Cheukting/mathqa huggingface dataset:
Question (general): the average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ?
Options: a ) 30.5 , b ) 26 , c ) 30 , d ) 18 , e ) 11
Rationale: "explanation : 18 + 22 + 7 * 3 = 61 / 2 = 30.5 answer : a"
Answer: a
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (other): 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
Question (physics): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (physics): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (other): 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
Question (general): 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