regisss/math_qa huggingface dataset:
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 100 and $ 105 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1000 , d ) 1200 , e ) 1440
Rationale: "$ 100 for 2 years = $ 50 per year . extra $ 5 yearned with the compound interest is the percent yearned on percent . so , $ 5 is yearned on $ 50 , which means that the interest = 10 % . this on the other hand means that half of the savings = 50 * 10 = $ 500 . twice of that = $ 1,000 . answer : c ."
Answer: c
Problem: a walks at 4 kmph and 4 hours after his start , b cycles after him at 10 kmph . how far from the start does b catch up with a ?
Options: a ) 62.6 km , b ) 26.7 km , c ) 22.8 km , d ) 19.5 km , e ) none
Rationale: "sol . suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 4 hours . ∴ x / 4 - x / 10 = 4 or x = 26.7 km . answer b"
Answer: b
Problem: barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 10 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 120 , b ) 600 , c ) 1000 , d ) 360 , e ) 240
Rationale: "let the additional invested amount for 10 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.10 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.10 x = 0.06 x + 0.06 * 2400 0.04 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.04 = 600 ans : b"
Answer: b
Problem: 100 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 150 , d ) 155 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 100 + 50 % ( 100 ) = 100 + 50 = 150 . answer c"
Answer: c
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 5 kmph and the other is going towards south 5 kmph . what time will they take to be 50 km apart ?
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: "to be ( 5 + 5 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 10 * 50 = 5 hrs answer is d"
Answer: d
Problem: what is the average ( arithmetic mean ) of the numbers 2 , 4 , 6 , 8 , 10 , 12 , 14 and 16 ?
Options: a ) 9 , b ) 10 , c ) 15 , d ) 12 , e ) 14
Rationale: "avg = sum of observations / number of observations avg = ( 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 ) / 8 = 9 answer is a"
Answer: a
Problem: a miniature roulette wheel is divided into 10 equal sectors , each bearing a distinct integer from 1 to 10 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun two times , approximately what is the probability that the product of the two winning sectors ’ integers will be even ?
Options: a ) 88 % , b ) 75 % , c ) 67 % , d ) 63 % , e ) 50 %
Rationale: the only way to have an odd product is if both integers are odd . p ( odd product ) = 1 / 2 * 1 / 2 = 1 / 4 p ( even product ) = 1 - 1 / 4 = 3 / 4 = 75 % the answer is b .
Answer: b
Problem: when the number 2 y 31129 is exactly divisible by 11 , then what can be the smallest whole number in place of y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 7 , e ) 8
Rationale: "the given number = 2 y 31129 sum of the odd places = 9 + 1 + 3 + 2 = 15 sum of the even places = 2 + 1 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 15 - ( 3 + y ) = divisible by 11 12 � y = divisible by 11 . y must be 1 , to make given number divisible by 11 . a"
Answer: a
Problem: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 17 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 2 : 5 , e ) 68 : 85
Rationale: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 17 - - > x ( a - b ) = 17 . since 17 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 17 . the above implies that either x = 1 and ( a - b ) = 17 or x = 17 anda - b = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 17 . for the original question only option which fits is e , 4 : 5 . cats = 17 * 4 = 68 and dogs = 17 * 5 = 85 . answer : e ."
Answer: e
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 15 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,15 = 15 / 100 x = 80 * 15 / 100 x = 12 12 / 10 = 1,2 = 120 % , answer c"
Answer: c
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 3 dm by 5 dm . the number of stones required is :
Options: a ) 3600 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 30 * 50 ) therefore , number of stones = ( 3600 * 1500 / 30 * 50 ) = 3600 answer : a"
Answer: a
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 6095 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 200 , c ) 230 , d ) 276 , e ) 1999
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 6095 [ 4 l - 40 ] = 6095 / 26.50 = 230 4 l = 270 l = 270 / 4 = 67.5 meters . answer : c"
Answer: c
Problem: jill has 28 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 48 , d ) 12 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 28 1 3 / 4 w = 28 w = 16 the total number of jars = 3 w = 48 answer : c
Answer: c
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 330 the other is
Options: a ) 330 , b ) 300 , c ) 210 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 330 = 210 answer is c ."
