Cheukting/mathqa huggingface dataset:
Question (other): in a certain alphabet , 8 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 8 + 24 = 32 ; next , we find the total # of letters without line : 40 - 32 = 8 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 8 - 0 = 8 . b"
Answer: b
Question (general): ( 18 ) 7 x ( 5832 ) - 2 ÷ ( 324 ) - 1 = ( 18 ) 7
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "explanation : ( 18 ) 7 x ( 183 ) - 2 ÷ ( 182 ) - 1 ( 18 ) 7 x ( 18 ) - 6 ÷ ( 18 ) - 2 ( 18 ) 7 - 6 + 2 = ( 18 ) 3 answer : option c"
Answer: c
Question (general): if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number w of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see w = 5 or 1 will give you same equation . . ans d"
Answer: d
Question (general): rajan is sixth from the left end and vinay is tenth from the right end in a row of boys . if there are 8 boys between rajan and vinay , how many boys are there in the row ?
Options: a ) 24 , b ) 66 , c ) 88 , d ) 27 , e ) 91
Rationale: explanation : number of boys in the row = ( 6 + 10 + 8 ) = 24 answer : a ) 24
Answer: a
Question (physics): a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 2.98 , b ) 2.88 , c ) 2.82 , d ) 2.86 , e ) 2.81
Rationale: "m = 6 s = 1.2 ds = 6 + 1.2 = 7.2 us = 6 - 1.2 = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 answer : b"
Answer: b
Question (general): find k if 64 / k = 8 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 64 / k = 8 and 64 / 8 = 8 , then k = 8 correct answer c"
Answer: c
Question (general): the unit digit in the product ( 445 * 534 * 999 * 234 ) is :
Options: a ) 2 , b ) 0 , c ) 6 , d ) 5 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 4 * 9 * 4 ) = 0 answer : b"
Answer: b
Question (general): the difference of two numbers is 1097 . on dividing the larger number by the smaller , we get 10 as quotient and the 17 as remainder . what is the smaller number ?
Options: a ) 230 , b ) 120 , c ) 95 , d ) 310 , e ) 320
Rationale: "solution : let the smaller number be x . then larger number = ( x + 1097 ) x + 1097 = 10 x + 17 9 x = 1080 x = 120 answer b"
Answer: b
Question (physics): a boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream , it takes 5 hours . what is the speed of the boat in still water ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 1
Rationale: explanation : rate downstream = ( 20 / 2 ) kmph = 10 kmph ; rate upstream = ( 20 / 5 ) kmph = 4 kmph speed in still water = 1 / 2 ( 10 + 4 ) kmph = 7 kmph answer : b
Answer: b
Question (general): a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 4 rows or 5 rows or 6 rows , then no tree will be left . find the least number of trees required .
Options: a ) 30 , b ) 60 , c ) 120 , d ) 240 , e ) 480
Rationale: "the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b"
Answer: b
Question (physics): a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 6 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 8 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 6 days whole work will be done by a in 6 * 4 / 3 = 8 days answer is d"
Answer: d
Question (physics): what distance will be covered by a bus moving at 72 kmph in 30 seconds ?
Options: a ) 877 m , b ) 600 m , c ) 167 m , d ) 176 m , e ) 546 m
Rationale: "explanation : 72 kmph = 72 * 5 / 18 = 20 mps d = speed * time = 20 * 30 = 600 m . answer : b"
Answer: b
Question (physics): steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 40 * 2 + 80 * 2 ) / ( 2 + 2 ) = 240 / 4 = 60 answer : c"
Answer: c
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 130 feet , b ) 22 feet , c ) 20 feet , d ) 15 feet , e ) 10 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 10 * breadth = 600 = > breadth = 60 feet area to be fenced = 2 b + l = 2 * 60 + 10 = 130 feet answer : option a"
Answer: a
Question (general): find the greatest number which leaves the same remainder when it divides 20 , 40 and 90 .
Options: a ) 18 , b ) 8 , c ) 12 , d ) 10 , e ) none of these
Rationale: "90 - 40 = 50 40 - 20 = 20 90 - 20 = 70 the h . c . f of 20 , 50 and 70 is 10 . answer : d"
Answer: d
Question (gain): what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 p . c . p . a ?
