regisss/math_qa huggingface dataset:
Problem: find the average marks of all the students in 2 separate classes , if the average marks of students in the first class of 55 students is 60 and that of another class of 48 students is 58
Options: a ) 55.1 , b ) 51.1 , c ) 53.1 , d ) 52.1 , e ) 59.1
Rationale: sum of the marks for the class of 55 students = 55 * 60 = 3300 sum of the marks for the class of 48 students = 48 * 58 = 2784 sum of the marks for the class of 103 students = 3300 + 2784 = 6084 average marks of all the students = 6084 / 103 = 59.1 answer : e
Answer: e
Problem: a train is 100 meter long and is running at the speed of 30 km per hour . find the time it will take to pass a man standing at a crossing .
Options: a ) 10 seconds , b ) 12 seconds , c ) 14 seconds , d ) 16 seconds , e ) none of these
Rationale: explanation : as we need to get answer in seconds , so never forget to convert speed into meter per second . speed = 30 km / hr = 30 * 5 / 18 m / sec = 25 / 3 m / sec distance = length of train = 100 meter required time = distancespeed = 100253 = 100 ∗ 325 = 12 sec answer : b
Answer: b
Problem: on a game show , a contestant is given 3 keys , each of which opens exactly one of the 3 identical boxes . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . the first box contains $ 4 , the second $ 400 , and the third $ 4000 . what is the probability that a contestant will win more than $ 4000 ?
Options: a ) 2 / 6 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 3 , e ) 1 / 2
Rationale: let ' s call the boxes that contain $ 4 , $ 400 , and $ 4000 , respectively , box a , box b , box c . these are opened , respectively , by key a , key b , and key c . we want to know the probability of winning more than $ 4000 . notice that if the distribution of keys is : box a = key b box b = key a box c = key c then the contestant wins exactly $ 4000 , not more than $ 4000 . the only configuration that leads to winning more than $ 1000 is : box a = key a box b = key b box c = key c i . e . , getting all three keys correct . that ' s the only way to be more than $ 4000 . so , really , the question can be rephrased : what is the probability of guessing the order of keys so that each key matches the correct box ? well , for a set of three items , the number of possible permutations is 3 ! = 3 * 2 * 1 = 6 . of those 6 possible permutations , only one of them leads to all three keys being paired with the right box . so , the answer is probability = 1 / 6 answer : b
Answer: b
Problem: the edges of a cuboid are 4 cm , 5 cm and 6 cm . find the volume of the cuboid ?
Options: a ) 120 , b ) 278 , c ) 378 , d ) 368 , e ) 367
Rationale: "4 * 5 * 6 = 120 answer : a"
Answer: a
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 1701 what is the least possible value of k ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "1701 = 3 * 3 * 3 * 3 * 3 * 7 thus k must include numbers at least up to the number 12 so that there are at least five appearances of 3 ( that is : 3 , 6 , 9 = 3 * 3 , and 12 ) . the answer is c ."
Answer: c
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 12 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 22 , e ) 32
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 12 ) x solve for r , r = 44 44 - 12 = 32 mpg e"
Answer: e
Problem: the side of a rhombus is 25 m and length of one of its diagonals is 10 m . the area of the rhombus is ?