Answer: c
Problem: a certain number when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) b"
Answer: b
Problem: 11 friends went to a hotel and decided to pay the bill amount equally . but 10 of them could pay rs . 60 each as a result 11 th has to pay rs . 50 extra than his share . find the amount paid by him .
Options: a ) 110 , b ) 111 , c ) 115 , d ) 123 , e ) none
Rationale: explanation : average amount paid by 10 persons = rs . 60 increase in average due to rs . 50 paid extra by the 11 th men = rs . 50 / 10 = rs . 5 therefore , average expenditure of 11 friends = rs . 60 + rs . 5 = rs . 65 therefore , amount paid by the 11 th men = rs . 65 + rs . 50 = rs . 115 correct option : c
Answer: c
Problem: at a certain zoo , the ratio of sea horse to penguins is 5 to 11 . if there are 85 more penguins than sea horses at the zoo , how many sea horses are there ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 70 , e ) 132
Rationale: 5 / 11 = x / x + 85 5 * 85 = 6 x x = 70 d . 70
Answer: d
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to place at a distance of 105 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 105 / 7.5 + 105 / 10.5 ] hours = 24 hours . answer b"
Answer: b
Problem: what is the remainder when 7 ^ 700 is divided by 100 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 7 ^ 700 ) mod 100 = [ 7 ^ ( 2 * 350 ) ] mod 100 = [ 49 ^ 350 ] mod 100 = [ ( 50 - 1 ) ^ 350 ] mod 100 = [ { 350 c 349 } * 50 * ( - 1 ) ^ 349 + 350 c 350 * ( - 1 ) ^ 350 ] mod 100 = [ - 350 * 50 + 1 ] mod 100 = 1 mod 100 so , evidently , the remainder will be 1 . answer : a"
Answer: a
Problem: a person bought 110 glass bowls at a rate of rs . 10 per bowl . he sold 100 of them at rs . 14 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 279 / 11 , e ) 279 / 8
Rationale: "cp = 110 * 10 = 1100 and sp = 100 * 14 = 1400 gain % = 100 * ( 1400 - 1100 ) / 1100 = 300 / 11 answer : b"
Answer: b
Problem: the difference between a number and its two - fifth is 45 . what is the number ?
Options: a ) 76 , b ) 56 , c ) 88 , d ) 66 , e ) 75
Rationale: "explanation : let the number be x . x – ( 2 / 5 ) x = 45 ( 3 / 5 ) x = 45 x = 75 answer : e"
Answer: e
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 4 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 24 , d ) 48 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d"
Answer: d
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 3 : 1 . in the subsequent n games , the ratio of the team ´ s wins to losses was 2 : 3 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 8 , b ) 9 : 2 , c ) 1 : 2 , d ) 5 : 4 , e ) 3 : 2
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 3 / 4 * 4 / 9 + 2 / 5 * 5 / 9 = 3 / 9 + 2 / 9 = 5 / 9 losses = 1 - 5 / 9 = 4 / 9 the ratio of wins to losses is 5 : 4 . the answer is d ."
Answer: d
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 124 billion gallons to 138 billion gallons . if the storm increased the amount of water in the reservoirs to 82 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 9 , b ) 14 , c ) 25 , d ) 30 , e ) 44
Rationale: "since we need to find only an approximate value and the answer choices are quite widespread , then use : 80 % instead of 82 % ( notice that this approximation gives the bigger tank capacity ) ; 140 billion gallons instead of 138 billion gallons ( notice that this approximation also gives the bigger tank capacity ) ; 130 billion gallons instead of 124 billion gallons ; . notice that the third approximation balances the first two a little bit . so , we ' ll have that : capacity ∗ 0.8 = 140 - - > capacity = 140 / 0.8 = 175 hence , the amount of water the reservoirs were short of total capacity prior to the storm was approximately 175 − 130 = 45 billion gallons . answer : e ."
