regisss/math_qa huggingface dataset:
Problem: the cyclist going at a constant rate of 18 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 48 miles per hour . the motor - cyclist stops to wait for the cyclist 15 minutes after passing cyclist , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: for the 15 minutes the motor - cyclist continues to overtake the cyclist , she is going at 30 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 18 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 30 / 18 * 15 or 25 minutes answer is ( a )
Answer: a
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 81 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 9
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 81 2 x = 18 = > x = 9 answer : e"
Answer: e
Problem: what is difference between biggest and smallest fraction among 1 / 3 , 3 / 4 , 4 / 5 and 5 / 6
Options: a ) 2 / 5 , b ) 1 / 2 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 1 / 3 = . 33 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 1 / 3 their difference is 5 / 6 - 1 / 3 = 3 / 6 = 1 / 2 option b"
Answer: b
Problem: in a renowned city , the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 6 persons are added ( 9 - 3 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e"
Answer: e
Problem: 894.7 – 573.07 – 95.007 = ?
Options: a ) 226.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 894.7 - ( 573.07 + 95.007 ) = 894.7 - 668.077 = 226.623 . answer a"
Answer: a
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 1800 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 1800 x = 30 the numbers are 3 * 30 , 4 * 30 , 5 * 30 hence required h . c . f . = 30 answer is b"
Answer: b
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 65 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 65 = > v = 55 ( option d ) ."
Answer: d
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 35 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1750 m , c ) 950 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 35 minutes = 15 / 18 * 35 * 60 = 1750 m answer is b"
Answer: b
Problem: the squared value of the diagonal of a rectangle is ( 64 + b 2 ) sq cm , where b is less than 8 cm . what is the breadth of that rectangle ?
Options: a ) 6 cm
b ) 10 cm
c ) 8 cm
d ) data inadequate
e ) none of these
Rationale: diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a
Answer: a
Problem: 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
Problem: 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
Problem: 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
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 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
Problem: 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
Problem: # 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
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 $ 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: ( 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: find the simple interest on rs . 300 for 9 months at 6 paisa per month ?
Options: a ) 142 , b ) 152 , c ) 162 , d ) 172 , e ) 182
Rationale: "i = ( 300 * 9 * 6 ) / 100 = 162 answer : c"
Answer: c
Problem: gary drove from point a to point b at 60 km / h . on his way back he took a train travelling at 110 km / h and therefore his trip back lasted 5 hours less . what is the distance ( in km ) between a and b ?
Options: a ) 600 . , b ) 630 . , c ) 660 . , d ) 690 . , e ) 720 .
Rationale: distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 - 5 thus , s 1 t 1 = s 2 t 2 60 t 1 = s 2 ( t 1 - 5 ) t 1 = 11 60 * 11 = 660 answer : c
Answer: c
Problem: when n is divided by 19 , the remainder is 7 . find thee difference between previous remainder and the remainder when 18 n is divided by 9 ?
Options: a ) 7 , b ) 5 , c ) 0 , d ) 3 , e ) 9
Rationale: let n = 7 ( leaves a remainder of 7 when divided by 19 ) 18 n = 18 ( 7 ) = 126 , which leaves a remainder of 0 when divided by 9 . difference = 7 - 0 = 7 . answer a
Answer: a
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 75 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: "75 % is 5 % - points below 80 % and 20 % - points above 55 % . so the ratio of solution p to solution q is 4 : 1 . mixture p is 4 / 5 = 80 % of the volume of mixture pq . the answer is d ."
Answer: d
Problem: a can complete a work in 15 days and b can do the same work in 9 days . if a after doing 5 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 4 days , c ) 6 days , d ) 7 days , e ) 10 days
Rationale: "the required answer = ( 15 - 5 ) * 9 / 15 = 40 / 10 = 6 days answer is c"
Answer: c
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 15 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 15 = 35 km apart , they take 1 hour to be 1000 m apart , they take 35 * 1000 / 1000 = 35 min . answer is c"
Answer: c
Problem: the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is :
Options: a ) 45 , b ) 46 , c ) 47 , d ) 48 , e ) 49
Rationale: weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a
Answer: a
Problem: the contents of a certain box consist of 14 apples and 24 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 18 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 24 oranges , so to get to 6 oranges , we should remove 24 - 6 = 18 oranges . answer a"
Answer: a
Problem: mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 96 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 96 ) is 96 % of juan ' s income ( 100 ) . answer : c"
Answer: c
Problem: a and b are two circles . the radius of a is four times as large as the diameter of b . what is the ratio between the areas of the circles ?
Options: a ) 1 : 8 .
b ) 1 : 2 .
c ) 1 : 24 .
d ) 1 : 64 .
e ) 1 : 6 .
Rationale: given : the radius of a is 4 times as large as the diameter of b . = > r ( a ) = 4 * d ( b ) = 4 * 2 * r ( b ) = 8 r ( b ) . the radius are in ratio of 1 : 8 thus the area will be in the ratio of square of radius . 1 : 64 . hence d .
