regisss/math_qa huggingface dataset:
Problem: a corporation paid $ 7 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 100 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 100 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 114 % , d ) 23 % , e ) 43 %
Rationale: "difference in ratios = ( 30 / 100 ) - ( 7 / 50 ) = ( 8 / 50 ) % change = ( change ( 8 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 114 % answer - c"
Answer: c
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 2 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 2 , c ) 12 , d ) 14 , e ) 15
Rationale: - > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 2 ^ 2 - 2 = 2 . thus , the answer is b .
Answer: b
Problem: the ratio of two quantities is 5 : 8 . if each of the quantities is increased by 10 , what is the ratio of the new quantities ?
Options: a ) 5 : 8 , b ) 50 : 78 , c ) 2 : 3 , d ) it can not be determined from the information given . , e ) 6 : 7
Rationale: since the ratio is 5 : 8 we can put the quantities as 5 k and 8 k . moreover increasing quantities implies that the quantities become 5 k + 10 and 8 k + 10 . so the ratio is ( 5 k + 10 ) : ( 8 k + 10 ) . the ratio value depend on the value of k . so it can not be determined from the information given . the answer is d
Answer: d
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: divide rs . 1500 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 337 , b ) 299 , c ) 375 , d ) 662 , e ) 201
Rationale: "a + b + c = 1500 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1500 = > 375 answer : c"
Answer: c
Problem: 80 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 28800 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none
Rationale: "answer ∵ 80 % of p = 23040 ∴ p = ( 23040 x 100 ) / 80 = 28800 correct option : a"
Answer: a
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1702 ?
Options: a ) s . 109 , b ) s . 115 , c ) s . 100 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1702 74 x = 1702 = > x = 23 5 x = 115 rs . answer : b"
Answer: b
Problem: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 18 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 7.5 , b ) 12.5 , c ) 17.5 , d ) 22.5 , e ) 27.5
Rationale: in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 18 = 1.5 km . the time it takes the hiker to complete this distance is 1.5 / 4 hours = 22.5 minutes the cyclist needs to wait 22.5 - 5 = 17.5 minutes the answer is c .
Answer: c
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 45 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 300 km , at what time will the truck and the car meet each other ?
Options: a ) 4 : 30 , b ) 5 : 00 , c ) 5 : 30 , d ) 6 : 00 , e ) 6 : 30
Rationale: "at 2 : 00 pm , the truck and the car are 255 km apart . the truck and the car complete a distance of 85 km each hour . the time it takes to meet is 255 / 85 = 3 hours . they will meet at 5 : 00 pm . the answer is b ."
Answer: b
Problem: two cars are driving toward each other . the first car is traveling at a speed of 75 km / h , which is 25 % slower than the second car ' s speed . if the distance between the cars is 1050 km , how many hours will it take until the two cars meet ?
Options: a ) 4 , b ) 4.5 , c ) 5 , d ) 5.5 , e ) 6
Rationale: "the speed of the first car is 75 km / h . the speed of the second car is 75 / 0.75 = 100 km / h . the two cars complete a total of 175 km each hour . the time it takes the cars to meet is 1050 / 175 = 6 hours . the answer is e ."
Answer: e
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 26 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 203 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 26 : x = > x = { \ color { blue } \ frac { 26 \ times 1 } { 0.128 } } = > x = 203.13 so time will be approx 203 seconds answer : e"
Answer: e
Problem: in a class of 38 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 38 - 29 = 9 play neither answer is c"
Answer: c
Problem: if the diameter of circle r is 80 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 74 % , b ) 64 % , c ) 84 % , d ) 94 % , e ) 34 %
Rationale: "let diameter of circle r , dr = 80 and diameter of circle s , ds = 100 radius of circle r , rr = 40 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 40 / 50 ) ^ 2 = ( 8 / 10 ) ^ 2 = 64 % answer : b"
Answer: b
Problem: find the perimeter and area of a square of side 9 cm .
Options: a ) 36 , b ) 49 , c ) 64 , d ) 81 , e ) 100
Rationale: "we know that the perimeter of square = 4 ã — side side = 9 cm therefore , perimeter = 4 ã — 9 cm = 36 cm now , area of the square = ( side ã — side ) sq . units = 9 ã — 9 cm â ² = 81 cm â ² answer : d"
Answer: d
Problem: the ratio of the volumes of two cubes is 9261 : 12167 . what is the ratio of their total surface areas ?