Answer: e
Problem: for what value of x between − 6 and 6 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 6 , b ) − 2 , c ) 0 , d ) 2 , e ) 6
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 6 will give the greatest value . . ans a"
Answer: a
Problem: a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is :
Options: a ) 22 , b ) 88 , c ) 12 , d ) 73 , e ) 29
Rationale: "explanation : s . i . for 3 years = rs . ( 12005 - 9800 ) = rs . 2205 . s . i . for 5 years = rs . = rs . 3675 principle = rs . ( 9800 - 3675 ) = rs . 6125 hence , rate = = 12 % answer : c ) 12 %"
Answer: c
Problem: how many seconds will a train 110 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 23 sec , c ) 24 sec , d ) 25 sec , e ) 26 sec
Rationale: "d = 110 + 150 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec e"
Answer: e
Problem: a teacher gave the same test to 3 history classes : a , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 90 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ?
Options: a ) 74 , b ) 75 , c ) 76 , d ) 77 , e ) 79
Rationale: ratio is 4 : 6 : 5 , numbers are 4 x , 6 x , 5 x total scores of each class is ( 65 * 4 x + 6 x * 90 + 77 * 5 x ) = 260 x + 540 x + 385 x = 1185 x total number of students = 15 x average = 1185 x / 15 x = 79 e is the answer
Answer: e
Problem: a merchant purchased a jacket for $ 54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 18
Rationale: "actual cost = $ 54 sp = actual cost + mark up = actual cost + 40 % sp = 54 * 100 / 60 on sale sp = 80 / 100 ( 54 * 100 / 60 ) = 72 gross profit = $ 18 answer is e"
Answer: e
Problem: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 19 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) $ 27.50 , b ) $ 28.50 , c ) $ 29.50 , d ) $ 30.50 , e ) $ 31.50
Rationale: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 19 ) = 0.8 x x = 1.2 ( 19 ) / 0.8 = 1.5 ( 19 ) = $ 28.50 the answer is b ."
Answer: b
Problem: three pipes of same capacity can fill a tank in 12 hours . if there are only two pipes of same capacity , the tank can be filled in ?
Options: a ) 18 , b ) 8 , c ) 12 , d ) 6 , e ) 4
Rationale: "the part of the tank filled by three pipes in one hour = 1 / 12 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 12 = 1 / 18 . the tank can be filled in 18 hours . answer : a"
Answer: a
Problem: what is the least number to be subtracted from 800 to make it a perfect square ?
Options: a ) 1 , b ) 16 , c ) 20 , d ) 71 , e ) 60
Rationale: "the numbers less than 800 and are squares of certain number is 784 . the least number that should be subtracted from 800 to make it perfect square = 800 - 784 = 16 . answer : b"
Answer: b
Problem: a train crosses a platform of 110 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 88 , c ) 77 , d ) 310 , e ) 52
Rationale: "length of the train be â € ˜ x â € ™ x + 110 / 15 = x + 250 / 20 4 x + 440 = 3 x + 750 x = 310 m answer : d"
Answer: d
Problem: bucket p has thrice the capacity as bucket q . it takes 80 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 80 , e ) 100
Rationale: "explanation : let capacity of q = 1 litre . then , capacity of p = 3 litre . given that it takes 80 turns for bucket p to fill the empty drum . = > capacity of the drum = 80 × 3 = 240 litre . number of turns required if both p and q are used having each turn together 240 / 3 + 1 = 60 litre . answer : option c"
Answer: c
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 47 minutes . the total distance ( in km ) is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "sol . let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 47 / 60 ⇔ 47 x / 60 = 47 / 60 ⇔ x = 1 . ∴ total distance = ( 3 * 1 ) km = 3 km . answer c"
Answer: c
Problem: weights of two friends ram and shyam are in the ratio 7 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 19 % , b ) 10 % , c ) 22 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 7 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 7 / 5 or , x = 22 % . answer : option c"
Answer: c
Problem: in town x , 90 percent of the population are employed , and 20 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 66 % , c ) 77 % , d ) 88 % , e ) 52 %
Rationale: "total employed people 90 % , out of which 20 are employed males , hence 70 % are employed females . ( employed females ) / ( total employed people ) = 70 / 90 = 7 / 9 = 77 % answer : c ."
