business by investing rs . 5000 / - and rs . 15000 / - respectively . find the x ’ s share out of a total profit of rs . 1600 :
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: x = rs . 5000 / - y = rs . 15000 / - x share 1 part & y share 3 parts total 4 parts - - - - - > rs . 1600 / - - - - - > 1 part - - - - - - - > rs . 400 / - x share = 1 part - - - - - > rs . 400 / - e
Answer: e
Question (general): if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 48 / r years . if pat ' s parents invested $ 5,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 48 / r years , then for r = 8 it ' ll double in 48 / 8 = ~ 6 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 3 = $ 15,000 . answer : b ."
Answer: b
Question (general): how many multiples of 7 are there between 9 and 89 , 9 and 89 inclusive ?
Options: a ) 11 , b ) 17 , c ) 16 , d ) 13 , e ) 12
Rationale: "7 multiples are . . . 14 , 21,28 , 35,42 , 49,56 , 63,70 , 77,84 , . . . , . . . , the answer is = 11 answer is a"
Answer: a
Question (general): 5 men are equal to as many women as are equal to 7 boys . all of them earn rs . 90 only . men ’ s wages are ?
Options: a ) 8 rs . , b ) 7 rs . , c ) 6 rs . , d ) 4 rs . , e ) 5 rs .
Rationale: 5 m = xw = 7 b 5 m + xw + 7 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : c
Answer: c
Question (general): when positive integer n is divided by 4 , the remainder is 2 . when n is divided by 7 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 3 . . c"
Answer: c
Question (geometry): the area of a triangle is with base 8.4 m and height 5.8 m ?
Options: a ) 11.36 m 2 , b ) 10.36 m 2 , c ) 18.36 m 2 , d ) 19.36 m 2 , e ) 24.36 m 2
Rationale: "1 / 2 * 8.4 * 5.8 = 24.36 m 2 answer : e"
Answer: e
Question (general): if p ( a ) = 8 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 16 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 2 , e ) 4 / 7
Rationale: "p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 16 / 15 ) / ( 8 / 15 ) = 2 . d"
Answer: d
Question (physics): the speed of a car is 90 km in the first hour and 42 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 92 kmph , c ) 75 kmph , d ) 65 kmph , e ) 66 kmph
Rationale: "s = ( 90 + 42 ) / 2 = 66 kmph e"
Answer: e
Question (general): if the sum of the first n positive integers is s , what is the sum of the first n positive integers divisible by 4 , in terms of s ?
Options: a ) s / 2 , b ) s , c ) 2 s , d ) 2 s + 2 , e ) 4 s
Rationale: "answer is e given sum of 1 2 3 . . . . . n = s sum of 4 , 8 , 12 . . . . 2 n = 4 [ sum ( 1 2 3 . . . . n ) ] = 4 s"
Answer: e
Question (general): in how many ways can the integer 48 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "method 1 : listing all multiples since given number is small 48 = 1 * 48 , 2 * 24 , 3 * 16 , 4 * 12 , 6 * 8 = > 5 ways method 2 : express given number as prime factors 48 = 6 * 8 = 2 * 3 * 2 ^ 3 = 2 ^ 4 * 3 total number of factors = ( 4 + 1 ) ( 1 + 1 ) = 5 * 2 = 10 since the given number is not a perfect square , there will be exact 5 pairs possible of the given 10 factors = > 5 ways option c"
Answer: c
Question (general): if w is 40 percent less than x , x is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 x , x = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Question (physics): a boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 2 hr 30 min , b ) 2 hr , c ) 4 hr , d ) 1 hr 15 min , e ) none of these
Rationale: "explanation : speed upstream = 2 / 2 = 1 km / hr speed downstream = 1 / ( ( 20 / 60 ) ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 5 km in still water = 5 / 2 = 2 ( 1 / 2 ) hours = 2 hour 30 minutes . answer : option a"
Answer: a
Question (gain): the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 5 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 10210 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 5 = rs 10210 answer : c"
Answer: c
Question (other): pencils , pens and exercise books in a shop are in the ratio of 14 : 4 : 3 . if there are 140 pencils , the number of exercise books in the shop is :
Options: a ) 30 , b ) 27 , c ) 35 , d ) 33 , e ) 37
Rationale: explanation : let pencils = 14 x , pens = 4 x & exercise books = 3 x . now , 14 x = 140 hence x = 10 number of exercise books = 3 x = 30 answer : a
Answer: a
Question (physics): a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 280 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 16 * 20 = 320 = length of train length of platform = 600 - 320 = 280 answer : c"
Answer: c
Question (physics): in a quiz the points in each round for the first , second , third and fourth position were 10050 , 2010 . no other points were given . rachel participated in several rounds in the competition and the product of her score was 10000 . in how many rounds did she participate ?
