Cheukting/mathqa huggingface dataset:
Question (general): a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 750 more than that by the previous schema , his sales were worth ?
Options: a ) s . 4,000 , b ) s . 6,000 , c ) s . 30,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 750 x = 6000 answer : b"
Answer: b
Question (general): what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 22 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 1 : 2 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3 : 6 = 1 : 2"
Answer: c
Question (gain): calculate how long it will take a swimmer to swim a distance of 7 km against the current of a river which flows at 2.5 km / hr , given that he can swim in still water at 4.4 km / h
Options: a ) 6.67 , b ) 1.67 , c ) 2.67 , d ) 3.67 , e ) 4.67
Rationale: "swim in still water at = 4.4 speed of river = 2.5 us = 4.4 - 2.5 = 1.9 distance = 7 t = 7 / 1.9 = 3.67 answer : d"
Answer: d
Question (geometry): a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 200 . the cost for 1 bat and 6 balls is $ 220 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 210 for the purchase ?
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: imo it should be c that is 3 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 200 1 b + 6 c = 220 solving both we get b that is bat = 40 and c that is ball = 30 new equation 210 to be divided in equal 3 b + 3 c = 210 3 * 40 + 3 * 30 = 210 120 + 90 = 210
Answer: c
Question (general): if the product of the integers from 1 to n is divisible by 686 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "686 = 7 x 7 x 7 x 2 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c ."
Answer: c
Question (geometry): find the area of a parallelogram with base 12 cm and height 18 cm .
Options: a ) 200 , b ) 216 , c ) 345 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 12 * 18 = 216 cm 2 answer : option b"
Answer: b
Question (general): if a number p is prime , and 2 p + 4 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "1 / 6 = 0.1666666 . . . ( a repeating pattern one digit long ) a"
Answer: a
Question (physics): a train 110 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: speed of train relative to man : 110 / 6 * 18 / 5 km / hr = 66 km / hr let speed of train = x therefore x + 6 = 66 x = 66 - 6 x = 60 km / hr answer : b
Answer: b
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , the how old is b ?
Options: a ) 10 years , b ) 12 years , c ) 14 years , d ) 15 years , e ) 16 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 x = 6 . hence , b ' s age = 2 x = 12 years . b )"
Answer: b
Question (general): a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 45000 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 90000 , c ) 85000 , d ) 190000 , e ) 250000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 45000 - > x = 150000 answer : b"
Answer: b
Question (general): in a certain company , the formula for maximizing profits is p = - 25 x ^ 2 + 7500 x , , where p is profit and x is the number of machines the company operates in its factory . what value for x will maximize p ? this one is from integratedlearning . here ' s what i did : the oa states : to find a maximum or minimum value of an equation with an exponent in it , you take the derivative of the equation , set it to zero , and solve . i dont really get what that means . so whoever solves it , could you plz post explanation of what the above sentence mean as well ?
Options: a ) 10 , b ) 50 , c ) 150 , d ) 200 , e ) 300
Rationale: recognize that 25 is a factor of 7500 . if we take this out , we have two parts to the equation : - x ^ 2300 x one part of the equation brings our value down , whereas the other part brings our value up . at this point , we can test the numbers in the answer choice . notice that they are very straight forward to square , and multiplication by 300 is very easy . a ) 10 - 3000 - 100 = 2900 b ) 50 - 15000 - 2500 = 12500 c ) 150 - 45000 - 22500 = 22500 d ) 200 - 60000 - 40000 = 20000 e ) 300 - recognize that this is zero therefore , answer is 150 . hope this helps those - like myself - who have n ' t thought about calculus for over half a decade . c
Answer: c
Question (geometry): in the coordinate plane , one of the vertices of a square is the point ( - 5 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ?
Options: a ) 100 , b ) 225 , c ) 169 , d ) 256 , e ) 324
Rationale: "one point ( - 5 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 5 - 3 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 d"
Answer: d
Question (geometry): the cost of the paint is rs . 30 per kg . if 1 kg of paint covers 18 sq . ft , how much will it cost to paint outside of a cube having 6 feet each side
Options: a ) rs . 962 , b ) rs . 672 , c ) rs . 540 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 6 ^ 2 = 216 sq . ft quantity of paint required = ( 216 / 18 ) = 12 kg cost of painting = 30 x 18 = rs . 540 answer : c"
Answer: c
Question (general): what is the smallest number which when diminished by 18 , is divisible 8 , 14 , 26 and 28 ?