Answer: c
Problem: the ages of two persons differ by 16 years . 6 years ago , the elder one was 3 times as old as the younger one . what are their present ages of the elder person ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: let present age of the elder person = x and present age of the younger person = x − 16 ( x − 6 ) = 3 ( x − 16 − 6 ) x − 6 = 3 x − 66 2 x = 60 x = 60 / 2 = 30 answer : option c
Answer: c
Problem: how many positive integers less than 90 are multiples of 6 but not multiples of 9 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the lcm of 6 and 9 is 18 . if x < 90 and x is divisible by 6 not by 9 - - > x is not divisible by 18 . from 1 - - > 90 , we have 5 numbers which is divisible by 18 : 18 , 36 , 54 , 72 , 90 . from 1 - - > 90 , we have ( 90 - 6 ) / 6 + 1 = 15 numbers divisible by 6 . therefore , our answer is 15 - 5 = 10 numbers . d"
Answer: d
Problem: two numbers are in the ratio of 6 : 8 . if 10 is subtracted from each , the new numbers are in the ratio 16 : 32 . find the smaller number .
Options: a ) 22 , b ) 12 , c ) 38 , d ) 15 , e ) 17
Rationale: "explanation : let the number be 6 x and 8 x . then , ( 6 x – 10 ) / ( 8 x – 10 ) = 1 / 2 2 ( 6 x – 10 ) = ( 8 x – 10 ) 12 x – 20 = 8 x – 10 4 x = 10 x = 2.5 the smaller number = ( 6 x 2.5 ) = 15 answer d"
Answer: d
Problem: a cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm . find the total area of the wet surface .
Options: a ) 69 m sqaure , b ) 49 m sqaure , c ) 52 m sqaure , d ) 64 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 5 * 1.40 + 7 * 1.40 ) ] + 7 * 5 = 69 m square option a"
Answer: a
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 9 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 9 ) = 36 / 18 = 2 / 1 . answer : a ."
Answer: a
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 27 cm .
Options: a ) 600 cm 2 , b ) 500 cm 2 , c ) 400 cm 2 , d ) 432 cm 2 , e ) 100 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 27 x 32 ) cm 2 = 432 cm 2 answer : option d"
Answer: d
Problem: on dividing a number by 56 , we get 28 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 56 x + 28 ( ∵ since the number gives 28 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 4 hence , if the number is divided by 8 , we will get 4 as remainder . answer : c"
Answer: c
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 10.50 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 10.50 when c . p = ( 100 * 10.50 ) / 21 = 50 answer : c
Answer: c
Problem: how many three - element subsets of { 5 , 6,7 , 8,9 } are there that do not contain the pair of elements 6 and 9 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "required subsets are = { 5 , 6,7 } , { 5 , 7,8 } , { 5 , 8,9 } , { 6 , 7,8 } , { 7 , 8,9 } = 5 answer : e"
Answer: e
Problem: if a lends rs . 1500 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 112.5 , b ) 122.5 , c ) 132.5 , d ) 67.5 , e ) 212.5
Rationale: "( 1500 * 1.5 * 3 ) / 100 = > 67.5 answer : d"
Answer: d
Problem: a man sitting in a train which is traveling at 45 kmph observes that a goods train , traveling in opposite direction , takes 8 seconds to pass him . if the goods train is 340 m long , find its speed
Options: a ) 102 kmph , b ) 106 kmph , c ) 108 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 340 / 8 m / sec = ( ( 340 / 8 ) × ( 18 / 5 ) ) kmph = 153 kmph . speed of goods train = ( 153 - 45 ) kmph = 108 kmph answer : option c"
Answer: c
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer q factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime q factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Problem: what is the sum of all possible solutions to | x - 5 | ^ 2 + | x - 5 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 10 , e ) 14
Rationale: "denote | x - 5 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 5 | , so it ' s an absolute value and thus can not be negative . y = | x - 5 | = 4 - - > x = 9 or x = - 1 . the sum = 10 answer : d ."
Answer: d
Problem: how many integers k greater than 100 and less than 1100 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 9 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 8 . 809 | 908 9 . 910 | 1001 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 9 sets with 10 such number in each set will give 9 x 10 = 90 integers . e"
Answer: e
Problem: anil had to do a multiplication . instead of taking 35 as one of the multipliers , he took 53 . as a result , the product went up by 540 . what is the new product ?