Options: a ) rs . 10111.00 , b ) rs . 10123.20 , c ) rs . 10123.00 , d ) rs . 10100.00 , e ) rs . 10110.00
Rationale: "= rs . ( 25000 x ( 1 + 12 / 100 ) ³ = rs . ( 25000 x 28 / 25 x 28 / 25 x 28 / 25 ) = rs . 35123.20 . c . i = rs ( 35123.20 - 25000 ) = rs . 10123.20 answer : b"
Answer: b
Question (probability): a bag contains 2 white marbles and 2 black marbles . if each of 2 girls and 2 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "first , total ways to select for all boys and girls , i . e 4 ! / ( 2 ! * 2 ! ) = 4 * 3 * 2 * 1 / 2 * 1 * 2 * 1 = 6 then there are one two way girls can have all same colors , either white or black . the number of ways in which 2 girls can select 2 white balls = 2 c 2 = 1 the number of ways in which 2 girls can select 2 black balls = 2 c 2 = 1 therefore , total favorable outcomes / total outcomes = 2 / 6 = 1 / 3 c"
Answer: c
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 100000 . if the profit at the end of a year is rs . 108000 , then the share of b is ?
Options: a ) 40000 , b ) 50000 , c ) 70000 , d ) 60000 , e ) 80000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 100000 * 6 ) = 7 : 20 total profit = rs . 108000 share of b = 20 / 27 ( 108000 ) = rs . 80000 answer : e"
Answer: e
Question (physics): matt and peter can do together a piece of work in 20 days . after they have worked together for 10 days matt stops and peter completes the remaining work in 10 days . in how many days peter complete the work separately .
Options: a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "together they complete the job in 20 days means they complete 10 / 20 of the job after 10 days . peter completes the remaining ( 10 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 10 / 20 ) = 20 b"
Answer: b
Question (general): a grocer has a sale of rs . 7435 , rs . 7927 , rs . 7855 , rs . 8230 and rs . 7562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?
Options: a ) rs . 1991 , b ) rs . 2991 , c ) rs . 3991 , d ) rs . 4991 , e ) rs . 5991
Rationale: "explanation : total sale for 5 months = rs . ( 7435 + 7927 + 7855 + 8230 + 7562 ) = rs . 39009 . required sale = rs . [ ( 7500 x 6 ) â € “ 39009 ] = rs . ( 45000 â € “ 39009 ) = rs . 5991 . answer e"
Answer: e
Question (physics): how many seconds will a 150 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 12 sec , b ) 30 sec , c ) 86 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 150 * 3 / 50 = 15 sec . answer : d"
Answer: d
Question (general): in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the fifth row ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 16
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 5 th row is 1 + 3 ( 4 ) = 13 the answer is c ."
Answer: c
Question (geometry): an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 7 : 5 , b ) 12 : 11 , c ) 17 : 15 , d ) 22 : 17 , e ) 27 : 25
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 2 y and y . 2 ( 3 x + 2 x ) = 2 ( 2 y + y ) 5 x = 3 y ( 5 / 3 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 2 y * y = 6 x ^ 2 : 2 y ^ 2 = 6 x ^ 2 : 2 * ( 25 / 9 ) * x ^ 2 = 54 : 50 = 27 : 25 the answer is e ."
Answer: e
Question (general): mixture contains alcohol and water in the ratio 4 : 3 . if 6 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 6.8 , c ) 27 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 24 x = 4 ( 3 x + 5 ) 12 x = 20 x = 1.7 quantity of alcohol = ( 4 x 1.7 ) litres = 6.8 litres . answer : b"
Answer: b
Question (physics): a cistern is filled by pipe a in 8 hours and the full cistern can be leaked out by an exhaust pipe b in 12 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 24 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: time taken to full the cistern = ( 1 / 8 - 1 / 12 ) hrs = 1 / 24 = 24 hrs answer : a
Answer: a
Question (gain): a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 238 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 220 : 113 , b ) 201 : 200 , c ) 210 : 201 , d ) 100 : 99 , e ) 113 : 77
Rationale: "explanation : 3 : 4 a = 3 / 7 * 238 = 102 402 : 400 201 : 200 answer : b"
Answer: b
Question (gain): a fruit seller had some apples . he sells 40 % apples and still has 420 apples . originally , he had :
Options: a ) 588 apples , b ) 742 apples , c ) 750 apples , d ) 600 apples , e ) 700 apples
Rationale: "suppose originally he had x apples . then , ( 100 - 40 ) % of x = 420 . 60 / 100 x x = 420 x = ( 420 x 100 ) / 60 = 700 . answer e"
Answer: e
Question (physics): it costs $ 2 for the first 1 / 6 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 15 per hour . if a certain customer uses the laundry machine for 2 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 42.25 . , b ) $ 40.25 . , c ) $ 38.25 . , d ) $ 36.25 . , e ) $ 34.25
Rationale: "2 hrs 25 min = 145 min first 10 min - - - - - - > $ 2 time left is 135 min . . . now , 60 min costs $ 15 1 min costs $ 15 / 60 145 min costs $ 15 / 60 * 145 = > $ 36.25 so , total cost will be $ 36.25 + $ 2 = > $ 38.25 hence answer will be c"
Answer: c
Question (general): when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 86.12 , what is the value of y ?
