regisss/math_qa huggingface dataset:
Problem: there are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 5 , b ) 1 , c ) 3 , d ) 6 , e ) 7
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 3 and for second = 2 so total methods = 3 * 2 = 6 answer : d"
Answer: d
Problem: a boy is traveling from his house to school at 10 km / hr and reached school 2 hours late . next day he traveled 20 km / hr and reached 1 hour early . then find the distance between house and school ?
Options: a ) 50 km , b ) 45 km , c ) 33 km , d ) 60 km , e ) 54 km
Rationale: let distance be x s 1 = 10 km / hr s 2 = 20 km / hr t 1 = x / 10 hr t 2 = x / 20 hr difference in time = 2 + 1 = 3 hr ( x / 10 ) - ( x / 20 ) = 3 x = 60 km answer is d
Answer: d
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 285 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 415 , e ) none of these
Rationale: "average would be : 350 = ( 285 + x ) / 2 on solving , x = 415 . answer : d"
Answer: d
Problem: a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 7.20 , what total number of apples and bananas did the customer purchase ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 7.20 until we get a multiple of $ 0.50 . $ 7.20 , $ 6.40 , $ 5.60 , $ 4.80 , $ 4.00 = 8 * $ 0.50 the customer purchased 8 bananas and 4 apples . the answer is c ."
Answer: c
Problem: in the first 7 overs of a cricket game , the run rate was only 4.2 . what should be the rate in the remaining 30 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 8.42 , c ) 8.3 , d ) 8.1 , e ) 6.21
Rationale: "required run rate = [ 282 - ( 4.2 * 7 ) ] / 30 = 252.60 / 40 = 8.42 answer : b"
Answer: b
Problem: an empty tank be filled with an inlet pipe ‘ a ’ in 42 minutes . after 12 minutes an outlet pipe ‘ b ’ is opened which can empty the tank in 30 minutes . after 6 minutes another inlet pipe ‘ c ’ opened into the same tank , which can fill the tank in 35 minutes and the tank is filled . find the time taken to fill the tank ?
Options: a ) 51.6 , b ) 51.5 , c ) 51.7 , d ) 51.1 , e ) 51.0
Rationale: assume total tank capacity = 210 liters now capacity of pipe a = 210 / 42 = 5 liters capacity of b = 210 / 30 = - 7 liters capacity of c = 210 / 35 = 6 min assume tank gets filled in x min after the third pipe got opened . so x × 5 + 6 × ( − 2 ) + 4 x = 210 x × 5 + 6 × ( − 2 ) + 4 x = 210 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 total time taken to fill the tank = 40.5 + 12 + 6 = 51.5 answer : b
Answer: b
Problem: in a group of 50 people , 25 have visited iceland and 23 have visited norway . if 21 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 50 = 25 + 23 - 21 + ( # in neither group ) = 23 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Problem: a container holds 4 quarts of alcohol and 4 quarts of water . how many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume ?
Options: a ) 4 / 3 , b ) 5 / 3 , c ) 7 / 3 , d ) 8 / 3 , e ) 10 / 3
Rationale: let the number of quarts that should be added to get the required ratio = x so total quarts of water = ( x + 4 ) but the original number of quarts of alcohol remains the same , so we have : 4 / ( x + 4 ) = 3 / 5 cross - multiply : now we have 20 = 3 x + 12 = > 3 x = 20 - 12 = > x = 8 / 3 answer - d
Answer: d
Problem: set a of 8 positive integers may have the same element and have 37 . and set b of 8 positive integers must have different elements and have 37 . when m and n are the greatest possible differences between 37 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 37 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 30 and 37 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 9 . so , 30 - 9 = 21 . the correct answer is b .
