Cheukting/mathqa huggingface dataset:
Question (gain): the cost price of 60 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?
Options: a ) 42 , b ) 45 , c ) 48 , d ) 50 , e ) 54
Rationale: "let the cost price = y the cost price of 60 articles = 60 y the selling price of x articles = 1.20 y * x 1.20 y * x = 60 y x = 60 / 1.2 = 50 the answer is d ."
Answer: d
Question (general): in township k each property is taxed at 10 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ?
Options: a ) $ 32 , b ) $ 50 , c ) $ 320 , d ) $ 400 , e ) $ 500
Rationale: "increase in house value = $ 24,000 - $ 20,000 = $ 4000 so , tax increase = 10 % of $ 4000 = $ 400 answer : d"
Answer: d
Question (gain): on a certain transatlantic crossing , 40 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.8 x had round trip tickets and took their cars . 0.8 x = 0.4 t x = 0.5 t the answer is c ."
Answer: c
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 3 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 5 is p ( 5 ) = 9.50 + 0.25 ( 5 – 1 ) = 9.50 + 0.25 * 4 ; salary grade of 3 is p ( 3 ) = 9.50 + 0.25 ( 3 – 1 ) = 9.50 + 0.25 * 2 ; p ( 5 ) - p ( 3 ) = 9.50 + 0.25 * 4 - 9.50 - 0.25 * 2 = 0.5 . answer : a ."
Answer: a
Question (general): in a certain game , a large container is filled with red , yellow , green , and blue beads worth , respectively , 7 , 5 , 3 , and 2 points each . a number of beads are then removed from the container . if the product of the point values of the removed beads is 30 , 870000 , how many red beads were removed ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 30 , 870,000 = 2 ^ 4 * 5 ^ 4 * 3087 = 2 ^ 4 * 3 * 5 ^ 4 * 1029 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 343 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 7 ^ 3 the answer is c .
Answer: c
Question (general): # 88 a necklace is made by stringing q no individual beads together in the repeating pattern red bead , green bead , white bead , blue bead , and yellow bead . if the necklace design begins with a red bead and ends with a white bead , then q could equal
Options: a ) 16 , b ) 28 , c ) 41 , d ) 54 , e ) 65
Rationale: you can just write out the pattern and count : rgwbyrgwbyrgwby . . . but to save time a good test taker will just look for a pattern . min # is 3 , because w is the third one . then every 5 beads another white comes , so it must be 3 + 5 + 5 + 5 . . and so on . . . 3 + 5 = 8 3 + 5 + 5 = 13 3 + 5 + 5 + 5 = 18 3 + 5 + 5 + 5 + 5 = 23 so you see it ends in either 8 or 3 . pick an answer that ends in either 8 or 3 . only one answer does , b .
Answer: b
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 $ 16 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 ) $ 20 , b ) $ 21 , c ) $ 22 , d ) $ 23 , e ) $ 24
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 ( 16 ) = 0.8 x x = 1.2 ( 16 ) / 0.8 = 1.5 ( 16 ) = $ 24 the answer is e .
Answer: e
Question (gain): rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 3000 . then his monthly salary is
Options: a ) rs . 15000 , b ) rs . 12000 , c ) rs . 9000 , d ) rs . 6000 , e ) rs . 3000
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 3000 â ‡ ” 20 / 100 x = 3000 â ‡ ” x = 3000 ã — 5 = 15000 . answer a"
Answer: a
Question (gain): the price of an item is discounted 6 percent on day 1 of a sale . on day 2 , the item is discounted another 6 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 82.3 % , b ) 84.6 % , c ) 85.6 % , d ) 89.6 % , e ) 79.2 %
Rationale: "let initial price be 100 price in day 1 after 6 % discount = 94 price in day 2 after 6 % discount = 88.36 price in day 3 after 10 % discount = 79.52 so , price in day 3 as percentage of the sale price on day 1 will be = 79.52 / / 94 * 100 = > 84.6 % answer will definitely be ( b )"
Answer: b
Question (gain): last year a certain bond price with a face value of 5000 yielded 9 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6923
Rationale: "interest = 0.09 * 5000 = 0.065 * selling price - - > selling price = 0.09 * 5000 / 0.065 - - > selling price = ~ 6,923 answer : e ."
Answer: e
Question (physics): a train of 40 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 3.9 , e ) 3.6
Rationale: d = 40 * 60 + 1500 = 3900 m t = 3900 / 60 * 18 / 5 = 234 sec = 3.9 mins answer : d
Answer: d
Question (gain): when a mobile is sold for rs . 7200 , the owner loses 20 % . at what price must that mobile be sold in order to gain 20 % ?