Options: a ) 746 , b ) 750 , c ) 789 , d ) 678 , e ) 897
Rationale: "required number = ( lcm of 8 , 14 , 26 and 28 ) + 18 = 728 + 18 = 746 option a"
Answer: a
Question (general): in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 11 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 9 / 5 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 11 ) = 36 / 20 = 9 / 5 . answer : d ."
Answer: d
Question (gain): two men started from the same place walk at the rate of 5 kmph and 5.5 kmph respectively . what time will they take to be 8.5 km apart , if they walk in the same direction ?
Options: a ) 10 hours , b ) 12 hours , c ) 17 hours , d ) 15 hours , e ) 20 hours
Rationale: "to be 0.5 km apart they take 1 hour to be 8.5 km apart they take = 1 / 0.5 * 8.5 = 17 hours answer is c"
Answer: c
Question (gain): ? % of 360 = 162
Options: a ) 277 , b ) 36 , c ) 45 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 162 or , ? = 162 × 100 / 360 = 45 answer c"
Answer: c
Question (other): how many factors does 35 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 6 * 4 = 24 answer c ."
Answer: c
Question (gain): at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the men are married ?
Options: a ) 3 / 4 , b ) 2 / 5 , c ) 4 / 5 , d ) 2 / 3 , e ) 1 / 4
Rationale: - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married man / total man , so 10 / 40 = 1 / 4 e
Answer: e
Question (general): p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is r ' s share ?
Options: a ) 108 , b ) 120 , c ) 134 , d ) 144 , e ) none of these
Rationale: explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 r ' s share = 378 * ( 6 / 21 ) = 108 . answer : option a
Answer: a
Question (physics): light glows for every 18 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 281 , b ) 277 , c ) 283 , d ) 384 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 18 = 276 . so total 277 times light ll glow answer : b"
Answer: b
Question (general): find the smallest number which leaves 2235 , 48 and 61 as remainders when divided by 26 , 39 , 52 and 65 respectively .
Options: a ) 67 , b ) 26 , c ) 99 , d ) 26 , e ) 91
Rationale: answer : d
Answer: d
Question (general): if k ^ 3 is divisible by 168 , what is the least possible value of integer k ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: k ^ 3 = 168 * x = 2 ^ 3 * 3 * 7 * x the factors of k must at minimum include 2 * 3 * 7 = 42 . the answer is b .
Answer: b
Question (physics): a and b can do a work in 20 days , b and c in 25 days , c and a in 30 days . if a , b and c work together , they will complete the work in ?
Options: a ) 10 days , b ) 12 days , c ) 16 days , d ) 20 days , e ) 25 days
Rationale: "a + b 1 day work = 1 / 20 b + c 1 day work = 1 / 25 c + a 1 day work = 1 / 30 adding we get 2 ( a + b + c ) = 1 / 20 + 1 / 25 + 1 / 30 = 37 / 300 a + b + c 1 day work = 37 / 600 a , b , c can finish the work in 600 / 37 days = 16 days approximately answer is c"
Answer: c
Question (physics): in what time will a train 100 m long cross an electric pole , it its speed be 136 km / hr ?
Options: a ) 2.6 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 136 * 5 / 18 = 37.8 m / sec time taken = 100 / 37.8 = 2.6 sec . answer : a"
Answer: a
Question (general): 5220 / ? * 15 = 2175
Options: a ) 34 , b ) 36 , c ) 33 , d ) 42 , e ) 24
Rationale: "b ( 5220 / ? ) * 15 = 2175 ? = ( 5220 * 15 ) / 2175 = > ? = 36"
Answer: b
Question (physics): the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 126 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 70 %
Rationale: answer : d 126 ° divided by 360 ° equals 0.35 , therefore the sector is equal to 35 % of the total
Answer: d
Question (general): what is the unit digit in 14 ^ 100 ?
