Cheukting/mathqa huggingface dataset:
Question (general): in the x - y plane , point ( x , y ) is a lattice point if both x and y are integers . a square has a center at ( 0 , 0 ) and side = 4 . some points , such as the center ( 0 , 0 ) , are inside the square , but a point such as ( 0 , 2 ) is on the square but not in the square . how many lattice points are in the square ?
Options: a ) 10 , b ) 9 , c ) 8 , d ) 5 , e ) 12
Rationale: the lattice points that are in the square , that lie on the x and y axes , are ( 0 , 0 ) , ( 0 , 1 ) , ( 1 , 0 ) , ( 0 , - 1 ) , and ( - 1 , 0 ) . the lattice points in the square and not on the x and y axes are ( 1 , 1 ) , ( - 1 , 1 ) , ( 1 , - 1 ) , and ( - 1 , - 1 ) . there are a total of 9 lattice points in the square . answer : b
Answer: b
Question (physics): a boy is travelling from his home to school at 5 km / hr and reached 5 min late . next day he travelled at 10 km / hr and reached 10 min early . distance between home and school ?
Options: a ) 2.5 km , b ) 3 km , c ) 4 km , d ) 5.6 km , e ) 6.5 km
Rationale: "let the distance be x t 1 = x / 5 hr t 2 = x / 10 hr difference in time = 5 + 10 = 15 = 1 / 4 hr x / 5 - x / 10 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer is a"
Answer: a
Question (physics): a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 168 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 168 / 21 = 8 hours option e"
Answer: e
Question (physics): a cube of side one meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ?
Options: a ) 1898 , b ) 1098 , c ) 1000 , d ) 2008 , e ) 1082
Rationale: along one edge , the number of small cubes that can be cut = 100 / 10 = 10 along each edge 10 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 10 * 10 * 10 = 1000 answer : c
Answer: c
Question (gain): at what price must an book costing $ 47.50 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 62.5 , d ) 82.5 , e ) 65.9
Rationale: "e $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 90 / 100 ) = 59.375 mp = 65.9 e"
Answer: e
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 8 rows or 6 rows or 4 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 60 , c ) 24 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 8 , 6,4 ) = 24 . answer : c"
Answer: c
Question (geometry): if the sides of a triangle are 78 cm , 72 cm and 30 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 765 cm 2 , c ) 1080 cm 2 , d ) 197 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 78 cm , 72 cm and 30 cm is right angled , where the hypotenuse is 78 cm . area of the triangle = 1 / 2 * 72 * 30 = 1080 cm 2 answer : c"
Answer: c
Question (other): if 60 % of a number is equal to one half of another number , what is the ratio of first number to the second number ?
Options: a ) 4 : 5 , b ) 5 : 6 , c ) 6 : 5 , d ) 5 : 4 , e ) 2 : 5
Rationale: "let 60 % of a = 1 / 2 b . then , 60 a / 100 = 1 b / 2 = > 3 a / 5 = 1 b / 2 a / b = ( 1 / 2 * 5 / 3 ) = 5 / 6 a : b = 5 : 6 . answer : b"
Answer: b
Question (physics): it takes avery 2 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 1 hour and 30 minutes , e ) 1 hour and 20 minutes
Rationale: "avery ' s efficiency is 100 / 2 = 50 % tom ' s = 100 / 5 = 20 % they worked together for 1 hour and finished 70 % of the job remaining = 30 % tom will complete 20 % in 60 minutes , and 10 % in 60 * 10 / 20 minutes = 30 minutes time taken by tom to finish the remaining on his own = 60 + 30 = 90 minutes answer : d"
Answer: d
Question (gain): an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 3 / 5 % , then the amount invested at 11 % was ?
Options: a ) 23777 , b ) 30000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 48 / 5 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 960000 x = 70000 sum invested at 9 % = rs . 70000 sum invested at 11 % = rs . ( 100000 - 70000 ) = rs . 30000 . answer : b"
Answer: b
Question (general): find the numbers which are in the ratio 3 : 2 : 2 such that the sum of the first and the second added to the difference of the third and the second is 20 ?