Answer: b
Problem: if 6 and 8 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 14 , e ) 56
Rationale: "60 n / 6 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 3 * 2 * 2 * 2 = 5 * n / 4 must be an integer for this to be true n must multiple of 4 , thus min of n = 4 hence b"
Answer: b
Problem: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters q long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = q , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
Answer: b
Problem: if the average of 8 x and 8 y is greater than 120 , and x is twice y , what is the least integer value of x ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 32 , e ) 42
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 8 x and 4 x is greater than 120 . average of 8 x and 4 x is 6 x . so , 6 x > 120 x > 20 answer : a"
Answer: a
Problem: when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 39 , what is the remainder when k is divided by 7 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 7
Rationale: cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 39 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 39 ) 17 is the only common number in both the sets . hence k = 17 answer : d
Answer: d
Problem: in may , the grounds keeper at spring lake golf club built a circular green with an area of 81 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 256 pi , e ) 324 pi
Rationale: "area of circle 81 pi sq feet = pi r ^ 2 therefore r = 9 now green radi doubled i . e r = 18 area = 324 pi e"
Answer: e
Problem: the batting average of a particular batsman is 61 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 202 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 61 * 46 = 2806 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2806 – 2552 = 254 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 254 2 x = 404 x = 202 runs answer b"
Answer: b
Problem: the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is ?
Options: a ) 377 , b ) 126 , c ) 111 , d ) 727 , e ) 121
Rationale: "let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c"
Answer: c
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area t of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Problem: there are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 26 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a"
Answer: a
Problem: the number 250 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ?
Options: a ) 18
b ) 22
c ) 21
d ) 20
e ) 19
Rationale: sum of the squares of 3 different positive integers = 250 15 ^ 2 + 3 ^ 2 + 4 ^ 2 = 250 now , sum of these 3 different integers = 15 + 3 + 4 = 22 ans - b
Answer: b
Problem: 13 ltr of water is added with 11 ltr of a solution containing 16 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 7.33 % , b ) 9 % , c ) 9.67 % , d ) 11 % , e ) 11.5 %
Rationale: "we have an 11 litre solution containing 16 % of alcohol in the water . = > quantity of alcohol in the solution = 11 ã — 16 / 100 now 13 litre of water is added to the solution . = > total quantity of the new solution = 11 + 13 = 24 percentage of alcohol in the new solution = 11 ã — 16 / 100 24 ã — 100 = 11 ã — 1610024 ã — 100 = 11 ã — 0.67 / 100 = 7.33 % a"
Answer: a
Problem: a straight line in the xy - plane has y - intercept of 49 . on this line the x - coordinate of the point is 71 and y - coordinate is 12 then what is the slope of the line ?
Options: a ) 0.5 , b ) 0.51 , c ) - 0.52 , d ) 0.31 , e ) - 0.49
Rationale: "eq of line = y = mx + c c = 49 x = 71 y = 12 substitute given : m = ( y - c ) / x = ( 12 - 49 ) / 71 = - 37 / 71 = - 0.52 correct option is c"
Answer: c
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1116 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 57 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1116 - 640 = 476 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 476 / 28 = 17 total hrs = 40 + 17 = 57 answer b 57"
Answer: b
Problem: a train 450 m long running at 126 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 271 , b ) 250 , c ) 350 , d ) 277 , e ) 232
Rationale: "length of the platform = 126 * 5 / 18 * 20 = 700 – 450 = 250 answer : b"
Answer: b
Problem: 200 is increased by 25 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 250 , d ) 190 , e ) 220
Rationale: explanation final number = initial number + 25 % ( original number ) = 200 + 25 % ( 200 ) = 200 + 50 = 250 . answer c
Answer: c
Problem: given that 268 x 74 = 19332 , find the value of 2.68 x . 74 .
Options: a ) 1.9332 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9332 answer a"
Answer: a
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 30 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 21 % , b ) 22.5 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.3 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 30 % income the savings increased by 100 % . or s = . 3 i or s = 30 % of income d is the answer"
Answer: d
Problem: the average age of applicants for a new job is 31 , with a standard deviation of 8 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 14 , c ) 15 , d ) 17 , e ) 30
Rationale: "within one standard deviation of the average age means 31 + / - 7 23 - - 31 - - 39 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 total = 17 d"
Answer: d
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 12 weavers in 12 days ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 30 , e ) 36
Rationale: "1 weaver can weave 1 mat in 4 days . 12 weavers can weave 12 mats in 4 days . 12 weavers can weave 36 mats in 12 days . the answer is e ."