Options: a ) 244.85 , b ) 224.95 , c ) 244.85 , d ) 224.95 , e ) 244.95
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 25 ; p = 10 a = 1 / 2 * 10 * √ 4 ( 25 ) 2 - ( 10 ) 2 = 1 / 2 * 10 * √ 2500 - 100 = 1 / 2 * 10 * √ 2400 a = 244.95 answer : e"
Answer: e
Problem: two dogsled teams raced across a 300 - mile course in wyoming . team a finished the course in 3 fewer hours than did team b . if team a ’ s average speed was 5 miles per hour greater than that of team b , what was team b ’ s average speed , in miles per hour ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: speed of b = s speed of a = s + 5 time taken by b = 300 / s time taken by a = 300 / ( s + 5 ) difference in their time is 3 hrs . 300 / s - 3 = 300 / ( s + 5 ) plug in the values from the option no need of choosing 12 & 18 it wo n ' t satisfy a ) if we take 15 then t ( b ) = 300 / 15 = 20 t ( a ) = 300 / 20 = 15 . hence from this option difference comes out to be 5 which is not correct b ) if we take 20 then t ( b ) = 300 / 20 = 15 t ( a ) = 300 / 25 = 12 difference in timing is 3 hence option d is correct
Answer: d
Problem: a metallic sheet is of rectangular shape with dimensions 52 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5120 , c ) 6420 , d ) 7500 , e ) 5760
Rationale: "l = ( 52 - 16 ) m = 36 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 36 x 20 x 8 ) m 3 = 5760 m 3 . answer : option e"
Answer: e
Problem: a shopkeeper forced to sell at cost price , uses a 700 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 11.11 % , d ) 42.85 % , e ) none of these
Rationale: "shopkeeper sells 700 g instead of 1000 g . so , his gain = 1000 - 700 = 300 g . thus , % gain = ( 300 * 100 ) / 700 = 42.85 % . answer : option d"
Answer: d
Problem: a man can do a piece of work in 7 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 7 , c ) 15 / 2 , d ) 21 / 4 , e ) 18 / 5
Rationale: "son ' s 1 day ' s work = ( 1 / 3 ) - ( 1 / 7 ) = 4 / 21 the son alone can do the work in 21 / 4 days answer is d"
Answer: d
Problem: what is log 3 ( 4 ) log 4 ( 5 ) . . . log 80 ( 81 ) ?
Options: a ) 1 , b ) 4 , c ) 81 , d ) log 80 243 , e ) e 81
Rationale: recall the change of base formula logb ( a ) = ln ( a ) ln ( b ) : ( alternatively , we can substitute logc for ln on the right , as long as the base is the same on the top and on the bottom . ) using this , we can rewrite the entire expression using natural logarithms , as ln ( 4 ) ln ( 3 ) ln ( 5 ) ln ( 4 ) ln ( 81 ) ln ( 80 ) = ln ( 81 ) ln ( 3 ) = log 3 ( 81 ) = log 3 ( 34 ) = 4 : correct answer b
Answer: b
Problem: 0.0005521 / 0.0000110 x 15.05 = ?
Options: a ) 7534 , b ) 255.4 , c ) 756.4 , d ) 755.4 , e ) 752.4
Rationale: "explanation : ? = 0.0005521 / 0.0000110 x 15.05 = 755.4 answer : option d"
Answer: d
Problem: the average of 6 observations is 16 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 9 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 96 + x ) / 7 = 15 = > x = 9 hence , the seventh observation is 9 . answer : c"
Answer: c
Problem: the total age of a and b is 16 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 16 , b ) 24 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 16 â € ¹ = â € º a - c = 16 . answer a"
Answer: a
Problem: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 25 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 23 % , b ) 28 % , c ) 33 % , d ) 38 % , e ) 43 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.25 ( 5 b + x ) = b + x 0.25 b = 0.75 x x = 0.33 b the answer is c ."
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 186 m , b ) 176 m , c ) 100 m , d ) 600 m , e ) 765 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 36 ) m = 600 m . answer : d"
Answer: d
Problem: the product of three consecutive numbers is 504 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 504 504 = 7 * 8 * 9 . so , the three numbers are 7 , 8 and 9 . and sum of smallest of these two = 7 + 8 = 15 . answer : option b"
Answer: b
Problem: if 3 ^ 20 x 2 ^ 20 = 6 ^ n what is the value of n ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "3 ^ 20 * 2 ^ 20 = 6 ^ n 6 ^ 20 = 6 ^ n therefore n = 20 b"
Answer: b
Problem: 20 men can do a work in 40 days . when should 20 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 0 days , b ) 10 days , c ) 20 days , d ) 30 days , e ) 40 days
Rationale: "total work to be done = 20 * 40 = 800 let 20 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 20 * 40 ) = 800 40 p = 0 = > p = 0 days answer : a"
Answer: a
Problem: mary and harry enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 800 more than harry did , what was the profit made by their business in that year ?
Options: a ) 45645433 , b ) 46457457 , c ) 4675 , d ) 3000 , e ) 3432
Rationale: say the profit was $ x . mary ' s share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 harry share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is d
Answer: d
Problem: a thief goes away with a santro car at a speed of 45 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 2 , b ) b ) 4 , c ) c ) 7 , d ) d ) 5 , e ) e ) 8
Rationale: explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 50 45 d = 20 rs = 50 – 45 = 5 t = 20 / 5 = 4 hours answer : option b
Answer: b
Problem: what is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?