Options: a ) 12 , 8,8 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: "let the numbers be a , b and c . a : b : c = 3 : 2 : 2 given , ( a + b ) + ( c - b ) = 20 = > a + c = 20 = > 3 x + 2 x = 20 = > x = 4 a , b , c are 3 x , 2 x , 2 x a , b , c are 12 , 8 , 8 . answer : a"
Answer: a
Question (gain): a shopkeeper loses 15 % , if an article is sold for rs . 170 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 247 , b ) s . 248 , c ) s . 240 , d ) s . 229 , e ) s . 212
Rationale: "given that sp = rs . 170 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 170 ) / 85 = 20 * 6 = rs . 200 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 200 * 120 ) / 100 = rs . 240 answer : c"
Answer: c
Question (general): mary ' s income is 50 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 90 % , e ) 64 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 90 ( 50 percent more than tim ' s income ) . thus , mary ' s income ( 90 ) is 90 % of juan ' s income ( 100 ) . answer : d ."
Answer: d
Question (gain): peter invests a sum of money and gets back an amount of $ 800 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 653 , b ) 664 , c ) 698 , d ) 744 , e ) 700
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 800 = 54 interest earned for 3 years = 54 * 3 = 162 amount invested = 815 - 162 = 653 answer : a"
Answer: a
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 200 resolutions .
Options: a ) 271.34 m , b ) 281.34 m , c ) 291.34 m , d ) 301.34 m , e ) 311.34 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 200 resolutions . = 200 * 2 * 22 / 7 * 22.4 = 28134 cm = 281.34 m answer : b"
Answer: b
Question (general): what is the value of 3 x ^ 2 − 1.8 x + 0.6 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0.6 , c ) 0.3 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.6 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.6 = 0 + 0.6 = 0.6 answer : b"
Answer: b
Question (gain): mr . hernandez , who was a resident of state x for only 12 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 720 , c ) $ 600 , d ) $ 300 , e ) $ 60
Rationale: "total tax for the year = 22,500 x 4 % = 900 as stated annual tax is prorated as per the duration of stay . prorated tax = 900 ( 12 / 12 ) = 900 answer a"
Answer: a
Question (general): the sum of digits of a two digit number is 12 , the difference between the digits is 6 . find the number
Options: a ) 85 , b ) 93 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 12 , x - y = 6 adding these 2 x = 18 = > x = 9 , y = 3 . thus the number is 93 answer b"
Answer: b
Question (general): how many 4 - digit numbers can be formed from the digits 0,2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and if the repetition is not allowed ?
Options: a ) 200 , b ) 240 , c ) 300 , d ) 360 , e ) 120
Rationale: "since , each desired number is divisible by 5 , so we must have either 0 or 5 at the unit place . so , the tens place can now be filled by any of the remaining 6 digits ( 2 , 3 , 6 , 7 , 9 , 0 or 5 ) the hundreds place can now be filled by any of the remaining 5 digits therefore the 3 - digit no can be formed by ( 4 * 5 * 6 * 2 ) = 240 ways ans - b"
Answer: b
Question (physics): if 8 workers can build 8 cars in 8 days , then how many days would it take 7 workers to build 7 cars ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 7 workers can build 7 / 8 car per day . the time required to build 7 cars is 7 / ( 7 / 8 ) = 8 days the answer is c ."
Answer: c
Question (physics): the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 45 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 450 ft , d ) 900 ft , e ) 1000 ft
Rationale: "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 45 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 10 . sub x = 10 either in ( x + 5 ) * 30 or in x * 45 to get the distance , which is 450 . so the correct choice is c ."