Options: a ) 0 , b ) 5 , c ) 2 , d ) 3 , e ) 6
Rationale: unit digit in 14 ^ 100 = unit digit in [ ( 14 ^ 4 ) ^ 25 ] but unit digit in 14 ^ 4 = 6 unit digit 14 ^ 100 = 6 answer is e
Answer: e
Question (geometry): if n is the smallest integer such that 864 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "865 can written as = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 - - > 2 ^ 5 * 3 ^ 3 - - - ( 1 ) so for 864 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 3 to make the power of 3 in ( 1 ) even option b is correct"
Answer: b
Question (physics): tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 5 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 30 , c ) 40 , d ) 70 , e ) 60
Rationale: "b 30 sum = ( n x n ) + n hence , 5 x 5 = 25 + 5 = 30"
Answer: b
Question (general): what is the sum of all digits for the number 10 ^ 25 - 58 ?
Options: a ) 197 , b ) 201 , c ) 205 , d ) 209 , e ) 213
Rationale: "10 ^ 25 is a 26 - digit number : 1 followed by 25 zeros . 10 ^ 25 - 58 is a 25 - digit number : 23 9 ' s and 42 at the end . the sum of the digits is 23 * 9 + 4 + 2 = 213 . the answer is e ."
Answer: e
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 24 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 24 = 6 k + 4 p = > k = 2 , p = 3 total red ' s in bag a will be 2 k = 4 c"
Answer: c
Question (physics): a can do a piece of work in 40 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 24 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 40 + 10 / 30 + 10 / x = 1 x = 24 days answer : a"
Answer: a
Question (general): what least value should be replaced by * in 2631 * 4 so the number become divisible by 3
Options: a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7
Rationale: "explanation : trick : number is divisible by 3 , if sum of all digits is divisible by 3 , so ( 2 + 6 + 3 + 1 + * + 4 ) = 16 + * should be divisible by 9 , 16 + 2 will be divisible by 2 , so that least number is 2 . answer : option d"
Answer: d
Question (other): the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 735 , krishan has ?
Options: a ) s . 4335 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680
Rationale: ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 735 : n & there n = 289 x 735 / 49 = rs . 4335 answer : a
Answer: a
Question (physics): a train 146 m long is running at a speed of 98 kmph . how long does it take to pass a man who is running at 12 kmph in the same direction as the train ?
Options: a ) 6 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : a . speed of the train relative to man = ( 98 - 12 ) kmph = ( 86 * 5 / 18 ) m / sec = ( 215 / 9 ) m / sec time taken by the train to cross the man = time taken by it to cover 146 m at 219 / 9 m / sec = 146 * 9 / 219 sec = 6 sec"
Answer: a
Question (general): nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 5 screws and 1 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4
Rationale: let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 5 s and 1 n = 5 s + 1 * 5 s = 10 s . . ratio = 15 s / 10 s = 15 / 10 = 3 / 2 d
Answer: d
Question (other): a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 5 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 9 : 100 , b ) 100 : 9 , c ) 12 : 100 , d ) 12 : 20 , e ) 13 : 100
Rationale: "water : soap = 3 : 5 soap : salt = 12 : 20 = > for 12 soap , salt = 20 = > for 5 soap , salt = ( 20 / 12 ) * 5 = 100 / 12 = 25 / 3 so , water : soap : salt = 3 : 5 : 25 / 3 = 9 : 15 : 25 after open container , water : soap : salt = 2.25 : 15 : 25 so , water : salt = 2.25 : 25 = 9 : 100 answer : a"
Answer: a
Question (physics): the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 94 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 94 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 94 * 7 ) = 1350 - ( 609 + 658 ) = 1350 - 1267 = 83 answer a"
Answer: a
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 1200 in 5 years ?
Options: a ) 12 , b ) 3 , c ) 14 , d ) 5 , e ) 6
Rationale: "450 = ( 750 * 5 * r ) / 100 r = 12 % . answer : a"
Answer: a
Question (gain): the difference between simple and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) rs . 7 , b ) rs . 3 , c ) rs . 8 , d ) rs . 1 , e ) rs . 4
Rationale: "s . i . = ( 1200 * 10 * 1 ) / 100 = rs . 120 c . i . = [ 1200 * ( 1 + 5 / 100 ) 2 - 1200 ] = rs . 123 difference = ( 123 - 120 ) = rs . 3 . answer : b"
Answer: b
Question (physics): stacy and heather are 25 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 9.0 mile , b ) 13.0 mile , c ) 11.0 mile , d ) 10.2 mile , e ) 12 mile
Rationale: ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 25 - 2.4 = 22.6 time taken = distance / speed = 22.6 / 11 = 2.05 hrs heather will cover = 5 * 2.4 = 10.2 miles . answer d
Answer: d
Question (physics): ganesh , ram and sohan together can do a work in 16 days . if ganesh and ram together can do a the same work in 24 days then , how long will take sohan to do the same work ?