Options: a ) 814 , b ) 800 , c ) 100 , d ) 200 , e ) 456
Rationale: "length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = ( 41 x 41 ) cm 2 . required number of tiles = ( 1517 x 902 ) / 41 x 41 = 814 . answer : a"
Answer: a
Problem: the average of runs of a cricket player of 10 innings was 40 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 10 , d ) 84 , e ) 17
Rationale: "average after 11 innings = 44 required number of runs = ( 44 * 11 ) - ( 40 * 10 ) = 484 - 400 = 84 . answer : d"
Answer: d
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 18 as remainder
Options: a ) 1235 , b ) 1346 , c ) 1378 , d ) 1634.4 , e ) 1489
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 18 5 x = 1347 x = 269.4 number = 269.4 + 1365 = 1634.4 d"
Answer: d
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 588 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 588 3 b 2 = 588 b 2 = 196 b = 14 m . answer : option e"
Answer: e
Problem: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 20 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 ) $ 30 , b ) $ 31 , c ) $ 32 , d ) $ 33 , e ) $ 34
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 ( 20 ) = 0.8 x x = 1.2 ( 20 ) / 0.8 = 1.5 ( 20 ) = $ 30 the answer is a ."
Answer: a
Problem: 21 friends went to a hotel and decided to pay the bill amount equally . but 20 of them could pay rs . 30 each as a result 21 st has to pay rs . 200 extra than his share . find the amount paid by him .
Options: a ) 120 , b ) 250 , c ) 110 , d ) 220 , e ) none
Rationale: "explanation : average amount paid by 20 persons = rs . 30 increase in average due to rs . 200 paid extra by the 21 st men = rs . 200 / 20 = rs . 10 therefore , average expenditure of 21 friends = rs . 30 + rs . 10 = rs . 40 therefore , amount paid by the 21 st men = rs . 40 + rs . 200 = rs . 240 correct option : e"
Answer: e
Problem: a train 125 m long passes a man , running at 3 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 48 , b ) 50 , c ) 28 , d ) 26 , e ) 29
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 3 ) km / hr . x - 3 = 45 = = > x = 48 km / hr answer : a"
Answer: a
Problem: if 10 lions can kill 10 deers in 10 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 10 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 10 ( lions ) * 10 ( min ) / 10 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 10 answer : b"
Answer: b
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 3 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 36 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 3 books / month = 36 books a year total number of books = 36 cs"
Answer: c
Problem: a can give b 100 meters start and c 300 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 110.22 meters , b ) 111.22 meters , c ) 222.22 meters , d ) 333.22 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 900 meters and c runs 700 meters . therefore , b runs 900 meters while c runs 700 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 700 ) / 900 = 777.77 meters thus , b can give c ( 1000 - 777.77 ) = 222.22 meters start answer : c"
Answer: c
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 740 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 350 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 × 1.2 z , x + y + z = 740 ( 1.25 × 1.2 + 1.2 + 1 ) z = 74 3.7 z = 740 , z = 200 answer : . b ."
Answer: b
Problem: a man buys an item at rs . 750 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 660 , b ) rs . 760 , c ) rs . 600 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 750 = 80 / 100 * 750 = 600 option c"
Answer: c
Problem: harry started a 4 - mile hike with a full 10 - cup canteen of water and finished the hike in 2 hours with 2 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 3 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 3 / 3 , d ) 3 / 1 , e ) 3 / 2
Rationale: "no of cups leaked during the trip = 2 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 3 miles = 3 . drink / mile = 3 / 3 answer : c"
Answer: c
Problem: salesperson a ' s compensation for any week is $ 260 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 6000 , b ) $ 8000 , c ) $ 10,000 , d ) $ 12,000 , e ) $ 14,000
Rationale: "260 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 200 x = $ 10,000 the answer is c ."