Answer: e
Problem: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 200 girls , the total number of students in the college is
Options: a ) 420 , b ) 520 , c ) 620 , d ) 620 , e ) none of these
Rationale: explanation : let the boy are 8 x and girls are 5 x = > 5 x = 200 = > x = 40 total students = 8 x + 5 x = 13 x = 13 ( 40 ) = 520 answer : b
Answer: b
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio q of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore q , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b
Answer: b
Problem: a boatman can row 96 km downstream in 8 hr . if the speed of the current is 4 km / hr , then find in what time will be able to cover 8 km upstream ?
Options: a ) 6 hr , b ) 2 hr , c ) 4 hr , d ) 1 hr , e ) none of these
Rationale: "explanation : speed downstream = 96 ⁄ 8 = 12 kmph speed of current = 4 km / hr speed of the boatman in still water = 12 - 4 = 8 kmph speed upstream = 8 - 4 = 4 kmph time taken to cover 8 km upstream = 8 ⁄ 4 = 2 hours . answer : option b"
Answer: b
Problem: the average age of 16 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 26
Rationale: "age of the 15 th student = 16 * 15 - ( 14 * 5 + 16 * 9 ) = 240 - 214 = 26 years answer is e"
Answer: e
Problem: a driver goes on a trip of 50 kilometers , the first 25 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: "the time for the first part of the trip was 25 / 60 = 5 / 12 hours . the time for the second part of the trip was 25 / 30 = 5 / 6 hours . the total time for the trip was 5 / 12 + 5 / 6 = 15 / 12 = 5 / 4 hours . the average speed for the trip was 50 / ( 5 / 4 ) = 40 kph the answer is c ."
Answer: c
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 2 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 2 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 2 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 6 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 6 w = 6 the answer is b ."
Answer: b
Problem: 895.7 – 573.07 – 95.007 = ?
Options: a ) 227.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 895.7 - ( 573.07 + 95.007 ) = 895.7 - 668.077 = 227.623 . answer a"
Answer: a
Problem: a train ride from two p to town q costs $ 6.85 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.65 . what is the cost of a bus ride from town p to town q ?
Options: a ) $ 1.40 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20
Rationale: "let x be the cost of a bus ride . x + ( x + 685 ) = 965 2 x = 280 x = $ 1.40 the answer is a ."
Answer: a
Problem: how much 60 % of 50 is greater than 42 % of 30 ?
Options: a ) 18 , b ) 91 , c ) 11 , d ) 17.4 , e ) 12
Rationale: "( 60 / 100 ) * 50 – ( 42 / 100 ) * 30 30 - 12.6 = 17.4 answer : d"
Answer: d
Problem: matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x = 100 i . e . y = 5 new sales = y + 1 = 6 answer : option d
Answer: d
Problem: what is the smallest positive integer x for which x 3 + 5 xx 3 + 5 x has a value more than 80 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "4 ^ 3 + 5 * 4 = 64 + 20 = 84 that ' s pretty close to 80 already so i can cancel d and e since they ' ll be more than 80 . b just needs to be checked just in case so . . . 3 ^ 3 + 5 * 3 = 27 + 15 = not close to 80 . therefore , 4 ( c ) is the smallest positive integer x for which x ^ 3 + 5 x has a value more than 80 . answer : c"
Answer: c
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.75 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 12 , b ) 72 , c ) 48 , d ) 99 , e ) 11
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.75 + 1.25 = 3 km = 3000 m . required time = 3000 * 3 / 125 = 72 sec . answer : b"
Answer: b
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 13 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 4 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9
Rationale: answer is a . x / x + 36 = 1 / 5 x = 9 13 - 9 = 4
Answer: a
Problem: a cylinder is inserted in a sphere d / h = 2 / 3 . find the surface area of the cylinder ?