Options: a ) 96 , b ) 87 , c ) 75 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 9 / y . the remainder in decimal form is given as . 12 therefore , 9 / y = . 12 solve for y and get 75 . c"
Answer: c
Question (physics): a truck driver starts with the speed of 70 kmph with the truck driver decreasing speed every two hours by 10 kmph . the truck driver ' s speed does not drop below 50 kmph . in how many hours will it take the truck driver to travel 500 kms ?
Options: a ) 480 minutes , b ) 492 minutes , c ) 504 minutes , d ) 528 minutes , e ) 540 minutes
Rationale: distance covered in first two hours = 70 ã — 2 = 140 km distance covered in next two hours = 60 ã — 2 = 120 km distance covered in next two hours = 50 ã — 2 = 100 km distance covered in next two hours = 50 ã — 2 = 100 km distance covered in first eight hours 140 + 120 + 100 + 100 = 460 km remaining distance = 500 â € “ 460 = 40 km . now , this distance will be covered at the speed of 50 km / hr . â ˆ ´ time taken = 40 â  „ 50 = 4 â  „ 5 hour . total time = 8 + 4 â  „ 5 = 8 4 â  „ 5 hour answer d
Answer: d
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 57.76 , the number of the member is the group is :
Options: a ) 57 , b ) 76 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 57.76 x 100 ) paise = 5776 paise numbers of members = 5776 squareroot = 76 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 44 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 3 , e ) 9
Rationale: "going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 ( caught ) no of bounce = 3 . . answer : d"
Answer: d
Question (geometry): how many cubes of edge 2 dm can be cut out of a meter cube ?
Options: a ) 296
b ) 289
c ) 270
d ) 125
e ) 278
Rationale: 1 * 1 * 1 = 2 / 10 * 2 / 10 * 2 / 10 * x x = 125 answer : d
Answer: d
Question (physics): length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 59 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 18 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 18 ) + x ] = 200 2 x + 18 = 100 2 x = 82 x = 41 . hence , length = x + 18 = 59 m a"
Answer: a
Question (physics): a cistern is filled by pipe a in 16 hours and the full cistern can be leaked out by an exhaust pipe b in 20 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 16 - 1 / 20 ) hrs = 1 / 80 = 80 hrs answer : d"
Answer: d
Question (general): village x has a population of 76000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 17 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 76000 - 1200 p = 42000 + 800 p 2000 p = 34000 p = 17 answer is b ."
Answer: b
Question (general): average of 10 matches is 34 , how many runs one should should score to increase his average by 5 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 89 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 39 so , required score = ( 11 * 39 ) - ( 10 * 34 ) = 429 - 340 = 89 answer : option d"
Answer: d
Question (physics): two pipes can fill a cistern in 14 and 16 hours respectively . the pipes are opened simultaneously and it is found that due to leakage in the bottom , 32 minutes extra are taken for the cistern to be filled up . if the cistern is full , in what time would the leak empty it ?
Options: a ) 110 hours , b ) 112 hours , c ) 115 hours , d ) 100 hours , e ) none of these
Rationale: cistern filled by both pipes in one hour = 1 ⁄ 14 + 1 ⁄ 16 = 15 ⁄ 112 th ∴ both pipes filled the cistern in 112 ⁄ 15 hrs . now , due to leakage both pipes filled the cistern in 112 ⁄ 15 + 32 ⁄ 60 = 8 hrs . ∴ due to leakage , filled part in one hour 1 ⁄ 8 ∴ part of cistern emptied , due to leakage in one hour = 15 ⁄ 112 - 1 ⁄ 8 = 1 ⁄ 112 th ∴ in 112 hr , the leakage would empty the cistern . answer b
Answer: b
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1110 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 11
Rationale: explanation : 1500 - - - - 390 100 - - - - ? = > 26 % answer : c
Answer: c
Question (gain): a restaurant spends one quarter of its monthly budget for rent and quarter of the rest for food and beverages . what percentage of the budget does the restaurant spend for food and beverages ?