Answer: c
Problem: a , b and c start a business each investing 2,000 . after 6 months a withdrew 1000 , b withdrew 1000 and c invests 1000 more . at the end of the year , a total profit of 6600 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 1,800 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 2000 ã — 6 + 1000 ã — 6 : 2000 ã — 6 + 1000 ã — 6 : 2000 ã — 6 + 3000 ã — 6 = 18000 : 18000 : 30000 = 18 : 18 : 30 b â € ™ s share = ( 6600 ã — 18 â  „ 66 ) = 1800 answer c"
Answer: c
Problem: in the third grade of windblown school there are 96 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 96 failed in math = 96 / 3 = 32 failed in literature = 108 / 6 = 16 the least failed in both can be 0 while max can be 16 answer a"
Answer: a
Problem: rajat , vikas and abhishek are submitting questions in the ratio 7 : 3 : 2 . if total number of questions submitted by them is 24 . find the number of questions submitted by vikas .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : number of questions submitted by vikas = ( 24 * 3 ) / ( 7 + 3 + 2 ) = 6 answer : d
Answer: d
Problem: a number divided by 64 leaves remainder 37 what is the remainder when same number divided by 5
Options: a ) 7 , b ) 8 , c ) 6 , d ) 3 , e ) 1
Rationale: add 64 + 37 = 101 now 101 divided by 5 so we get 1 as reaminder answer : e
Answer: e
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 80 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 80 * ( 100 % + 20 % ) = $ 96 number of articles to be sold for $ 96 to incur a 20 % loss : $ 96 / $ 2.40 = 40 thus , solution c is correct ."
Answer: c
Problem: divide rs . 1100 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 400 , c ) s . 600 , d ) s . 900 , e ) s . 1100
Rationale: "a + b + c = 1100 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1100 = > 275 answer : e"
Answer: e
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 9 managers , if 2 managers will not attend the meeting together ?
Options: a ) 35 , b ) 91 , c ) 120 , d ) 126 , e ) 150
Rationale: "we can either choose all 5 people from 7 manager who have no problems or choose 4 from the 7 and 1 from the 2 managers who have a problem sitting together so 7 c 5 + ( 7 c 4 * 2 c 1 ) this is 21 + 70 91 ans : b"
Answer: b
Problem: a number when divided by 296 leaves 75 as remainder . when the same number is divided by 37 , the remainder will be :
Options: a ) 1 , b ) 5 , c ) 3 , d ) 4 , e ) 11
Rationale: "let x = 296 q + 75 = ( 37 x 8 q + 37 x 2 ) + 1 = 37 ( 8 q + 2 ) + 1 thus , when the number is divided by 37 , the remainder is 1 . answer a"
Answer: a
Problem: a certain car increased its average speed by 5 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 2 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: "in the third time interval the average speed of the car was 2 + 5 + 5 = 12 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 12 * 1 / 12 = 1 miles . answer : a ."
Answer: a
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 60 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 12 sec , d ) 67 sec , e ) 13 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 60 * 100 / 18 = 1000 / 3 rs = 60 + 40 = 100 * 5 / 18 t = 1000 / 3 * 18 / 500 = 12 sec answer : c"
Answer: c
Problem: what will be the vulgar fraction of 0.60
Options: a ) 3 / 7 , b ) 3 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.6 = 60 / 100 = 3 / 5 option b"
Answer: b
Problem: how many 3 digit positive integers w exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Problem: find the missing figures : 0.2 % of ? = 0.02
Options: a ) 50 , b ) 100 , c ) 10 , d ) 1000 , e ) 110
Rationale: "let 0.2 % of x = 0.02 . then , 0.2 * x / 100 = 0.02 x = [ ( 0.02 * 100 ) / 0.2 ] = 100 . answer is b ."
Answer: b
Problem: find the value of 18396 x 9999 = m ?
Options: a ) 194852714 , b ) 183941604 , c ) 183851704 , d ) 183951714 , e ) 183768244
Rationale: "18396 x 9999 = 18396 x ( 10000 - 1 ) = 18396 x 10000 - 18396 x 1 = 183960000 - 18396 = 183941604 b"
Answer: b
Problem: the sum of the squares of three numbers is 100 , while the sum of their products taken two at a time is 48 . their sum is :
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 100 xy + yz + zx = 48 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 100 + ( 2 * 48 ) ( x + y + z ) ^ 2 = 196 so x + y + z = 14 answer : e"
Answer: e
Problem: if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 then find , 13 * 15 * 17 = ?