Options: a ) 23.12
b ) 24.12
c ) 25.12
d ) 26.12
e ) 27.12
Rationale: take r = 1 , h = 3 = 2 * 3.14 * r * r + 2 * 3.14 * r * h = 2 * 3.14 * r ( r + h ) = 2 * 3.14 * 1 ( 1 + 3 ) = 2 * 3.14 ( 4 ) = 25.12 answer : c
Answer: c
Problem: how many 4 x 5 x 8 cubes could fit in a 10 x 16 x 84 box ?
Options: a ) 84 , b ) 90 , c ) 85 , d ) 77 , e ) 64
Rationale: the answer is a ) 84 . the 10 x 16 x 84 box has an area of 13,440 . the 4 x 5 x 8 cubes have an area of 160 . if you divide 13,440 by 160 , you get 84 .
Answer: a
Problem: the measurements obtained for the interior dimensions of a rectangular box are 150 cm by 150 cm by 225 cm . if each of the three measurements has an error of at most 1 centimeter , which of the following is the closes maximum possible difference , in cubic centimeters , between the actual capacity of the box and the capacity computed using these measurements ?
Options: a ) 90,000
b ) 95,000
c ) 93,000
d ) 92,000
e ) 91,000
Rationale: the options are well spread so we can approximate . changing the length by 1 cm results in change of the volume by 1 * 150 * 225 = 33,750 cubic centimeters ; changing the width by 1 cm results in change of the volume by 150 * 1 * 225 = 33,750 cubic centimeters ; changing the height by 1 cm results in change of the volume by 150 * 150 * 1 = 22,500 cubic centimeters . so , approximate maximum possible difference is 33,750 + 33,750 + 22,500 = 90,000 cubic centimeters . answer : a
Answer: a
Problem: what will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?
Options: a ) 1 : 1
b ) 1 : 2
c ) 2 : 3
d ) 2 : 1
e ) none of these
Rationale: explanation : as far as questions of area or volume and surface area are concerned , it is all about formulas and very little logic . so its a sincere advice to get all formulas remembered before solving these questions . lets solve this , area of rectangle = l ∗ b area of triangle = 1 / 2 l ∗ b ratio = l ∗ b : 1 / 2 l ∗ b = 1 : 1 / 2 = 2 : 1 option d
Answer: d
Problem: if one positive integer is greater than another positive integer by 4 , and the difference of their cubes is 316 , what is their sum ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 7 ^ 3 = 343 the two numbers are 3 and 7 . the answer is c ."
Answer: c
Problem: the average age of an adult class is 40 years . 10 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 10 x 32 = ( y + 10 ) x 36 â ‡ ’ 40 y + 320 = 36 y + 360 â ‡ ’ 4 y = 40 â ˆ ´ y = 10 a"
Answer: a
Problem: a king has 1000 bottles of wine , a queen wants to kill the king and sends a servant to poison the wine . fortunately the king ' s guard ' s catch d servant after he has only poisoned one bottle and the guard do n ' t know which bottle is poisoned . furthermore it takes one month to have an effect , and there is an anniversary party coming up in 5 weeks time ! the king decides he will get some of the prisoners in his vast dungeons to drink the wine . how many minimum prisoners does it required to sample the wine to find out the poisoned bottle so that the guests will still be able to drink the rest of the wine at his anniversary party in 5 weeks time ?