Answer: c
Question (general): a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1242 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1242 or 9 x = 1242 or x = 138 . required number = 138 . answer : e"
Answer: e
Question (gain): in an election , candidate a got 85 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 347000 , d ) 356000 , e ) 404600
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 85 % therefore , the number of valid votes polled in favour of candidate a = 85 % of 476000 = 85 / 100 × 476000 = 40460000 / 100 = 404600 e )"
Answer: e
Question (general): find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 306.09 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"
Answer: c
Question (gain): a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price . if the retailer decreases the retail price by 20 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 42 , d ) 44 , e ) 50
Rationale: "answer : d = 44 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 80 % increase makes retail price = 180 . now 20 % decrease - > ( 1 - 20 / 100 ) * 180 = 144 . now compared to the wholesale price of 100 , 44 % increase is what will have the same effect as increasing the wholesale price ."
Answer: d
Question (geometry): the slant height of a cone is 22 cm and radius of the base is 7 cm , find the curved surface of the cone ?
Options: a ) 426 , b ) 284 , c ) 483 , d ) 256 , e ) 428
Rationale: "π * 22 * 7 = 483 answer : c"
Answer: c
Question (gain): one night 40 percent of the female officers on a police force were on duty . if 240 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 300 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 240 number of female officers on duty on that night = 240 / 2 = 120 ( 40 / 100 ) * f = 120 = > f = 300 answer b"
Answer: b
Question (probability): there are 4 red shoes & 6 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 2 , d ) 2 / 15 , e ) 2 / 16
Rationale: "taking 4 red shoe the probablity is 4 c 2 from 10 shoes probablity of taking 2 red shoe is 4 c 2 / 10 c 2 = 2 / 15 answer : d"
Answer: d
Question (general): how much water should be added to 14 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 26 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 14 + x ) ) ) 2 = 5 % * ( 14 + x ) - - - - - - - - > x = 26 ans c"
Answer: c
Question (physics): a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 8 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 25
Rationale: on the way down , the rate is 1.5 * 8 = 12 miles per day . the distance of the route down the mountain is 2 * 12 = 24 miles . the answer is d .
Answer: d
Question (general): what is the 20 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 2 nd , 4 th , 6 th , . . . ) to the right of the decimal point is alternating by 2 , 0 , 7 thus 20 th digit is 2 . answer : b ."
Answer: b
Question (gain): the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6.6 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 55 , d ) rs . 50 , e ) none
Rationale: solution t . d = [ b . g x 100 / r x t ] = rs . ( 6.6 x 100 / 12 x 1 ) = rs . 55 . answer c
Answer: c
Question (general): the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 92 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 92 ( x - 5 ) 80 x - ( 5 * 20 ) = 92 ( x - 5 ) 360 = 12 x = > x = 30 answer : c"
Answer: c
Question (general): if x is to be chosen at random from the integers between 1 to 6 , inclusive , and y is to be chosen at random from the integers between 7 and 10 , inclusive , what is the probability that x + y will be even ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 6 * 2 / 4 = 1 / 4 p ( x and y are both odd ) = 3 / 6 * 2 / 4 = 1 / 4 p ( x + y is even ) = 1 / 4 + 1 / 4 = 1 / 2 the answer is a ."
Answer: a
Question (general): a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 7.5 $ then total value is 300 * 7.5 = 2250 . answer : option e is correct answer . ."
Answer: e
Question (gain): a bowl was filled with 10 ounces of water , and 0.08 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 40 % , d ) 4 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 08 * 50 = . 08 * 100 / 2 = 8 / 2 = 4 percent of the original amount of water evaporated during this period = ( 4 / 10 ) * 100 % = 40 % answer c"
Answer: c
Question (gain): machine a and machine b are each used to manufacture 440 sprockets . it takes machine a 10 hours longer to produce 440 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2
Rationale: "machine b : takes x hours to produce 440 sprockets machine a : takes ( x + 10 ) hours to produce 440 sprockets machine b : in 1 hour , b makes 440 / x sprockets machine a : in 1 hour , a makes 440 / ( x + 10 ) sprockets equating : 1.1 ( 440 / ( x + 10 ) ) = 440 / x 484 / ( x + 10 ) = 440 / x 484 x = 440 x + 4400 44 x = 4400 x = 100 a makes 440 / ( 110 ) = 4 sprockets per hour answer : c"
Answer: c
Question (physics): two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 42 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 72 sec , b ) 132 sec , c ) 192 sec , d ) 252 sec , e ) none
Rationale: "solution relative speed = ( 42 - 40 ) kmph = 2 kmph = ( 2 x 5 / 18 ) m / sec = ( 10 / 18 ) m / sec time taken = ( 350 x 18 / 10 ) sec = 630 sec . answer e"
Answer: e
Question (physics): the sum of three consecutive even numbers is 87 . find the middle number of the three ?