Options: a ) 89 , b ) 49 , c ) 68 , d ) 268 , e ) 55
Rationale: d 268 ( 17 * 15 ) + 13 = 268
Answer: d
Problem: if 20 men can build a wall 66 metres long in 6 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 53 m , b ) 46 m , c ) 94 m , d ) 49 m , e ) 64 m
Rationale: "let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 6 : 3 : : 56 : x therefore ( 20 x 6 x x ) = ( 35 x 3 x 56 )  x = ( 35 x 3 x 56 ) / 120 = 49 hence , the required length is 49 m . answer is d"
Answer: d
Problem: the calendar of the year 2024 can be used again in the year ?
Options: a ) 2288 , b ) 2052 , c ) 2778 , d ) 2719 , e ) 1711
Rationale: "explanation : given year 2024 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2024 + 28 = 2052 answer : b ) 2052"
Answer: b
Problem: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 6 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 6 = 30 km imo , correct answer is ` ` b . ' '
Answer: b
Problem: a sixth grade teacher asked her students to draw rectangles with positive integer length and a perimeter of 42 . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with is ?
Options: a ) 50 sq units
b ) 60 sq units
c ) 70 sq units
d ) 80 sq units
e ) 90 sq units
Rationale: sum of length and breadth will be 21 units . 42 / 2 = 21 area will be max when lxb = 11 x 10 = 110 sq units area will be min when lxb = 20 x 1 = 20 sq units . . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with = 110 - 20 = 90 sq units answer : e
Answer: e
Problem: 3 partners a , b , c starts a business . twice a ' s capital is equal to thrice b ' s capital and b ' s capital is 4 times c ' s capital . out of a total profit of rs . 16500 at the end of the year , b ' s share is
Options: a ) rs . 4000 , b ) rs . 6000 , c ) rs . 7500 , d ) rs . 6600 , e ) none
Rationale: solution let c = x . then , b = 4 x and 2 a = 3 x 4 x = 12 x or a = 6 x . ∴ a : b : c = 6 x : 4 x : x = 6 : 4 : 1 . so b ' s capital = rs ( 16500 x 4 / 11 ) = rs . 6000 . answer b
Answer: b
Problem: a retailer sells 6 shirts . the first 2 he sells for $ 40 and $ 50 . if the retailer wishes to sell the 6 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 4 shirts ?
Options: a ) $ 37.00 , b ) $ 40.00 , c ) $ 45.50 , d ) $ 48.00 , e ) $ 52.50
Rationale: "first 2 shirts are sold for $ 40 and $ 50 = $ 90 . to get average price of $ 50 , total sale should be 6 * $ 50 = $ 300 so remaining 4 shirts to be sold for $ 300 - $ 90 = $ 210 answer should be 210 / 4 = $ 52.50 that is e"
Answer: e
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8800 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 3300 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8800 = 35200 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3200 salary of may is rs . 6500 salary of january = rs . 3300 answer : a"
Answer: a
Problem: with both inlets open , a water tank will be filled with water in 20 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 1,500 , c ) 1,750 , d ) 1,200 , e ) 1,300
Rationale: "the work done by inlet a and b together in 1 min = 1 / 20 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 20 ) - ( 1 / 120 ) = 1 / 24 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 24 ) - ( 1 / 120 ) = 50 cubic meter i . e . 1500 cubic meter answer : option b"
Answer: b
Problem: the ratio between the radii of two spheres is 1 : 3 . find the ratio between their volumes ?
Options: a ) 1 : 28
b ) 1 : 27
c ) 1 : 29
d ) 1 : 39
e ) 1 : 22
Rationale: explanation : r 1 : r 2 = 1 : 3 r 13 : r 23 = 1 : 27 answer : option b
Answer: b
Problem: every year taylor goes to the same carnival , and he attempts to shoot a basketball into a small hoop , hoping that he will win a 10 - foot tall teddy bear . if the probability that taylor does not make a basket is 1 / 3 , what is the probability that taylor makes exactly one basket in 3 tries ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 7
Rationale: probability of basket = 2 / 3 probability of no basket = 1 / 3 required probability = 3 * 2 / 3 * 1 / 3 * 1 / 3 = 2 / 9 b is the answer .
Answer: b
Problem: the average of 13 result is 20 . average of the first 8 of them is 20 and that of the last 8 is 40 . find the 8 th result ?