Options: a ) 10,400 , b ) 10,600 , c ) 10,800 , d ) 11,000 , e ) 11,200
Rationale: 80 : 7200 = 120 : x x = ( 7200 x 120 ) / 80 = 10800 . hence , s . p . = rs . 10,800 . answer : option c
Answer: c
Question (general): ( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + 0.015 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.68 , b ) 0.08 , c ) 0.05 , d ) 0.06 , e ) none of them
Rationale: "given expression = ( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + ( 0.15 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.15 - 0.1 ) = 0.05 answer is c ."
Answer: c
Question (general): a retailer sells 7 shirts . the first 2 he sells for $ 38 and $ 42 . if the retailer wishes to sell the 7 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 5 shirts ?
Options: a ) $ 54.00 , b ) $ 57.00 , c ) $ 58.00 , d ) $ 60.50 , e ) $ 63.00
Rationale: first 2 shirts are sold for $ 38 and $ 42 = $ 80 . to get average price of $ 50 , total sale should be 7 * $ 50 = $ 350 so remaining 5 shirts to be sold for $ 350 - $ 80 = $ 270 answer should be 270 / 5 = $ 54.00 that is a
Answer: a
Question (physics): a person crosses a 500 m long street in 4 minutes . what is his speed in km per hour ?
Options: a ) 7.5 , b ) 2.6 , c ) 3.9 , d ) 8.2 , e ) 2.7
Rationale: "distance = 500 meter time = 4 minutes = 4 x 60 seconds = 240 seconds speed = distance / time = 500 / 240 = 2.08 m / s = 2.08 ã — 18 / 5 km / hr = 7.5 km / hr answer : a"
Answer: a
Question (general): if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 160 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,440
Rationale: "10 / 100 p = 160 > > p = 160 * 100 / 10 = 1600 1600 - 160 = 1440 answer : e"
Answer: e
Question (physics): if the perimeter of a rectangular garden is 600 m , its length when its breadth is 100 m is ?
Options: a ) 227 , b ) 247 , c ) 200 , d ) 277 , e ) 121
Rationale: "2 ( l + 100 ) = 600 = > l = 200 m answer : c"
Answer: c
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 50 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 50 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 150 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 150 - 90 ) / 90 * 100 = 50 % answer : d ."
Answer: d
Question (general): you need to pick any number from ' 1 , 3 , 5 , 7 , 9 , 11 , 13 and 15 ' to make below equation true . ( ) + ( ) + ( ) = 30 can you solve it ?
Options: a ) 29 , b ) 30 , c ) 31 , d ) 32 , e ) 33
Rationale: solution : 3 ! + 15 + 9 = 30 explanation : 3 ! = 3 * 2 * 1 = 6 6 + 15 + 9 = 30 answer b
Answer: b
Question (physics): ram and shyam start a two - length swimming race at the same moment but from opposite ends of the pool . they swim in lanes at uniform speeds , but hardy is faster than andy . they 1 st pass at a point 18.5 m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec . after setting off on the return length , the swimmers pass for the 2 nd time just 10.5 m from the shallow end . how long is the pool ?
Options: a ) 65 , b ) 60 , c ) 55 , d ) 50 , e ) 45
Rationale: let x = length of pool at first meeting , combined distance = x at second meeting , combined distance = 3 x if andy swims 18.5 m of x , then he will swim 3 * 18.5 = 55.5 m of 3 x andy ' s total distance to second meeting = x + 10.5 m x + 10.5 = 55.5 m x = 45 m e
Answer: e
Question (gain): jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 4 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 920.24 answer : d ."
Answer: d
Question (general): what least number must besubtracted from 427398 so that remaining no . is divisible by 15 ?
Options: a ) 725117481 , b ) 343564689 , c ) 454564690 , d ) 759900434 , e ) 656590009
Rationale: on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a
Answer: a
Question (physics): one copy machine can make 30 copies a minute , and a second copy machine makes 20 copies a minute . if the two copiers work together , how long would it take them to make 2,000 copies ?
Options: a ) 20 minutes , b ) 40 minutes , c ) 45 minutes , d ) 50 minutes , e ) 55 minutes
Rationale: "total work done by both machines in a minute = 30 + 20 = 50 copies total number of copies required = 2000 time = 2000 / 50 = 40 mins answer b"
Answer: b
Question (general): little john had $ 8.50 . he spent $ 1.25 on sweets and gave to his two friends $ 1.20 and $ 2.20 . how much money was left ?