Options: a ) 1 : 12 , b ) 85 : 31 , c ) 51 : 45 , d ) 58 : 67 , e ) 53 : 58
Rationale: "ratio of the sides = ³ √ 9261 : ³ √ 12167 = 21 : 23 ratio of surface areas = 212 : 232 = 53 : 58 answer : e"
Answer: e
Problem: a and b together can do a work in 3 days . if a alone can do it in 12 days . in how many days can b alone do it ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 25
Rationale: "a 4 1 / 3 â € “ 1 / 12 = 1 / 4 = > 4"
Answer: a
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 18 percent alcohol by volume ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300
Rationale: "18 % is 8 % - points higher than 10 % but 12 % - points lower than 30 % . thus there should be 3 parts of solution x for 2 parts of solution y . we should add 200 ml of solution y . the answer is c ."
Answer: c
Problem: if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 100 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 35 , d ) 350 , e ) 700
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 100 % of 10 is 10 . . . . ( 70 * 100 ) / 10 = 700 . . . . ans : e"
Answer: e
Problem: if p is a prime number greater than 5 , what is the remainder when p ^ 2 is divided by 6 .
Options: a ) 4 , b ) can not be determined , c ) 2 , d ) 6 , e ) 1
Rationale: take square of any prime number remainder will be 1 ans e
Answer: e
Problem: a sum of rs . 2200 has been divided among a , b and c such that a gets 1 / 4 of what b gets and b gets 1 / 5 of what c gets . what is b ' s share ?
Options: a ) 342 , b ) 352 , c ) 322 , d ) 332 , e ) 362
Rationale: "let c ' s share = rs . x then b ' s share = x / 5 a ' s share = x / 5 × 1 / 4 = x / 20 hence , x + x / 5 + x / 20 = 2200 ⇒ x ( 1 + 1 / 5 + 1 / 20 ) = 2200 ⇒ x ( 25 / 20 ) = 2200 ⇒ x ( 5 / 4 ) = 2200 ⇒ x = 2200 × 4 / 5 = 440 × 4 = rs . 1760 b ' s share = x / 5 = 1760 / 5 = rs . 352 answer is b ."
Answer: b
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 4 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.75 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 4 is p ( 4 ) = 9.50 + 0.25 ( 4 – 1 ) = 9.50 + 0.25 * 3 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 4 ) - p ( 1 ) = 9.50 + 0.25 * 4 - 9.50 = 0.75 . answer : a ."
Answer: a
Problem: the price of a t . v . set worth rs . 8000 is to be paid in 20 installments of rs . 750 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 7250 , b ) 7200 , c ) 7820 , d ) 6000 , e ) 2799
Rationale: "money paid in cash = rs . 750 balance payment = ( 8000 - 1000 ) = rs . 7250 answer : a"
Answer: a
Problem: in an examination , 40 % of total students failed in hindi , 40 % failed in english and 15 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 40 + 45 - 15 ) = 100 - 70 = 30 answer : c"
Answer: c
Problem: some students are standing in a circle in which 6 th and the 16 th student are standing opposite to each other . find how many students were present there .
Options: a ) 10
b ) 15
c ) 20
d ) 25
e ) 30
Rationale: ( n / 2 ) - x = 6 n - x = 16 solving these two = > n = number of students = 20 answer : c
Answer: c
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 13000 , what will the population be in 2 years ?
Options: a ) 15730 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 10002
Rationale: the required population is = 13000 ( 1 + 10 / 100 ) ^ 2 = 13000 * 11 / 10 * 11 / 10 = 15730 answer is a
Answer: a
Problem: find the compound interest on $ 46,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.05 , b ) 2552.32 , c ) 2524.34 , d ) 7250.75 , e ) 9012.55
Rationale: "principal = $ 46000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 46000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 53250.75 ci . = $ ( 53250.75 - 46000 ) = $ 7250.75 answer d ."
Answer: d
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a
Answer: a
Problem: how many positive integer solutions does the equation 5 x + 10 y = 100 have ?
Options: a ) 2 , b ) 33 , c ) 38 , d ) 35 , e ) 14
Rationale: formula : ( constant ) / ( lcm of two nos ) = 100 / ( 5 * 10 ) = 2 answer : a
Answer: a
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 3025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 220
Rationale: "given that the area of the square = 3025 sq . units = > side of square = √ 3025 = 55 units the radius of the circle = side of the square = 55 units length of the rectangle = 2 / 5 * 55 = 22 units given that breadth = 10 units area of the rectangle = lb = 22 * 10 = 220 sq . units answer : option e"
Answer: e
Problem: what is the difference between the ci on rs . 5000 for 1 years at 4 % per annum ci yearly and half yearly ?