Options: a ) 48 , b ) 58 , c ) 68 , d ) 78 , e ) 100
Rationale: solution : work done by three of them together in 1 day = 1 / 16 . . . . . . . . . . . . ( 1 ) work done by ganesh and ram together in 1 day = 1 / 24 . . . . . ( 2 ) so , work done by sohan in one day = ( 1 ) - ( 2 ) = ( 1 / 16 ) - ( 1 / 24 ) = 1 / 48 = > total days taken by sohan to complete the work alone = 48 days . answer a
Answer: a
Question (gain): one fourth of one third of two fifth of a number is 25 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 180 , d ) d ) 200 , e ) e ) 300
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 25 then x = 25 * 30 = 750 40 % of 750 = 300 answer : option e"
Answer: e
Question (gain): the cost price of an article is 56 % of the marked price . calculate the gain percent after allowing a discount of 13 % .
Options: a ) 23.4 % , b ) 44.5 % , c ) 55.3 % , d ) 57.4 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 56 . s . p = rs . 87 . â ˆ ´ gain % = [ 31 / 56 * 100 ] % = 55.3 % . answer c"
Answer: c
Question (physics): two trains each 260 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12.48 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 260 m + 260 m = 520 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 520 * 3 / 125 = 12.48 sec answer : option c"
Answer: c
Question (other): 1024 people in village 720 speak tamil , 562 speak english while 346 speak both . person who don not speack english or tamil speak hindi . what is probibility that person speak hindi
Options: a ) 13 / 128 , b ) 12 / 128 , c ) 11 / 126 , d ) 11 / 127 , e ) 11 / 128
Rationale: n ( t ) = 720 n ( e ) = 562 n ( t ^ e ) = 346 n ( tue ) = 720 + 562 - 346 = 936 now , n ( h ) = 1024 - 936 = 88 p ( h ) = 88 / 1024 = 11 / 128 = 0.085 answer : e
Answer: e
Question (physics): a train 140 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 78 kmph
Rationale: "speed of train relative to man : 140 / 6 * 18 / 5 km / hr = 84 km / hr let speed of train = x therefore x + 6 = 84 x = 84 - 6 x = 78 km / hr answer : e"
Answer: e
Question (physics): the speed of a train is 120 kmph . what is the distance covered by it in 8 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 16 kmph , d ) 18 kmph , e ) 12 kmph
Rationale: "120 * 8 / 60 = 16 kmph answer : c"
Answer: c
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 260 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 260 m , b ) 270 m , c ) 643 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 260 / 26 = 20 x + 260 = 520 x = 260 . answer : a"
Answer: a
Question (gain): if albert ’ s monthly earnings rise by 14 % , he would earn $ 678 . if , instead , his earnings rise by only 15 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 689 , c ) 683 , d ) 690 , e ) 693
Rationale: "= 678 / 1.14 ∗ 1.15 = 683 = 683 answer is c"
Answer: c
Question (physics): a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 45 minutes . the total distance is ?
Options: a ) 1 km , b ) 2.87 km , c ) 3 km , d ) 4 km , e ) 5 km
Rationale: "b 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 45 / 60 47 x / 60 = 45 / 60 = > x = 0.95 . total distance = 3 * 0.95 = 2.87 km ."
Answer: b
Question (general): a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container .
Options: a ) 26.34 litres , b ) 27.36 liters , c ) 28 litres , d ) 29.16 litres , e ) can not be determined
Rationale: solution amount of milk left after 3 operations [ 40 ( 1 - 4 / 40 ) 3 ] litres = ( 40 x 9 / 10 x 9 / 10 x 9 / 10 ) = 29.16 litres answer d
Answer: d
Question (general): if grapes are 90 % water and raisins are 17 % water , then how many kilograms did a quantity of raisins , which currently weighs 14 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 108.6 , b ) 110.4 , c ) 112.6 , d ) 114.8 , e ) 116.2
Rationale: "let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 83 % of the raisins , 0.1 x = 0.83 ( 14 kg ) . then x = 8.3 * 14 = 116.2 kg . the answer is e ."
Answer: e