Options: a ) 2 , b ) can not be determined , c ) 4 , d ) 6 , e ) 10
Rationale: correct answer is b because we are given that there wo n ' t be any points awarded for rounds other than 1 st four position . thus , it may happen that she played 150 rounds out of only 8 rounds were there in which she was awarded some points .
Answer: b
Question (general): how many positive integers less than 50 have a reminder 2 when divided by 7 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "take the multiples of 7 and add 2 0 x 7 + 2 = 2 . . . . 6 x 7 + 2 = 44 there are 7 numbers answer e"
Answer: e
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the area of the field . what is the length of the field ?
Options: a ) 13 , b ) 16 , c ) 34 , d ) 43 , e ) 42
Rationale: "explanation : a / 2 = 8 * 8 = > a = 8 * 8 * 2 x * 2 x = 8 * 8 * 2 x = 8 = > 2 x = 16 answer : option b"
Answer: b
Question (general): how many three digit numbers n are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Question (gain): in one hour , a boat goes 11 km along the stream and 5 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) km / hr = 8 kmph . answer c"
Answer: c
Question (general): arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 5 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 5 0 = a + d - 4 a + d = 4 a = d ( as they are twin brothers ) a = d = 2 a is the answer"
Answer: a
Question (physics): a and b go around a circular track of length 900 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 186 sec , d ) 180 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 900 / ( 36 * 5 / 18 ) , 900 / ( 54 * 5 / 18 ) } = lcm ( 90 , 60 ) = 180 sec . answer : d"
Answer: d
Question (physics): working together , jose and jane can complete an assigned task in 12 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 48 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 12 12 ( x + y ) = xy next , we ' re told 1 job takes 48 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 48 x + y = 96 so xy = 1152 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 36 days for jose and 32 days for jane . answer : e
Answer: e
Question (gain): one fourth of one third of two fifth of a number is 15 . what will be the 40 % of that number is ?
Options: a ) 120 , b ) 130 , c ) 150 , d ) 180 , e ) 250
Rationale: "( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 15 then x = 15 * 30 = 450 40 % of 450 = 180 answer d"
Answer: d
Question (general): the ages of ashley and mary are in the ratio 4 : 7 . the sum of their ages is 22 . find the ages of ashley .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: a : m = 4 : 7 let the ages of a & m be x & 22 - x x / 22 - x = 4 / 7 x = 8 a = 8 yrs answer : b
Answer: b
Question (physics): two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 180 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 12 sec , c ) 30 sec , d ) 50 sec , e ) 1 min
Rationale: "they meet every 180 / 7 + 8 = 12 sec answer is b"
Answer: b
Question (physics): a clock shows the time as 12 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 30 minutes , e ) 40 minutes
Rationale: "there are 6 hours in between 12 a . m . to 6 p . m . 6 * 5 = 30 minutes . answer : d"
Answer: d
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 36 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2882 , c ) 2999 , d ) 2667 , e ) 1392
Rationale: "let the side of the square plot be a ft . a 2 = 36 = > a = 6 length of the fence = perimeter of the plot = 4 a = 24 ft . cost of building the fence = 24 * 58 = rs . 1392 . answer : e"
Answer: e
Question (other): a person want to give his money of $ 4500 to his 4 children a , b , c , d in the ratio 2 : 4 : 5 : 4 . what is the a + b share ?