Options: a ) $ 5.85 , b ) $ 6.85 , c ) $ 3.85 , d ) $ 2.85 , e ) $ 4.85
Rationale: "john spent and gave to his two friends a total of 1.25 + 1.20 + 2.20 = $ 4.65 money left 8.50 - 4.65 = $ 3.85 correct answer is c ) $ 3.85"
Answer: c
Question (physics): in covering a distance of 48 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 8 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 48 / x - 48 / 2 x = 3 6 x = 48 x = 8 km / hr . answer : option e"
Answer: e
Question (other): find the number of different prime factors of 1250
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "explanation : l . c . m of 1250 = 2 x 5 x 5 x 5 x 5 2 , 5 number of different prime factors is 2 . answer : option b"
Answer: b
Question (physics): the speed of a bus increases by 2 kmph after every one hour . if the distance travelled in the first one hour was 35 km , what was the total distance travelled in 12 hours ?
Options: a ) 550 , b ) 500 , c ) 552 , d ) 560 , e ) 580
Rationale: dist 1 st hr = 35 km speed of bus by 2 kmph 2 nd hr = 37 km 3 rd hr = 39 km tot = 35 + 37 + 39 + . . . . ( 12 terms ) 12 / 2 ( 2 * 35 + ( 12 - 1 ) 2 ] = 6 * 92 = 552 answer c
Answer: c
Question (gain): harkamal purchased 8 kg of grapes at the rate of 90 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1055 , b ) b ) 1215 , c ) c ) 1065 , d ) d ) 1070 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 90 × 8 = 720 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 720 + 495 = 1215 . b )"
Answer: b
Question (general): the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 16 terms of the arithmetic progression ?
Options: a ) 300 , b ) 120 , c ) 150 , d ) 160 , e ) 270
Rationale: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 16 . . . we get 15 / 2 [ 2 a + 14 d ] = 16 [ a + 7 d ] = 16 * 10 = 160 . . . answer is d . . ."
Answer: d
Question (probability): there are 3 red shoes & 7 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 12 , d ) 1 / 15 , e ) 1 / 16
Rationale: "taking 2 red shoe the probablity is 3 c 2 from 10 shoes probablity of taking 2 red shoe is 3 c 2 / 10 c 2 = 1 / 15 answer : d"
Answer: d
Question (physics): it will take 16 days for mary to complete a certain task alone . she worked for 8 days before she was joined by her sister . both of them completed the remaining task in 2 and half days . if her sister had joined her when she started the task , how many days would it have taken ?
Options: a ) 6 , b ) 8 , c ) 2 , d ) 5 , e ) 4
Rationale: explanation : mary and her sister complete half work in 2.5 days = > they can complete whole work in 5 days answer : option d
Answer: d
Question (general): on dividing 73 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 8 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 18
Rationale: "d = ( d - r ) / q = ( 73 - 1 ) / 9 = 72 / 9 = 8 a )"
Answer: a
Question (general): shruti purchased several number of 3 articles p , q and r in the proportion 3 : 2 : 3 . if the unit costs of the articles p , q and r are 200 , rs . 90 and rs . 60 respectively , how many articles of q must have been purchased in the total purchases of rs . 4800 ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: explanation : let the number of articles of types p , q and r be 3 a , 2 a and 3 a respectively . thus , we get , ( 200 x 3 a ) + ( 90 x 2 a ) + ( 60 x 3 a ) = 4800 960 a = 4800 a = 5 hence , the number of articles of type “ q ” = 2 x 5 = 10 answer b
Answer: b
Question (gain): a distributor sells a product through an on - line 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 $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 40 % profit on the cost of the item ?
Options: a ) 18 , b ) 30 , c ) 22 , d ) 22.5 , e ) 27
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 40 % of the final price - - > ( final price ) * 0.6 = $ 18 - - > ( final price ) = $ 30 . answer : b ."
Answer: b
Question (other): a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 9 are wrong and the other digits are correct , then the correct answer would be :
Options: a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 556881
Rationale: 987 = 3 x 7 x 47 so , the required number must be divisible by each one of 3 , 7 , 47 553681 - > ( sum of digits = 28 , not divisible by 3 ) 555181 - > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by 3 , 7 , 47 answer c
Answer: c
Question (general): the least number which when increased by 5 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 427 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these
Rationale: solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 5 = 859 . answer b
Answer: b
Question (gain): what is the compound interest on rs . 8500 at 7.5 % p . a . compounded half - yearly for 2 1 / 2 years .