Options: a ) 1590 , b ) 1600 , c ) 1950 , d ) 1630 , e ) 1760
Rationale: explanation : let the number that anil wanted to multiply be ' y ' . he was expected to find the value of 35 y . instead , he found the value of 53 y . the difference between the value that he got ( 53 y ) and what he was expected to get ( 35 y ) is 540 . = > 53 y - 35 y = 540 = > ( 53 - 35 ) * y = 540 = > y = 30 therefore , the correct product = 53 * 30 = 1590 answer : a
Answer: a
Problem: at what rate percent of simple interest will a sum of money double itself in 33 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 3.03 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 33 ) = 100 / 33 = 3.03 % answer : d"
Answer: d
Problem: a 360 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 216 , e ) 112
Rationale: "s = 360 / 6 * 18 / 5 = 216 kmph answer : d"
Answer: d
Problem: a trader bought a car at 30 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 110 , c ) 112 , d ) 113 , e ) 98
Rationale: "original price = 100 cp = 70 s = 70 * ( 140 / 100 ) = 98 100 - 112 = 2 % answer : e"
Answer: e
Problem: one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 25 students are not between 3 years old and 4 years old , how many children are in the nursery school ?
Options: a ) 51 , b ) 20 , c ) 40 , d ) 50 , e ) 55
Rationale: "x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 25 x / 10 = 5 x = 50 answer : d"
Answer: d
Problem: a train is 310 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 36 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 310 + 140 = 500 meter time = distance / speed = 450 * ( 2 / 25 ) = 36 seconds answer : a"
Answer: a
Problem: a 49 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 49 = 14 answer : e"
Answer: e
Problem: there are 6 boxes numbered 1 , 2 , . . . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is :
Options: a ) 5 , b ) 21 , c ) 33 , d ) 60 , e ) 6
Rationale: "explanatory answer list down possibilities : from only 1 box all the way to all 6 if only one of the boxes has a green ball , it can be any of the 6 boxes . so , we have 6 possibilities . if two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes . 12 , 23 , 34 , 45 , 56 . if 3 of the boxes have green balls , there are 4 possibilities : 123 , 234 , 345 , 456 . if 4 boxes have green balls , there are 3 possibilities : 1234 , 2345 , 3456 . if 5 boxes have green balls , there are 2 possibilities : 12345 , 23456 . if all 6 boxes have green balls , there is just 1 possibility . total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21 . choice b"
Answer: b
Problem: the overall age of x and y is 18 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 18
Rationale: "e 18 ( x + y ) â € “ ( y + z ) = 18 x â € “ z = 18"
Answer: e
Problem: tom , working alone , can paint a room in 8 hours . peter and john , working independently , can paint the same room in 4 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 6 / 7 , d ) 1 / 7 , e ) 3 / 7
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 8 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 4 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 8 * ( t + 4 ) + 1 / 4 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 8 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 8 - - > t = 2 / 7 ; hence peter has done 1 / 4 * ( 2 / 7 + 2 ) = 1 / 4 * 16 / 7 = 16 / 28 = 8 / 14 = 4 / 7 answer : a"
Answer: a
Problem: a boy rides his bicycle 10 km at an average sped of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately .
Options: a ) 10.2 kmph , b ) 10.4 kmph , c ) 10.8 kmph , d ) 11.8 kmph , e ) none
Rationale: sol . total distance travelled = ( 10 + 12 ) km / hr = 22 km / hr . total time taken = [ 10 / 12 + 12 / 10 ] hrs = 61 / 30 hrs ∴ average speed = [ 22 * 30 / 61 ] km / hr = 10.8 km / hr . answer c
Answer: c
Problem: ( a / 2 ) / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 1 , 2 , or 4 . what is the largest possible value of the expression ?
Options: a ) 8 / 2 , b ) 2 / 4 , c ) 1 / 8 , d ) 2 / 4 , e ) 4 / 6
Rationale: ( a / 2 ) / ( b / c ) = ( a * c ) / 2 b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 2 * 4 ) / 2 * 1 = 8 / 2 answer a
Answer: a
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 190 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 494 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 190 x = 38 total number of students = 13 x = 13 * 38 = 494 answer is d"
Answer: d
Problem: if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction ?