Options: a ) $ 1000 , b ) $ 2000 , c ) $ 1800 , d ) $ 1500 , e ) $ 1600
Rationale: "a ' s share = 4500 * 2 / 15 = $ 600 b ' s share = 4500 * 4 / 15 = $ 1200 a + b = $ 1800 answer is c"
Answer: c
Question (general): if the price of a certain computer increased 30 percent from y dollars to 351 dollars , then 2 y =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = y after 30 % price increase price = y + ( 30 / 100 ) * y = 1.3 y = 351 ( given ) i . e . y = 351 / 1.3 = $ 270 i . e . 2 y = 2 * 270 = 540 answer : option a"
Answer: a
Question (gain): if price of t . v set is reduced by 22 % , then its sale increases by 86 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 22 + 86 + ( - 22 * 86 ) / 100 = - 22 + 86 - 19 = 45 answer : b"
Answer: b
Question (other): there are 76 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "editing my solution : number of switches = 76 number of switches turned on by a : 3 , 6 , . . . 75 = 25 number of switches turned on by b : 5 , 10 , . . . . 75 = 15 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 25 - 6 ) + ( 15 - 6 ) = 28 answer : a"
Answer: a
Question (gain): each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 99 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3300 , c ) $ 6000 , d ) $ 6400 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 99 x = 3300 answer b"
Answer: b
Question (geometry): a goat is tied to one corner of a square plot of side 12 m by a rope 7 m long . find the area it can graze ?
Options: a ) 32
b ) 36.5
c ) 38.5
d ) 39
e ) 39.5
Rationale: area covered by goat = pi * r ^ 2 / 4 ( here we divide by 4 because rope is tied at the corner of the plot and only 1 / 4 part , the goat can graze ) where r = 7 m = length of rope so area = ( 22 / 7 ) * 7 * 7 / 4 = 38.5 sq m answer : c
Answer: c
Question (general): a retailer bought a hat at wholesale and marked it up 60 % to its initial price of $ 24 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the wholesale price . then 1.6 x = 24 and x = 24 / 1.6 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 6 more . the answer is d ."
Answer: d
Question (geometry): the cube root of . 000343 is
Options: a ) 0.7 , b ) 0.07 , c ) 0.007 , d ) 7 , e ) none of these
Rationale: "explanation : ( . 000343 ) 1 / 3 = ( 343 / 106 ) 1 / 3 = ( 7 * 7 * 7 / 102 * 102 * 102 ) 1 / 3 = 7 / 102 = 7 / 100 = 0.07 answer b"
Answer: b
Question (physics): a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 200 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: "the distance between the nest and the ditch is 200 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 200 = 6000 . d = st 6000 / 1.5 = t , i think we can take 6000 meters as 6 km , then only we get t = 4 . ( 1000 meters = 1 km ) d )"
Answer: d
Question (gain): 3 seventh of a number is 12 more than 40 % of that number . what will be the 30 % of that number ?
Options: a ) a ) 148 , b ) b ) 210 , c ) c ) 63 , d ) d ) 248 , e ) e ) 258
Rationale: 3 / 7 x – 40 / 100 x = 12 x = 35 * 12 35 * 12 * 30 / 100 = 126 / 2 = 63 answer : c
Answer: c
Question (general): find last digits of ( 1023 ^ 3923 ) + ( 3081 ^ 3921 )
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: we have ( 1023 ^ 3923 ) + ( 3081 ^ 3921 ) ( 3923 / 4 ) = 4 n + 3 ( 3921 / 4 ) = 4 n + 1 where n can be any integer now through cyclicity we can obtain or you can learn the chart from arun sharma number ending in 4 n + 1 4 n + 2 4 n + 3 4 n 1 1 1 1 1 2 2 4 8 6 3 3 9 7 1 in this way 7 + 1 = 8 is the unit ' s place digit answer : a
Answer: a
Question (physics): the sum of 4 consecutive even numbers is 36 . find the sum of the squares of these numbers ?