Options: a ) 23.5 % , b ) 32.5 % , c ) 35 % , d ) 18.75 % , e ) 20 %
Rationale: spend on rent = 1 / 4 spend on food and beverage = 1 / 4 of remaining = 1 / 4 * 3 / 4 = 3 / 16 so 3 / 16 = 18.75 % d is the answer
Answer: d
Question (general): a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 10 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %
Rationale: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.1 x ) = 0.88 x . the difference is 12 % . the answer is b ."
Answer: b
Question (general): of 3 numbers , the third is twice the second and the second is 4 times the first . if their average is 78 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 8 x . so , x + 4 x + 8 x = 78 × 3 = 234 . 13 x = 234 x = 234 / 13 hence , smallest number x = 18 . answer : a
Answer: a
Question (geometry): the area of a square is 625 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 20 cm less than the side of the square .
Options: a ) 5 : 12 , b ) 5 : 13 , c ) 2 : 9 , d ) 1 : 15 , e ) 1 : 5
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 625 a = 25 l = 3 a and b = a - 20 b : l = a - 20 : 3 a = 5 : 75 = 1 : 15 answer : d"
Answer: d
Question (physics): two pipes a and b can separately fill a tank in 20 and 15 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 540 liters , c ) 820 liters , d ) 900 liters , e ) 580 liters
Rationale: "1 / 20 + 1 / 15 - 1 / x = 1 / 15 x = 12 20 * 45 = 900 answer : d"
Answer: d
Question (geometry): the area of a triangle is with base 3 m and height 10 m ?
Options: a ) 88 m 2 , b ) 10 m 2 , c ) 66 m 2 , d ) 15 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 3 * 5 = 15 m 2 answer : c"
Answer: c
Question (gain): a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 50 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 2 hours ?
Options: a ) 32 % , b ) 36 % , c ) 40 % , d ) 44 % , e ) 48 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.5 ( 6 ) = 3 gallons at the start , the amount of water is 0.5 ( 6 ) = 3 gallons after 2 hours , the amount of water is 3 - 0.5 ( 2 ) = 2 gallons the concentration of water is 2 / ( 3 + 2 ) = 2 / 5 = 40 % the answer is c ."
Answer: c
Question (physics): in what time will a train 55 m long cross an electric pole , it its speed be 36 km / hr ?
Options: a ) 5.5 , b ) 4.5 , c ) 3.5 , d ) 2.5 , e ) 1.5
Rationale: "speed = 36 * 5 / 18 = 10 m / sec time taken = 55 / 10 = 5.5 sec . answer : a"
Answer: a
Question (physics): a leak in the bottom of a tank can empty the tank in 6 hrs . an pipe fills water at the rate of 4 ltrs / minute . 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 ) 2345 , b ) 2350 , c ) 2457 , d ) 4657 , e ) 5760
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 e"
Answer: e
Question (general): if m and n are positive integers and m ^ 2 + n ^ 2 = 20 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,600
Rationale: "you need to integers which squared are equal 20 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 stop . the integers ca n ' t be greater than 4 or we will score above 20 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 the only pair that matches is 4 ^ 2 + 2 ^ 2 = 20 . so 4 ^ 3 + 2 ^ 3 = 72 . answer a . )"
Answer: a
Question (physics): a train is moving at 6 / 7 of its usual speed . the train is 10 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 10 minutes represents 1 / 6 of the usual time . the usual time is 1 hour . the answer is b ."
Answer: b
Question (gain): a shopkeeper sells 20 % of his stock at 20 % profit ans sells the remaining at a loss of 10 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) 15500 , b ) 16000 , c ) 15000 , d ) 17000 , e ) 20000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 6 / 5 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.90 = 19 x / 25 = 36 x / 50 total sp = 12 x / 50 + 36 x / 50 = 48 x / 50 overall loss = x - 48 x / 50 = 2 x / 50 2 x / 50 = 600 = > x = 15000 answer : c"
Answer: c