Options: a ) 1 / 2 , b ) 3 / 5 , c ) 5 / 7 , d ) 9 / 11 , e ) 3 / 4
Rationale: "let the original fraction be x / y then , 115 % of x / 92 % of y = 15 / 16 115 x / 92 y = 15 / 16 x / y = 3 / 4 answer is e"
Answer: e
Problem: simplify : 32 ÷ 8 × 24 + 16 =
Options: a ) 130 , b ) 124 , c ) 120 , d ) 115 , e ) 112
Rationale: "32 ÷ 8 × × 24 + 16 = > 4 × × 24 + 16 = 96 + 16 = 112 option e"
Answer: e
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 5 gallons of water and 10 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b"
Answer: b
Problem: the tax on a commodity is diminished by 32 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 24 %
Rationale: "100 * 100 = 10000 68 * 112 = 7616 10000 - - - - - - - 2384 100 - - - - - - - ? = 24 % answer : e"
Answer: e
Problem: 106 x 106 - 94 x 94 = ?
Options: a ) 2400 , b ) 2000 , c ) 1904 , d ) 1906 , e ) none of them
Rationale: "= ( 106 ) ^ 2 - ( 94 ) ^ 2 = ( 106 + 94 ) ( 106 - 94 ) = ( 200 x 12 ) = 2400 answer is a"
Answer: a
Problem: of the 90 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 90 - 50 - ( 40 - 35 ) = 90 - 55 = 35 answer e"
Answer: e
Problem: how many cuboids of length 5 m , width 6 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 4 , b ) 6 , c ) 10 , d ) 8 , e ) 11
Rationale: "( 18 ã — 15 ã — 12 ) / ( 5 ã — 3 ã — 2 ) = 6 answer is b ."
Answer: b
Problem: when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 26 = 26 - x or , 4 x = 52 or , x = 13 . d answer ."
Answer: d
Problem: the sum of digits of a two digit number is 11 , the difference between the digits is 5 . find the number
Options: a ) 85 , b ) 94 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 11 , x - y = 5 adding these 2 x = 16 = > x = 8 , y = 3 . thus the number is 83 answer c"
Answer: c
Problem: if x , y , and z are positive integers and 3 x = 7 y = 5 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 25 , c ) 71 , d ) 35 , e ) 45
Rationale: "given 3 x = 7 y = 5 z x + y + z in terms of x = x + ( 3 x / 7 ) + ( 3 x / 5 ) = 71 x / 35 now checking with each of the answers and see which value gives a minimum integer value . a x = 35 / 71 * 15 , not an integer b , d , e can be ruled out similarly . c is minimum value as x = 71 * 35 / 71 = 35 answer is c"
Answer: c
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 288
Rationale: "white : yellow = x : ( x + 90 ) = 8 : 13 - - > 13 x = 8 x + 720 - - > x = 144 . the total # of balls originally x + x = 144 + 144 = 288 . answer : e ."
Answer: e
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 10 minutes , a combustion reaction creates 10000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: solution : 10,000 carbon dioxide molecules are created over a period of 10 minutes . therefore 10,000 / 10 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a .
Answer: a
Problem: if two girls starting from same point , walking in the opposite directions with 5 km / hr and 10 km / hr as average speeds respectively . then the distance between them after 5 hours is ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "explanation : total distance = distance traveled by person a + distance traveled by person b = ( 5 ã — 5 ) + ( 10 ã — 5 ) = 25 + 50 = 75 km answer : d"
Answer: d
Problem: in the junior basketball league there are 15 teams , 1 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 9 .
Rationale: "total teams = 15 bad teams = ( 1 / 3 ) * 15 = 5 rich teams = 8 so maximum value that the both rich and bad can take will be 8 . so e = 9 can not be that value . ans e ."