Options: a ) 35 , b ) 37 , c ) 46 , d ) 90 , e ) 100
Rationale: "sum of all the 13 results = 13 * 20 = 260 sum of the first 7 of them = 8 * 20 = 160 sum of the last 7 of them = 8 * 40 = 320 so , the 8 th number = 260 + 160 - 320 = 100 . e"
Answer: e
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 4 boys and 12 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 4 boys + 12 girls = 4 ã — 6 / 4 + 12 = 6 + 12 = 18 girls 8 days to complete the work answer : option d
Answer: d
Problem: the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 40 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 50 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 40 kg . as the price falls by 20 % , new price for 40 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 40 = rs . 2 per kg . rice can bought now at = 100 / 2 = 50 kg . answer : option d"
Answer: d
Problem: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money j did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ j = 20 answer : b
Answer: b
Problem: a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 1 / 20,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: total number of ways of choosing one student from each group is = 800 * 1000 number of cases in which a sibling pair will be got is = 40 thus the probability that the 2 students selected will be a sibling pair is = 40 / ( 800 * 1000 ) = 1 / 20,000 c
Answer: c
Problem: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 5 w widgets ?
Options: a ) 4 , b ) 30 , c ) 8 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 5 * 6 = 30 days to produce 2 w widgets . answer : b"
Answer: b
Problem: find value for x from below equation ? x + 1 = 2
Options: a ) - 5 , b ) 1 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 2 - 1 2 . simplify both sides : x = 1 b"
Answer: b
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 170 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 250 , d ) 500 , e ) 821
Rationale: "p - 170 = ( p * 4 * 8 ) / 100 p = 250 answer : c"
Answer: c
Problem: little john had $ 10.50 . he spent $ 2.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?
Options: a ) $ 1.85 , b ) $ 3.85 , c ) $ 4.85 , d ) $ 6.85 , e ) $ 5.85
Rationale: "john spent and gave to his two friends a total of 2.25 + 2.20 + 2.20 = $ 6.65 money left 10.50 - 6.65 = $ 3.85 correct answer is b ) $ 3.85"
Answer: b
Problem: a and b can do a piece of work in 12 days and 16 days respectively . both work for 3 days and then a goes away . find how long will b take to complete the remaining work ?
Options: a ) 6 days , b ) 12 days , c ) 15 days , d ) 9 days , e ) 8 days
Rationale: "3 / 12 + ( 3 + x ) / 16 = 1 x = 9 days answer : d"
Answer: d
Problem: what is the square root of 225 ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 45 , e ) 15
Rationale: "15 x 15 = 225 answer e"
Answer: e
Problem: a motorcycle importer is planning on increasing the price of a certain model by $ 1000 . at this new price 8 fewer motorcycles will be sold per month , but the total revenues will increase by $ 26000 to $ 594000 . what is the number of motorcycles the manufacturer will sell at this new price ?
Options: a ) 61 , b ) 62 , c ) 65 , d ) 63 , e ) 64
Rationale: responding to a pm : to solve this question , i will make an equation in x and then make educated guesses . here ' s how : assuming x motorcycles were sold every month initially . ( 568000 / x + 1000 ) ( x - 8 ) = 594000 ( 568 / x + 1 ) ( x - 8 ) = 594 now 568 = 8 * 71 assuming x = 71 ( we have all integers so it is obvious that 568 / x should be an integer . we get 9 * 66 = 594 ( matches ) so he will sell 71 - 8 = 63 bikes this month answer ( d )
Answer: d
Problem: 1 / 0.02 is equal to
Options: a ) 50 , b ) 2.5 , c ) 25 , d ) . 25 , e ) none of these
Rationale: explanation : 1 / 0.02 = ( 1 * 100 ) / 2 = 100 / 2 = 50 option a
Answer: a
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 14
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 10000 x 7 ) + 6000 ( x - 7 ) x = 14 . answer e"
Answer: e
Problem: what is the remainder when 3 ^ 29 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 29 has the form 4 k + 1 , so the units digit of 3 ^ 29 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Problem: obra drove 200 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 41.66 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 200 π / 480 π = 41.66 % hence , answer is c ."