Options: a ) 1 , b ) 499 , c ) 500 , d ) 999 , e ) 10
Rationale: since you need 10 digits to represent 1000 numbers in binary , you will need 10 prisoners . now the logic is this : every bottle has a unique number from 1 to 1000 and a unique binary representation from 0000000001 to 1111101000 . now you have 10 prisoners . each bottle will be tasted by the prisoners depending on the binary representation of the bottle . wherever there is 1 , the bottle will be tasted by that prisoner ( assuming units digit represents the 1 st prisoner , tens digit the 2 nd prisoner and so on . . . ) 1 st bottle is 0000000001 so it will be tasted by only the 1 st prisoner . 2 nd bottle is 0000000010 so it will be tasted by only the 2 nd prisoner . 3 rd bottle is 0000000011 so it will be tasted by the 1 st and 2 nd prisoners . and so on . . . 1000 th bottle is 1111101000 so it will be tasted by 4 th , 6 th , 7 th , 8 th , 9 th and 10 th prisoners . at the end of a month , we see which prisoners die . say , only the 3 rd prisoner dies . this means the poisoned bottle number is 0000000100 = 3 . say 1 st , 7 th and 9 th prisoners die . this means the poisoned bottle number is 0101000001 = 321 ans : e
Answer: e
Problem: 30 square stone slabs of equal size were needed to cover a floor area of 120 sq . m . find the length of each stone slab ?
Options: a ) 120 cm
b ) 200 cm
c ) 88 cm
d ) 666 cm
e ) 776 cm
Rationale: area of each slab = 120 / 30 m 2 = 4 m 2 length of each slab √ 4 = 2 m = 200 cm b
Answer: b
Problem: if x and y are positive integers and 18 x = 12 y what is the least possible value of xy ?
Options: a ) 14 , b ) 28 , c ) 36 , d ) 84 , e ) 252
Rationale: "18 x = 12 y = > x / y = 2 / 3 = > 3 x = 2 y 3 ( 3 ) = 2 ( 3 ) = > x * y = 9 but it is not given 3 ( 6 ) = 2 ( 6 ) = > x * y = 36 c"
Answer: c
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.90 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6468
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.90 ) = rs . 6468 . answer : e ) 6468"
Answer: e
Problem: two containers of milk contain mixtures of water and milk in ratio 5 : 4 and 7 : 9 . in what ratio they should be mixed so that mixture is of 6 : 6 ratio ?
Options: a ) 6 : 5 , b ) 7 : 5 , c ) 9 : 8 , d ) 8 : 9 , e ) 8 : 7
Rationale: 6 / 6 - 5 / 4 = = > - 1 / 4 7 / 9 - 6 / 6 = = > - 2 / 9 now , - 1 / 4 = - 2 / 9 = = > 1 / 4 = 2 / 9 = = > 9 : 8 answer : c
Answer: c
Problem: 3 , 5 , 7 , 11 , 13 , 17 , 19 , ____
Options: a ) 25 , b ) 36 , c ) 23 , d ) 49 , e ) 27
Rationale: "the sequence is a series of prime numbers , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 . . . . answer : c ."
Answer: c
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 360 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 360 envelopes they will take 360 / 60 mins . i . e . , 6 mins . answer : a"
Answer: a
Problem: if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 4 x years from now ?
Options: a ) 31 , b ) 35 , c ) 30 , d ) 40 , e ) 28
Rationale: "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 4 x years from now , age will be 15 + 4 * 4 = 31 option a"
Answer: a
Problem: the present population of a town is 220 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 242 , e ) 250
Rationale: "p = 220 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 220 * ( 1 + 10 / 100 ) = 220 * ( 11 / 10 ) = 242 answer is d"
Answer: d
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × b = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x b = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x b b = 7 ^ 2 = 49 answer d"
Answer: d
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 2 strokes ?