Answer: d
Problem: a can run 192 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 24 metre , d ) 15 metre , e ) 28 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 192 / 32 = 6 m / s distance covered by b in 4 seconds = speed ã — time = 6 ã — 4 = 24 metre i . e . , a beat b by 24 metre answer is c"
Answer: c
Problem: a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 585.75 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 791
Rationale: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1585.75 = > x = 791 e"
Answer: e
Problem: three pipes a , b and c can fill a tank from empty to full in 30 minutes , 20 minutes and 10 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution q in the liquid in the tank after 3 minutes ?
Options: a ) 1 / 11 , b ) 2 / 11 , c ) 3 / 11 , d ) 4 / 11 , e ) 5 / 11
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by b in 3 minutes = 3 / 20 required ratio = 3 / 20 * 20 / 11 = 3 / 11 answer : c"
Answer: c
Problem: if a 5 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 100 % , b ) 200 % , c ) 300 % , d ) 400 % , e ) 500 %
Rationale: "the area a of the large cube is 5 * 5 * 6 = 150 square cm . the area of the 125 small cubes is 125 * 6 = 750 = 5 a , an increase of 400 % . the answer is d ."
Answer: d
Problem: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 550 ?
Options: a ) 249 , b ) 498 , c ) 676 , d ) 823 , e ) 274
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 550 y = 2 x + 2 548 = 2 x x = 274 answer : e . 274"
Answer: e
Problem: one copy machine can make 30 copies a minute , and a second copy machine makes 15 copies a minute . if the two copiers work together , how long would it take them to make 900 copies ?
Options: a ) 15 minutes , b ) 20 minutes , c ) 25 minutes , d ) 30 minutes , e ) 35 minutes
Rationale: "total work done by both machines in a minute = 30 + 15 = 45 copies total number of copies required = 900 time = 900 / 45 = 20 mins answer b"
Answer: b
Problem: two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 10 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 4 / 3 , c ) 15 / 4 , d ) 56 / 15 , e ) 17 / 5
Rationale: "rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 10 combined = 8 / 30 work done in 2 days = 8 / 15 work left = 7 / 15 rate * time = work left 1 / 8 * time = 7 / 15 time = 56 / 15 d"
Answer: d
Problem: if xy = 4 , x / y = 16 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6
Rationale: "very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 16 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 16 - - - > y ^ 2 = 4 / 16 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a ."
Answer: a
Problem: if a boat is rowed downstream for 24 km in 4 hours and upstream for 48 km in 24 hours , what is the speed of the boat and the river ?
Options: a ) 4 , 3 , b ) 4 , 4 , c ) 3 , 3 , d ) 4 , 5 , e ) 4 , 2
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 6 ; us = 2 x = ( 6 + 2 ) / 2 = 8 / 2 = 4 km / hr y = ( 6 - 2 ) / 2 = 4 / 2 = 2 km / hr answer : e"
Answer: e
Problem: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 50 % full . if the original contents of the reservoir totaled 280 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 115 billion gallons , volume of water in the reservoir = 280 + 120 = 400 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 400 / 0.5 = 800 billion gallons therefore percentage of reservoir that was full before the storm = ( 280 / 800 ) * 100 = 35 % option c"
Answer: c
Problem: in a garden , there are 12 rows and 14 columns of mango trees . the distance between two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "each row contains 14 plants . leaving 2 corner plants , 12 plants in between have ( 12 x 2 ) metres & 1 metre on each side is left . length = ( 24 + 2 ) m = 26 m . answer : d"
Answer: d
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 86 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 86 thus m = 688 - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 688 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 16 ans : e"
Answer: e
Problem: a cycle is bought for rs . 800 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 20 , c ) 35 , d ) 88 , e ) 11
Rationale: "800 - - - - 180 100 - - - - ? = > 35 % answer : c"
Answer: c
Problem: a man invests some money partly in 12 % stock at 108 and partly in 10 % stock at 60 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 2 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 12 % stock at 108 , investment = rs . ( 108 / 12 ) = rs . 9 . for an income of rs . 1 in 10 % stock at 60 , investment = rs . ( 60 / 10 ) = rs . 6 . ∴ ratio of investments = 9 : 6 = 3 : 2 answer b"
Answer: b
Problem: a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train .
Options: a ) 150 , b ) 278 , c ) 100 , d ) 776 , e ) 191
Rationale: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : c"
Answer: c
Problem: laura took out a charge account at the general store and agreed to pay 8 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 37.8 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 8 % interest = ( 8 / 100 ) * 35 = 2.8 $ total amount that laura owes a year later = 35 + 2.8 = 37.8 $ answer d"
Answer: d
Problem: a man purchased 3 blankets @ rs . 100 each , 4 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 600 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: explanation : 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 a
Answer: a
Problem: rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 850 , b ) $ 840 , c ) $ 860 , d ) $ 870 , e ) $ 880
Rationale: "50 pages typed 1 x 40 pages typed 2 x ( original + one revision ) 10 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 40 ( 6 + 4 ) + 10 ( 6 + 4 + 4 ) = 300 + 400 + 140 = 840 answer - b"
Answer: b
Problem: a gambler has won 40 % of his 30 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.7 x = 0.6 ( x + 30 ) 0.1 x = 6 x = 60 the answer is e .