Options: a ) rs . 2.04 , b ) rs . 2.12 , c ) rs . 2.23 , d ) rs . 3 , e ) rs . 3.04
Rationale: c . i . when interest compounded yearly = rs . 5000 x 1 + 4 x 1 + x 4 100 100 = rs . 5000 x 26 x 51 25 50 = rs . 5304 . c . i . when interest is compounded half - yearly = rs . 5000 x 1 + 2 3 100 = rs . 5000 x 51 x 51 x 51 50 50 50 = rs . 5306.04 difference = rs . ( 5306.04 - 5304 ) = rs . 2.04 a
Answer: a
Problem: 140 is what percent of 40 ?
Options: a ) 5 % , b ) 20 % , c ) 50 % , d ) 350 % , e ) 500 %
Rationale: "40 * x = 140 - - > x = 3.5 - - > 3.5 expressed as percent is 350 % . answer : d ."
Answer: d
Problem: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 56 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 980 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 26 tickets = 20 * 26 = 520 revenue generated from sales of 56 tickets = 120 + 340 + 520 = 980 $ answer d"
Answer: d
Problem: in the annual cultural programme of indra prastha there was this math quiz going on . yudhisthir faced this last question that will bring the champion ' s trophy . what will be thesolution for the given problem ? the function f is defined is defined asf ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) what is f ( 29 ) ?
Options: a ) 200 , b ) 230 , c ) 140 , d ) 170 , e ) none of these
Rationale: explanation : f ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) put x = 13 f ( 2 * 13 + 3 ) = ( 13 - 3 ) * ( 13 + 4 ) = 10 * 17 f ( 29 ) = 170 answer : d
Answer: d
Problem: a driver goes on a trip of 70 kilometers , the first 35 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 30 , b ) 32 , c ) 35 , d ) 36 , e ) 40
Rationale: "the time for the first part of the trip was 35 / 48 hours . the time for the second part of the trip was 35 / 24 hours . the total time fro the trip was 35 / 48 + 35 / 24 = 105 / 48 = 35 / 16 hours . the average speed for the trip was 70 / ( 35 / 16 ) = 32 kph the answer is b ."
Answer: b
Problem: one day a car rental agency rented 2 / 3 of its cars , including 3 / 5 of its cars with cd players . if 3 / 4 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 10 % , b ) 35 % , c ) 45 % , d ) 66.7 % , e ) 90 %
Rationale: let us try to solve this by getting some number for total cars . let there be 3,4 and 5 = 60 cars . . . ( we have taken denominators of 2 / 3,3 / 4 and 3 / 5 least common number ) . 2 / 3 ( 60 ) = 40 cars . . . total rented cars , then 1 / 3 ( 60 ) = 20 cars were not rented . 3 / 4 ( 60 ) = 45 cars with cd players . . . total cdp cars now 3 / 5 ( 3 / 4 ) = 3 / 5 ( 45 ) = 27 cdp cars and these are cars that we rented . non rented cdp = total cdp - rented cdp = 45 - 27 = 18 . 18 / 20 = 90 % . answer : e
Answer: e
Problem: if 183 is divisible by 11 , find the value of the smallest natural no . n ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: in aptitude tests , we get questions on divisibility by 11 . a number is divisible by 11 , when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11 the given number is n 183 . ( sum of digits at even places ) – ( sum of digits at odd places ) = 0 ( 8 + n ) - ( 3 + 1 ) = 0 ( 8 + n ) - 4 = 0 here the value of n must be 7 b
Answer: b
Problem: joshua and jose work at an auto repair center with 3 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 10 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: two methods 1 ) probability of chosing josh first = 1 / 5 probability of chosing jose second = 1 / 4 total = 1 / 20 probability of chosing jose first = 1 / 5 probability of chosing josh second = 1 / 4 total = 1 / 20 final = 1 / 20 + 1 / 20 = 1 / 10 b
Answer: b
Problem: a can do a piece of work in 40 days ; b can do the same in 40 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 ) 20 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 40 + 10 / 40 + 10 / x = 1 x = 20 days answer : a"
Answer: a
Problem: in a 280 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 280 m in 7 / 56 * 280 = 35 seconds since a beats b by 7 seconds , a runs 280 m in ( 35 - 7 ) = 28 seconds hence , a ' s time over the course = 28 seconds answer : e"
Answer: e
Problem: in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what z percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Problem: in a kilometer race , a beats b by 80 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 176 sec , d ) 115 sec , e ) 123 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 80 = 125 sec . time taken by a = 125 - 10 = 115 sec . answer : d"
Answer: d
Problem: if n is the smallest integer such that 144 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: "144 can written as = 2 * 2 * 2 * 2 * 3 * 3 - - > 2 ^ 4 * 3 ^ 2 - - - ( 1 ) so for 144 * 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 2 in ( 1 ) even option a is correct"
Answer: a
Problem: claire has a total of 86 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 60 , d ) 54 , e ) 60
Rationale: "g + h = 86 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 86 - h or 3 ( 86 - h ) + 4 h = 300 h = 300 - 258 = 42 then g = 96 - 42 = 54 d"
Answer: d
Problem: jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 12 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 33.75 , e ) 42
Rationale: "let a = amount of 4 % acid and b = amount of 12 % acid . now , the equation translates to , 0.04 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 04 a + . 12 b = . 05 ( 60 ) = > 4 a + 12 b = 300 but b = 60 - a therefore 4 a + 12 ( 60 - a ) = 300 = > 16 a = 420 hence a = 26.25 . b = 60 - 26.25 = 33.75 answer : d"
Answer: d
Problem: how much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ?