Options: a ) 3 / 4 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 so removed = 1 - 1 / 4 = 3 / 4"
Answer: a
Problem: a man purchased 3 blankets @ rs . 100 each , 6 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 3 * 100 + 6 * 150 = 1200 1500 – 1200 = 300 a"
Answer: a
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 270 . the amount of the bill is
Options: a ) 2200 , b ) 2520 , c ) 2600 , d ) 3354 , e ) none of these
Rationale: "explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 270 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 270 or x = 2250 . p . w . = rs . 2250 sum due = p . w . + t . d . = rs . ( 2250 270 ) = rs . 2520 answer : b"
Answer: b
Problem: for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 25 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
Options: a ) 0.05 , b ) 0.36 , c ) 0.2 , d ) 0.25 , e ) 0.6
Rationale: "index for females = ( 25 - 8 ) / 25 = 17 / 25 = 0.68 index for males = ( 25 - 17 / 25 = 8 / 25 = 0.32 index for females exceeds males by 0.68 - 0.32 = 0.36 answer : b"
Answer: b
Problem: at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 62 , b ) 171 , c ) 475 , d ) 513 , e ) 684
Rationale: "total automobile instalment credit = 57 * 3 = 171 total consumer instalment credit = 171 ∗ 100 / 36 = 475 ; answer = c . 475"
Answer: c
Problem: the perimeter of a semi circle is 122 cm then the radius is ?
Options: a ) 17 , b ) 28 , c ) 24 , d ) 11 , e ) 12
Rationale: "36 / 7 r = 122 = > r = 24 answer : c"
Answer: c
Problem: what is the units digit of ( 493 ) ( 915 ) ( 381 ) ( 756 ) ( 28 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 1 . imo b ."
Answer: b
Problem: if the average ( arithmetic mean ) of a and b is 150 , and the average of b and c is 90 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 120 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 300 b + c = 180 a - c = 120 . imo option c ."
Answer: c
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of e is less than the square root of e . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "e = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Problem: claire has a total of 92 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 ) 68 , c ) 54 , d ) 57 , e ) 60
Rationale: "g + h = 92 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 92 - h or 3 ( 92 - h ) + 4 h = 300 h = 300 - 276 = 24 then g = 92 - 24 = 68 b"
Answer: b
Problem: a car ferry can hold up to 60 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 5 tons ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20
Rationale: "the weight of one car and one truck is 5.75 tons . 60 / 5.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is e ."
Answer: e
Problem: if a man walks at the rate of 4 kmph , he misses a train by only 6 min . however , if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train . the distance covered by him to reach the station is
Options: a ) 3 km , b ) 4 km , c ) 5 km , d ) 6 km , e ) 7 km
Rationale: let the distance covered be d and time taken to reach the station in time t d / 4 = t + 6 / 60 - - - ( 1 ) d / 5 = t - 6 / 60 - - - ( 2 ) ( 1 ) - ( 2 ) gives d / 4 - d / 5 = ( 6 + 6 ) / 60 d / 20 = 12 / 60 d = 12 * 20 / 60 = 4 km answer : b
Answer: b
Problem: what is the sum of all even integers between 99 and 301 ?
Options: a ) 20200 , b ) 20000 , c ) 40400 , d ) 40000 , e ) 44000
Rationale: "a = 100 , tn = 300 a + ( n - 1 ) d = 300 = > n = 101 sn = n / 2 ( a + l ) = 101 / 2 ( 100 + 300 ) sn = 20200 answer : a"
Answer: a
Problem: a person was asked to state his age in years . his reply was , ` ` take my age 4 years hence , multiply it by 4 and subtract 4 times my age 4 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 32 , c ) 27 , d ) 26 , e ) 19
Rationale: "explanation : let the present age of person be x years . then , 4 ( x + 4 ) - 4 ( x - 4 ) = x < = > ( 4 x + 16 ) - ( 4 x - 16 ) = x < = > x = 32 . . answer : b"
Answer: b
Problem: the average ( arithmetic mean ) of the even integers from 24 to 48 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 12 to 24 inclusive ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "so , according to a mean of a set of even numbers from 24 to 48 = ( 24 + 48 ) / 2 = 36 and mean of a set of even numbers from 12 to 24 = ( 12 + 24 ) / 2 = 18 difference = 36 - 18 = 18 answer : c ."