Options: a ) 31 , b ) 21 , c ) 29 , d ) 22 , e ) 12
Rationale: "middle number = 87 / 3 = 29 ans c"
Answer: c
Question (geometry): the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1170 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 180 , d ) 321 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1170 x = 40 required perimeter = 2 ( 40 + 50 ) = 180 c"
Answer: c
Question (geometry): there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is 7 - third that of the smaller circle . find the circumference of the smaller circle .
Options: a ) 165 ∏ cm , b ) 65 ∏ cm , c ) 12 ∏ cm , d ) 14 ∏ cm , e ) 16 ∏ cm
Rationale: let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c
Answer: c
Question (general): the average of first four prime numbers greater than 30 is ?
Options: a ) 38 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "31 + 37 + 41 + 43 = 152 / 4 = 38 answer : a"
Answer: a
Question (general): kim bought a total of $ 2.65 worth of postage stamps in 4 denominations . if she bought an equal number of 2 - cent and 20 - cent stamps and twice as many 10 - cent stamps as 5 - cent stamps , what is the least number of 1 - cent stamps she could have bought ?
Options: a ) 5 , b ) 10 , c ) 55 , d ) 80 , e ) 95
Rationale: let : # of 2 and 20 cents stamps = n # of 10 cent stamps = 2 n # of 1 cent stamps = m therefore : 2 n + 20 n + 10 ( 2 n ) + m = 265 cents 42 n + m = 265 forleastnumber of 1 cents stamps , maximize 50 n . hence , 42 * 5 + m = 265 m = 55 i . e . 55 stamps 1 cents each answer : c
Answer: c
Question (gain): a and b put in rs . 200 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 210 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 49 , c ) 39 : 42 , d ) 39 : 47 , e ) 17 : 20
Rationale: "explanation : 1 : 2 a = 2 / 3 * 210 = 140 340 : 400 17 : 20 answer : e"
Answer: e
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 , b ) 388 , c ) 266 , d ) 299 , e ) 261
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 9 = 150 meter . answer : a"
Answer: a
Question (physics): a certain car can travel 40 minutes on a gallon of gasoline at 50 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 50 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 40 mins ( @ 50 miles / hr ) = ( 50 / 50 ) * 40 = 40 miles fuel used to travel 80 miles = ( 80 / 40 ) = 2 gallon i . e . used fuel = ( t - 8 ) = 2 gallon i . e . t = 10 gallons i . e . used fuel = ( 2 / 10 ) * 100 = 20 % b"
Answer: b
Question (general): the average weight of 8 students decreases by 5 kg when one of them weighing 86 kg is replaced by a new student . the weight of the student is
Options: a ) 46 kg , b ) 48 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 5 kg = > ( 86 - x ) / 8 = 5 = > x = 46 answer : a"
Answer: a
Question (gain): a football team lost 5 yards and then gained 8 . what is the team ' s progress ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 8 = 3 yards b"
Answer: b
Question (physics): a and b go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 60 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 176 sec , c ) 178 sec , d ) 187 sec , e ) 180 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 { 600 / ( 36 * 5 / 18 ) , 600 / ( 60 * 5 / 18 ) } = 180 sec . answer : e"
Answer: e