Answer: e
Problem: one night a certain hotel rented 4 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 60 % , b ) 70 % , c ) 80 % , d ) 90 % , e ) 100 %
Rationale: "the rooms which were not rented is 1 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 1 / 5 ) = 1 = 100 % the answer is e ."
Answer: e
Problem: a is 30 % more efficient than b . how much time they will working together take to complete a job which a alone could have done in 23 days ?
Options: a ) 25 days , b ) 13 days , c ) 14 days , d ) 20 days , e ) 15 days
Rationale: "the ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b can do work in x days then 10 : 13 : : 23 : x x = ( 23 * 13 ) / 10 x = 299 / 10 a ' s 1 day ' s work = 1 / 23 b ' s 1 day ' s work = 10 / 299 ( a + b ) ' s 1 day ' s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 a and b together can do work in 13 days answer ( b )"
Answer: b
Problem: this year , mbb consulting fired 6 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 100.0 % , c ) 102.8 % , d ) 103.4 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 6 % reduction in employees lead to 94 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 94 employees is 94 * 1100 = 103400 now the new salary is more than previous salary by x % . x = ( 103400 / 100000 ) * 100 = 103.4 % so the answer is d"
Answer: d
Problem: the average age of a group of 10 students is 20 years . if 2 more students join the group , the average age increases by 1 year . the average age of the new students is
Options: a ) 23 , b ) 21 , c ) 19.5 , d ) 20 , e ) 22.5
Rationale: "total age of 10 students = 10 * 20 = 200 and the total age of 16 students = 21 * 15 = 315 . let the average age of 2 new students be x . therefore total age of the new students = 2 x . so total age of 12 student = 200 + 5 x = 315 , x = 23 hence , the correct answer is a ."
Answer: a
Problem: in the set of positive integers from 1 to 100 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 405 , e ) 500
Rationale: "reduce 1 - 100 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 - - 95 are valid multiples . add them - - > 500 e"
Answer: e
Problem: find the cost of fencing around a circular field of diameter 12 m at the rate of rs . 3.50 a meter ?
Options: a ) 131.95 , b ) 132.9 , c ) 140.33 , d ) 123.4 , e ) 190.4
Rationale: "2 * 22 / 7 * 6 = 37.7 37.7 * 3 1 / 2 = rs . 131.95 answer : a"
Answer: a
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 28 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 01
Rationale: "explanation : as there is meal for 70 adults and 28 have their meal , the meal left can be catered to 42 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 42 adults = 54 children hence , the meal can be catered to 54 children . answer : b"
Answer: b
Problem: a side of beef lost 25 percent of its weight in processing . if the side of beef weighed 540 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 720 , d ) 840 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 75 / 100 ) * x = 540 = > x = ( 540 * 100 ) / 75 = 720 answer c"
Answer: c
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 5 / 243 , b ) 25 / 243 , c ) 64 / 243 , d ) 80 / 243 , e ) 16 / 17
Rationale: one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 2 ^ 3 / 3 ^ 5 we have 5 ! / 2 ! * 3 ! = 10 such cases so , 2 ^ 3 * 10 / 3 ^ 5 = 80 / 243 answer : d .
Answer: d
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 940 , what is the reduced price for kg ?
Options: a ) 72 , b ) 47 , c ) 40 , d ) 28 , e ) 20
Rationale: "940 * ( 30 / 100 ) = 282 - - - - 6 ? - - - - 1 = > rs . 47 answer : b"
Answer: b
Problem: the compound ratio of 5 : 6 , 3 : 2 and 6 : 5 ?
Options: a ) 1 : 1 , b ) 1 : 87 , c ) 1 : 6 , d ) 3 : 2 , e ) 1 : 2
Rationale: "5 / 6 * 3 / 2 * 6 / 5 = 3 / 2 3 : 2 answer : d"
Answer: d
Problem: a certain company reported that the revenue on sales increased 30 % 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 ) 39 %
Rationale: assume the revenue in 2000 to be 100 . then in 2003 it would be 130 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 130 ) / 130 = 50 / 130 = 39 % answer : e .
Answer: e
Problem: if a man lost 5 % by selling oranges at the rate of 8 a rupee at how many a rupee must he sell them to gain 52 % ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 4 , e ) 2
Rationale: "95 % - - - - 8 152 % - - - - ? 95 / 152 * 8 = 5 answer : a"
Answer: a
Problem: there are 32 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 1800 , b ) 1820 , c ) 1150 , d ) 1122 , e ) 1900
Rationale: the total number of stations = 34 from 34 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 34 p 2 ways . 34 p 2 = 34 * 33 = 1122 answer : d
Answer: d
Problem: a and b together can do a work in 4 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 6 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 4 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 4 ) - ( 1 / 12 ) = 6 days answer : option a"
Answer: a
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.9 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 72 , c ) 48 , d ) 96 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.9 = 3 km = 3000 m . required time = 3000 * 3 / 125 = 72 sec . answer : b"
Answer: b