Answer: c
Problem: 2 friends a and b running up hill and then to get down length of road - 440 yads a on his return journey met b going up at 20 yards from top if a has finished race 5 minute earlier than b then how much time a had taken to complete the race ?
Options: a ) 100 minute , b ) 110 minute , c ) 120 minute , d ) 130 minute , e ) 140 minute
Rationale: total journey = 440 * 2 = 880 a meet b 20 yards from top in getting down it means he has covered 440 + 20 = 460 yards while b is 420 yards . so he is 40 yards ahead of b which is equals to 5 minute . so 40 yards in 5 min 880 yards will be in 5 * 880 / ( 40 ) = 110 minute answer : b
Answer: b
Problem: a train speeds past a pole in 25 seconds and a platform 500 m long in 35 seconds . its length is :
Options: a ) 1150 m , b ) 2250 m , c ) 1450 m , d ) 1350 m , e ) 1250 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 x + 500 / 35 = x / 25 x = 1250 m . answer : option e"
Answer: e
Problem: the average age of 40 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 22 , b ) 27 , c ) 28 , d ) 26 , e ) 56
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 40 ) = 56 years answer : e"
Answer: e
Problem: 14 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 2548
Rationale: "no . of ways of picking 2 biology books ( from 14 books ) = 14 c 2 = ( 14 * 13 ) / 2 = 91 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 91 * 28 = 2548 ( option e )"
Answer: e
Problem: the average of non - zero number and its square is 5 times the number . the number is :
Options: a ) 9 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: let the number be x . then , ( x + x 2 ) / 2 = 5 x = > x 2 - 9 x = 0 = > x ( x - 9 ) = 0 = > x = 0 or x = 9 so , the number is 9 . answer : a
Answer: a
Problem: evaluate : 50 - 12 ÷ 4 × 2 =
Options: a ) 44 , b ) 54 , c ) 16 , d ) 27 , e ) 30
Rationale: "according to order of operations , 12 ÷ 4 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 4 × 2 = 3 × 2 = 6 hence 50 - 12 ÷ 4 × 2 = 50 - 6 = 44 correct answer a ) 44"
Answer: a
Problem: if 40 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 150 , c ) 75 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 40 % of 3 / 5 of x = 36 40 / 100 * 3 / 5 * x = 36 x = ( 36 * 50 / 12 ) = 150 required number = 150 . correct option : b"
Answer: b
Problem: the sum and the product of two numbers are 24 and 23 respectively , the difference of the number is ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 22
Rationale: explanation : x + y = 24 xy = 23 ( x - y ) 2 = ( x + y ) 2 - 4 xy ( x - y ) 2 = 576 - 92 = > ( x - y ) = 22 answer : e
Answer: e
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 7 . 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 7 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 7 is p ( 7 ) = 9.50 + 0.25 ( 7 – 1 ) = 9.50 + 0.25 * 6 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 7 ) - p ( 1 ) = 9.50 + 0.25 * 6 - 9.50 = 1.5 . answer : d ."
Answer: d
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 2800 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 2800 envelopes b will take 2800 / 1400 hrs = 2 hrs so the answer is choice a"
Answer: a
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units d digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : d . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Problem: ron has had 3 pay cuts in her salary in the past 6 months . if the first pay cut was 5 % , the second pay cut was 10 % and the third was 15 % . what will be the percentage decrease , if the salary is decreased in a single shot ?
Options: a ) 29.33 % , b ) 27.33 % , c ) 17.33 % , d ) 27.99 % , e ) 29.33 %
Rationale: let rs . 100 be initial salary . salary after 1 st decrease , 5 % = 95 salary after 2 nd decrease , 10 % = 85.5 i . e . reduced by 10 percent of 95 salary after 3 rd decrease , 15 % = 72.675 i . e . reduced by 15 percent of 85.5 so if its decreased in single shot = i = ( ( b - a ) / b ) * 100 = 27.33 % answer : b
Answer: b
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 50 .