Options: a ) 1409.85 , b ) 1717.85 , c ) 1427.85 , d ) 2717.85 , e ) 1817.85
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 10 , 217.85 c . i . > > 10 , 217.85 - 8500 > > rs . 1717.85 answer : b"
Answer: b
Question (gain): a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 140 ) / 140 = 40 / 140 = 2 / 7 = ~ 29 % . answer : e ."
Answer: e
Question (other): the l . c . m of two numbers is 48 . the numbers are in the ratio 2 : 3 . the sum of numbers is ?
Options: a ) 22 , b ) 67 , c ) 40 , d ) 88 , e ) 11
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : c"
Answer: c
Question (other): if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 65 , what is the common ratio of the g . p ?
Options: a ) 4 , b ) 1 / 4 , c ) 2 , d ) 9 , e ) 1 / 9
Rationale: 65 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 65 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 65 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 64 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 64 = r ^ 3 r = 4 a
Answer: a
Question (general): when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 3 of 300 = 100 total amount in her account = 400 answer c"
Answer: c
Question (physics): a man traveled a total distance of 1200 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 400 , b ) 440 , c ) 480 , d ) 520 , e ) 560
Rationale: total distance traveled = 1200 km . distance traveled by plane = 400 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 400 = 1200 5 x / 3 = 800 x = 480 km the answer is c .
Answer: c
Question (gain): in town x , 64 percent of the population are employed , and 40 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 38 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 40 are employed males , hence 24 % are employed females . ( employed females ) / ( total employed people ) = 24 / 64 = 38 % answer : a ."
Answer: a
Question (general): find the average of all prime numbers between 1 and 5 .
Options: a ) 30 , b ) 3.6 , c ) 5.6 , d ) 6.6 , e ) none
Rationale: "sol . there are five prime numbers between 1 and 5 . they are 2 , 3 , 5 , 7 , 11 â ˆ ´ required average = [ 2 + 3 + 5 + 7 + 11 / 5 ] = 28 / 5 = 5.6 answer c"
Answer: c
Question (gain): a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 237 for it , the cost price of the cricket bat for a is :
Options: a ) 150 , b ) 120 , c ) 158 , d ) 160 , e ) 210
Rationale: "125 % of 120 % of a = 237 125 / 100 * 120 / 100 * a = 237 a = 237 * 2 / 3 = 158 . answer c"
Answer: c
Question (general): how many numbers between 100 and 756 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 16 , e ) 99
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 756 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 756 : 756 / 42 = 18 hence , 42 * 16 = 756 is the last number divisible by 42 within 756 hence , total numbers divisible by 2 , 3 , 7 together are ( 18 â € “ 2 ) = 16 answer : d"
Answer: d
Question (geometry): if the sides of a cube are in the ratio 9 : 5 . what is the ratio of their diagonals ?
Options: a ) 9 : 5 , b ) 16 : 9 , c ) 4 : , d ) 3 : 4 , e ) 3 : 8
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 5 d 1 : d 2 = 9 : 5 where √ 3 cancelled both side answer : a"
Answer: a
Question (physics): a and b together do a work in 20 days . b and c together in 15 days and c and a in 12 days . so a , b and c together finish same work in how many days ?
Options: a ) 12 , b ) 15 , c ) 8 , d ) 10 , e ) 11
Rationale: ( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 so , all three together finish work in 10 days answer d
Answer: d
Question (physics): if a train , travelling at a speed of 180 kmph , crosses a pole in 6 sec , then the length of train is ?
Options: a ) 300 , b ) 125 , c ) 288 , d ) 266 , e ) 121
Rationale: d = 180 * 5 / 18 * 6 = 300 m answer : a
Answer: a
Question (gain): a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 36 . find the profit percentage ?
Options: a ) 80 % , b ) 50 % , c ) 59 % , d ) 40 % , e ) 53 %
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 180 ( 36 * 5 ) profit percentage = ( 180 - 100 ) / 100 * 100 = 80 % answer : a"
Answer: a
Question (physics): a can do a piece of work 60 days . b can do work in 90 days . in how many days they will complete the work together ?
Options: a ) 36 days , b ) 32 days , c ) 19 days , d ) 17 days , e ) 18 days
Rationale: lcm = 180 , ratio = 60 : 90 = 2 : 3 no of days = 180 / ( 2 + 3 ) = 180 / 5 = 36 days answer : a
Answer: a
Question (general): what least number should be added to 1536 , so that the sum is completely divisible by 21 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "1536 ÷ 21 = 73 reminder - 3 3 + 18 = 21 hence 18 should be added to 1536 so that the sum will be divisible by 21 answer : c"
Answer: c