Options: a ) 296 , b ) 252 , c ) 344 , d ) 388 , e ) none of these
Rationale: let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c
Answer: c
Question (physics): two trains , each 150 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 90 , b ) 98 , c ) 60 , d ) 88 , e ) 12
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 150 + 150 ) / 8 = 3 x = > x = 25 / 2 . so , speed of the faster train = 50 / 2 = 25 * 18 / 5 = 90 km / hr . answer : a"
Answer: a
Question (general): with an average speed of 40 km / hr a car reaches its destination on time . if it goes with an average speed of 35 km / h , it is late by 15 minutes . the total journey is ?
Options: a ) 30 km , b ) 40 km , c ) 70 km , d ) 80 km , e ) 90 km
Rationale: let the total journey be x km . x / 35 - x / 40 = 15 / 60 solving for x , we get x = 70 therefore , total journey = 70 km . answer : c
Answer: c
Question (general): find the remainder q when 12 ^ 190 is divided by 1729 ?
Options: a ) 12 , b ) 1 , c ) 1728 , d ) 1717 , e ) 4
Rationale: 12 ^ ( 190 ) can be written as . ( ( 12 ^ 3 ) ^ 63 ) * 12 . 12 ^ 3 when divided by 1729 gives a remainder q - 1 . so in the numerator we have - 12 . now acccording to remainder theorm the answer will be 1729 - 12 = 1717 . d
Answer: d
Question (gain): how much 70 % of 100 is greater than 60 % of 80 ?
Options: a ) 18 , b ) 99 , c ) 22 , d ) 26 , e ) 71
Rationale: "( 70 / 100 ) * 100 – ( 60 / 100 ) * 80 70 - 48 = 22 answer : c"
Answer: c
Question (probability): the main line train starts at 5.00 am and the harbor line train starts at 5.02 am . each train has the frequency of 10 minutes . if a guy goes in the morning at a random time what is the probability of he getting main line train ?
Options: a ) . 5 , b ) 0.6 , c ) 0.4 , d ) 0.7 , e ) 0.8
Rationale: out of 10 minutes there is only 2 minutes chance of getting harbour line train and there is 8 minutes chance for getting main line train . so , probability = 8 / 10 = 0.8 answer : e
Answer: e
Question (gain): an uneducated retailer marks all his goods at 60 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 20 % , b ) 13.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 160 . s . p . = 75 % of rs . 160 = rs . 120 . ∴ gain % = 20 % . answer a"
Answer: a
Question (physics): a plane flies 420 miles with the wind and 350 miles against the wind in the same length of time . if the speed of the wind is 23 mph , what is the speed of the plain in still air ?
Options: a ) 253 mph . , b ) 275 mph . , c ) 296 mph . , d ) 278 mph . , e ) 235 mph .
Rationale: the speed of the plane in still air = x miles / hour the speed of the wind is 23 mph speed with the wind = ( x + 23 ) mph speed against the wind = ( x – 23 ) mph time = distance / speed according to the problem , 420 / ( x + 23 ) = 350 / ( x – 23 ) 420 ( x – 23 ) = 350 ( x + 23 ) 420 x – 9660 = 350 x + 805 420 x – 350 x = 8050 + 9660 70 x = 17710 x = 17710 / 70 x = 253 therefore , the speed of the plane in still air = 253 mph . correct answer a
Answer: a
Question (gain): rs 80000 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 9000 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 = 80000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 9000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 90000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 90000 = 80000 + y so y = 10000 then x = 80000 - 10000 = 70000 first part = 70000 answer : e"
Answer: e