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 50 , remainder will be - 4 i . e . n will be 4 less than a multiple of 50 . so you must add 12 to n to make it a multiple of 50 c"
Answer: c
Problem: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 222 marks in the second test and failed by 39 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 232 , c ) 246 , d ) 625 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 36 marks in the second test . pass mark in the second test = 222 + 39 = 252 45 / 100 m = 261 pass mark in the first test = 40 / 100 m = 40 / 45 * 261 = 232 answer : b"
Answer: b
Problem: if the sum of the first n positive integers is s , what is the sum of the first n positive integers divisible by 3 , in terms of s ?
Options: a ) s / 2 , b ) s , c ) 2 s , d ) 3 s , e ) 4 s
Rationale: "answer is d given sum of 1 2 3 . . . . . n = s sum of 3 , 6 , 9 . . . . 3 n = 3 [ sum ( 1 2 3 . . . . n ) ] = 3 s"
Answer: d
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 60 , b ) 277 , c ) 48 , d ) 99 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.4 = 2.5 km = 2500 m . required time = 2500 * 3 / 125 = 60 sec . answer : a"
Answer: a
Problem: if x # y is defined to equal x ^ 2 / y for all x and y , then ( - 1 # 2 ) # 2 =
Options: a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 12 , d ) 1 / 8 , e ) - 4 / 3
Rationale: "( - 1 ) ^ 2 / 2 = 1 / 2 ( 1 / 2 ) ^ 2 / 2 = 1 / 8 so d is my answer"
Answer: d
Problem: a can do a piece of work in 4 days . b can do it in 6 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 12 days , c ) 66 days , d ) 77 days , e ) 44 days
Rationale: c = 1 / 2 - 1 / 4 - 1 / 6 = 1 / 12 = > 12 days answer : b
Answer: b
Problem: how many seconds will a 800 metre 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 ) 25 , b ) 30 , c ) 40 , d ) 48 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 800 * 3 / 50 = 48 sec answer : d"
Answer: d
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.52 , d ) 2.72 , e ) none of these
Rationale: "1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each ` ` part ' ' is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 850 * 2 * ( 4 / 5 ) = 1360 2160 + 1360 = 3520 solving for units gives us 3.52 so the answer is c"
Answer: c
Problem: at veridux corporation , there are 210 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 55
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 210 â € “ 90 = 120 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 210 â € “ 40 = 170 must be associates . now , in the â € œ associate â €  row , 135 + e = 170 , which means e = 35 â € ” the other 35 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 35 = 90 , which means b = 55 . there are fifteen female managers in this company . thus , the answer = ( e ) ."
Answer: e
Problem: 7 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 40 , b ) 48 , c ) 45 , d ) 42 , e ) 22
Rationale: "though 2 * ( 7 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 6 , so he ' ll play 12 matches . similarly , second guy has to play with the rest of 5 as his 2 games with the first guy are already played . so he plays 10 matches . this continues like this and the total matches are 12 + 10 + 8 . . . + 2 12 + 10 + . . . + 2 = 2 ( 6 + 5 + . . . + 1 ) = 2 ( ( 6 * 7 ) / 2 ) = 6 * 7 = 42 . answer : d"
Answer: d
Problem: what is value of x if 32 - y = 16 x - y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 2 , e ) 6
Rationale: "32 - y = 16 x - y 32 = 16 x - y + y 16 x = 32 x = 2 answer is option d"
Answer: d
Problem: find the cost of fencing around a circular field of diameter 18 m at the rate of rs . 2.50 a meter ?
Options: a ) 138 , b ) 132 , c ) 150 , d ) 140 , e ) 222
Rationale: "2 * 22 / 7 * 9 = 56 56 * 2 1 / 2 = rs . 140 answer : d"
Answer: d
Problem: what is the least value of x . so that 23 x 58 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 8 = 18 + x least value of x may be 0 therefore 18 + 0 = 18 is divisible by 3 . answer : option b"
Answer: b