Answer: e
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2028 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 11 , b ) 17 , c ) 26 , d ) 101 , e ) 1322
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2028 3 b 2 = 2028 b 2 = 676 = 26 ( b > 0 ) b = 26 m . answer : c"
Answer: c
Problem: find the least number which when divided by 5 , 67 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder
Options: a ) 1683 , b ) 1684 , c ) 1685 , d ) 1582 , e ) 1584
Rationale: explanation : l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is a
Answer: a
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 6 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 6 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 6 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 32 . ans . a ."
Answer: a
Problem: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.267 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 0 , c ) 27 , d ) 54 , e ) can not be determined
Rationale: "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . b"
Answer: b
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 22 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 166 , c ) 86 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 22 = 40 5 * quotient = 40 quotient = 8 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 8 ) + 6 = 166 . b )"
Answer: b
Problem: a sum fetched total simple interest of 4016.25 at the rate of 11 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 8925 , b ) 8032.5 , c ) 7302.3 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 55 % of p = 4016.25 or , p = 7302.3 answer c"
Answer: c
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , three boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) 13.5 sec
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 18 = 10 m / s now , length of train = 9 ã — 15 = 135 m â ˆ ´ required time = 135 â  „ 10 = 13.5 sec . answer e"
Answer: e
Problem: what is the cp of rs 100 stock at 8 discount , with 1 / 5 % brokerage ?
Options: a ) 92.9 , b ) 96.3 , c ) 92.2 , d ) 96.7 , e ) 92.8
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 8 + 1 / 5 92.2 thus the cp is rs 92.2 . answer : c"
Answer: c
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 27 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 27 kg zinc , mixture , melted = [ 20 / 9 x 27 ] kg = 60 kg . answer b"
Answer: b
Problem: if x is an integer such that 3 < x < 10 , 5 < x < 18 , 9 > x > – 2 , 8 > x > 0 , and x + 1 < 9 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "3 < x < 10 , 6 < x < 18 , - 2 < x < 9 0 < x < 8 x < 8 from above : 6 < x < 8 - - > x = 7 . answer : c ."
Answer: c
Problem: if n is a positive integer greater than 1 , then p ( n ) represents the product of all the prime numbers less than or equal to n . the second smallest prime factor of p ( 12 ) + 11 is
Options: a ) 2 , b ) 11 , c ) 13 , d ) 17 , e ) 211
Rationale: p ( 12 ) + 11 = 2 ∗ 3 ∗ 5 ∗ 7 ∗ 11 + 11 = 11 ( 2 ∗ 3 ∗ 5 ∗ 7 + 1 ) = 11 ∗ 211 . both 11 and 211 are primes : 11 is the smallest prime of p ( 12 ) + 11 and 211 is the second smallest prime of p ( 12 ) + 11 . answer : e .
Answer: e
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 140 marks , the no of questions he attempts correctly is :
Options: a ) a ) 35 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 40
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 140 = > 5 x = 200 = > x = 40 answer : e"
Answer: e
Problem: the average ( arithmetic mean ) of 4 different integers is 70 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 13 , e ) 33
Rationale: "total of integers = 70 * 4 = 280 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 280 - ( 90 + 89 + 88 ) = 280 - 267 = 13 answer : d"
Answer: d
Problem: double of quarter of 6 percent written as a decimal is :
Options: a ) 0.03 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 6 % = 0.03 answer : a"
Answer: a
Problem: p and q can complete a work in 20 days and 12 days respectively . p alone started the work and q joined him after 4 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 20 work done by q in 1 day = 1 / 12 work done by p in 4 days = 4 × ( 1 / 20 ) = 1 / 5 remaining work = 1 – 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 20 + 1 / 12 = 8 / 60 = 2 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 2 / 15 ) = 6 total days = 4 + 6 = 10 answer : option b"
Answer: b
Problem: if in one hour , a canoe rows at 16 km / hr downstream and 9 km / hr upstream , calculate the speed of a boat in still water ( in km / hr ) .
Options: a ) 18 kmph , b ) 15.5 kmph , c ) 12.5 kmph , d ) 13.5 kmph , e ) 22.5 kmph
Rationale: speed in still water = ( 16 + 9 ) 1 / 2 kmph = 12.5 kmph . answer : c
Answer: c
Problem: a rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it . one parallel to the length and the other parallel to breadth . the cost of graveling the roads at 75 paise per sq meter is ?