Options: a ) 0
b ) 36
c ) 180
d ) 216
e ) 384
Rationale: no of cubes that can be accommodated in box = ( 10 * 12 * 16 ) / ( 4 * 4 * 4 ) 12 * 16 in numerator can be perfectly divided by 4 * 4 in denominator . side with length 10 ca n ' t be perfectly divided by 4 and hence is the limiting factor . closet multiple of 4 less that 10 is 8 . so vacant area in cube = = 12 * 16 * ( 10 - 8 ) = 12 * 16 * 2 = 384 answer : e
Answer: e
Problem: it is currently 8 : 34 pm . at what time in the morning was it exactly 39,668 minutes ago ?
Options: a ) 7 : 22 , b ) 7 : 24 , c ) 7 : 26 , d ) 7 : 28 , e ) 7 : 30
Rationale: divide 39,668 by 60 to convert to minutes : 39,668 / 60 = 661 r 8 . that is 661 hours , 8 minutes . all of the answer choices are during the same hour before : 34 , so we can assume the 661 hours takes the time back into the 7 am hour to 7 : 34 am . going back 8 more minutes yields the time 7 : 26 am . c
Answer: c
Problem: a palindrome is a number that reads the same forward and backward . for example . 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits , 1 , 2 , 3 , how many such palindromes are possible ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 27
Rationale: xyzyx x can be 1 , 2 , or 3 , thus 3 options . y can be 1 , 2 , or 3 , thus 3 options . z can be 1 , 2 , or 3 , thus 3 options . total 3 ^ 3 = 27 . answer : e .
Answer: e
Problem: a train 125 m long passes a man , running at 20 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 28 , d ) 26 , e ) 65
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 20 ) km / hr . x - 20 = 45 = = > x = 65 km / hr answer : e"
Answer: e
Problem: if 20 % of ( x - y ) = 14 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 17.6 % , e ) 25 %
Rationale: "20 % of ( x - y ) = 14 % of ( x + y ) 20 / 100 ( x - y ) = 14 / 100 ( x + y ) 6 x = 34 y required percentage = y / x * 100 = 6 y / 34 y * 100 = 17.64 % answer is d"
Answer: d
Problem: if rs . 510 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively :
Options: a ) rs . 260 , b ) rs . 360 , c ) rs . 350 , d ) rs . 364 , e ) rs . 362
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 510 * 2 / 17 = rs . 60 b ' s share = 510 * 3 / 17 = rs . 90 c ' s share = 510 * 12 / 17 = rs . 360 . answer : b"
Answer: b
Problem: what is the dividend . divisor 15 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 140 , b ) b ) 134 , c ) c ) 148 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 15 * 9 + 5 d = 135 + 5 d = 140 answer a"
Answer: a
Problem: an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the cases .
Options: a ) 4 : 3 , b ) 8 : 7 , c ) 4 : 1 , d ) 6 : 5 , e ) none of these
Rationale: "explanation : let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer is b"
Answer: b
Problem: stacy and heather are 10 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 ) 6.0 mile , b ) 3.0 mile , c ) 4.0 mile , d ) 3.45 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 10 - 2.4 = 7.6 time taken = distance / speed = 7.6 / 11 = 0.69 hrs heather will cover = 5 * 0.69 = 3.45 miles . answer d"
Answer: d
Problem: a man can row upstream at 26 kmph and downstream at 40 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 37 , c ) 30 , d ) 33 , e ) 18
Rationale: "us = 26 ds = 40 m = ( 40 + 26 ) / 2 = 33 answer : d"
Answer: d