Options: a ) rs . 259 , b ) rs . 252 , c ) rs . 258 , d ) rs . 251 , e ) rs . 252
Rationale: "area of cross roads = 55 * 4 + 35 * 4 - 4 * 4 = 344 sq m cost of graveling = 344 * ( 75 / 100 ) = rs . 258 answer : c"
Answer: c
Problem: a salesman ` s commission is 5 % on all sales upto rs . 10000 and 4 % on all sales exceeding this . he remits rs . 31100 to his parent company after deducing his commission . find the total sales .
Options: a ) 32500 , b ) 2500 , c ) 22500 , d ) 30000 , e ) 40000
Rationale: let his total sales be rs . x . now ( total sales ) – ( commission ) = rs . 31100 x - [ ( 5 % of 10000 + 4 % of ( x - 10000 ) ] = 31100 x - [ ( ( 5 / 100 ) * 10000 + ( 4 / 100 ) * ( x - 10000 ) ] = 31100  x - 500 - ( ( x - 10000 ) / 25 ) = 31100  x - ( x / 25 ) = 31200  24 x / 25 = 31200  x = [ ( 31200 * 25 ) / 24 ) = 32500 . total sales = rs . 32500 answer a
Answer: a
Problem: approximately how many revolutions will be made by a car tire with a 15 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 669 , b ) 660 , c ) 360 , d ) 720 , e ) 1,440
Rationale: diameter of car tire = 15 inches radius of car tire = 7.5 inches = 7.5 * 2.54 cm = 19.05 cm circumference of the car tire = 2 * pi * 19.05 = 2 * 3.14 * 19.05 = 119.63 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 119.63 = 668.73 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer a
Answer: a
Problem: the area of an isosceles trapezoid with sides of length 5 and bases of length 7 and 13 is ?
Options: a ) 40
b ) 41
c ) 42
d ) 43
e ) 44
Rationale: isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 13 will be divided into 3 parts = 7 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 20 * 4 = 40 a
Answer: a
Problem: 16 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 ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 240
Rationale: 2 * 16 c 2 = 2 * 120 = 240 the answer is e .
Answer: e
Problem: the grade point average of one third of the classroom is 30 ; the grade point average of the rest is 33 . what is the grade point average of the whole class ?
Options: a ) 44 , b ) 41 , c ) 38 , d ) 35 , e ) 32
Rationale: "let n = total students in class total points for 1 / 3 class = 30 n / 3 = 10 n total points for 2 / 3 class = 33 * 2 n / 3 = 22 n total points for whole class = 10 n + 22 n = 32 n 32 n total class points / n total students = 32 grade point average for total class answer : e"
Answer: e
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 4,4 ) , ( 7,4 ) , ( 5,9 ) , ( 8,9 ) ?
Options: a ) 21 .
b ) 28 .
c ) 5 .
d ) 49 .
e ) 52 .
Rationale: delta x will give us the dimension of one side of the parallelogram = 5 - 4 = 1 unit delta y will give us the dimension of the other side of parallelogram = 9 - 4 = 5 unit area of parallelogram = 1 * 5 = 5 answer is c
Answer: c
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 18 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 36 , e ) 96
Rationale: "a 54 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 54 miles"
Answer: a
Problem: average expenditure of a person for the first 3 days of a week is rs . 360 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 400 , e ) none
Rationale: "explanation : assumed mean = rs . 360 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 360 + rs . 40 = rs . 400 correct option : d"
Answer: d
Problem: what approximate value will come in place of the question mark ( ? ) in the below question ? ( 47 % of 1442 - 36 % of 1412 ) + 63 = ?
Options: a ) 237 , b ) 278 , c ) 278 , d ) 252 , e ) 271
Rationale: explanation : since there are 5 cups of each kind , prepared with milk or tea leaves added first , are identical hence , total number of different people ways of presenting the cups to the expert is 10 ! / ( 5 ! x 5 ! ) = 252 answer : d ) 252
Answer: d
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 47 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 47 has the form 4 k + 3 , so the units digit of 93 ^ 47 is 7 . the units digit if powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a