Answer: c
Problem: if the price of a certain computer increased 20 percent from d dollars to 351 dollars , then 2 d =
Options: a ) 540 , b ) 585 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = d after 30 % price increase price = d + ( 20 / 100 ) * d = 1.2 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 292,5 i . e . 2 d = 2 * 292.5 = 585 answer : option b"
Answer: b
Problem: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 20 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 7.5 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 20 = 2 / 15 hence , tank will be filled in 15 / 2 = 7.5 hour option ( a )"
Answer: a
Problem: what must be added to each term of the ratio 2 : 3 , so that it may become equal to 4 : 5 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 9 , e ) 8
Rationale: let the number to be added be x , then ( 2 + x ) : ( 3 + x ) = 4 : 5 ⇒ ( 2 + x ) / ( 5 + x ) = 4 / 5 5 ( 2 + x ) = 4 ( 3 + x ) 10 + 5 x = 12 + 4 x 5 x - 4 x = 12 - 10 x = 2 answer : 2
Answer: a
Problem: obra drove 180 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 37.5 % , b ) 12.5 % , c ) 18.75 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 180 π / 480 π = 37.5 % hence , answer is a ."
Answer: a
Problem: the average of 8 numbers is 21 . if each of the number is multiplied by 8 , the average of the new set of numbers is :
Options: a ) 168 , b ) 667 , c ) 288 , d ) 1991 , e ) 111
Rationale: "average of new numbers = ( 21 × 8 ) = 168 answer : a"
Answer: a
Problem: if 14 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 56 days
Rationale: "14 * 80 = 20 * x x = 56 days answer : e"
Answer: e
Problem: in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.855 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 4 : 5
Rationale: "using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.855 0.9 – 0.1 x = 0.855 x = 0.45 thus ratio of both flours is 4 : 5 e"
Answer: e
Problem: two terms are in 3 : 4 , if 10 is added to each of the terms , they will be 4 : 5 . find second term ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 40 , e ) 35
Rationale: solution : let the two numbers be 3 x and 4 x . then , ( 3 x + 10 ) / ( 4 x + 10 ) = 4 / 5 . = > 15 x + 50 = 16 x + 40 = > x = 10 . . ' . second term = 4 * 10 = 40 . answer is d
Answer: d
Problem: a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 18 kilometer long bridge , at the same speed ?
Options: a ) 14 min , b ) 20 min , c ) 18 min , d ) 19 min , e ) 13 min
Rationale: "s = 600 / 40 = 15 mps s = 18000 / 15 = 1200 sec = 20 min . answer : b"
Answer: b
Problem: two pipes a and b can fill a tank in 18 hours and 24 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 15 hours , c ) 10 hours , d ) 10 2 / 7 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 18 part filled by b in 1 hour = 1 / 24 part filled by ( a + b ) in 1 hour = 1 / 18 + 1 / 24 = 7 / 72 both the pipes together fill the tank in 72 / 7 = 10 2 / 7 hours answer is d"
Answer: d
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle
Options: a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 28 cm
Rationale: "explanation : let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x ^ 2 sq . cm . new length = ( 2 x − 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x − 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 5 ) ( x + 5 ) = 2 x ^ 2 + 75 ⇒ 2 x ^ 2 + 10 x − 5 x − 25 = 2 x ^ 2 + 75 ⇒ 5 x − 25 = 75 ⇒ 5 x = 75 + 25 = 100 ⇒ x = 1005 = 20 cm length = 2 x = 2 × 20 = 40 cm answer : option c"
Answer: c
Problem: the list price of an article is rs . 70 . a customer pays rs . 59.85 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 6 % , e ) 5 %
Rationale: "option e explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 59.85 x = 5 %"
Answer: e
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 = 6 * 0 + 2 * 7.2 + 8 - 9.8 = 0 + 14.4 - 1.8 12.6 answer a"
Answer: a
Problem: two persons start running simultaneously around a circular track of length 250 m from the same point at speeds of 20 kmph and 40 kmph . when will they meet for the first time any where on the track if they are moving in the opposite direction ?
Options: a ) 144 , b ) 15 , c ) 18 , d ) 32 , e ) 38
Rationale: time taken to meet the first time = length of track / relative speed = 250 / ( 20 + 40 ) ( 5 / 18 ) = 250 / 60 * ( 18 / 5 ) = 15 sec . answer : b
Answer: b
Problem: sixteen percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 63 % , e ) 75 %
Rationale: initially 84 % and 16 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 84 so , the required % is [ ( 3 / 4 ) ∗ 84 / 100 ] ∗ 100 = 63 % answer : d
Answer: d
Problem: if a square mirror has a 20 - inch diagonal , what is the approximate perimeter q of the mirror , in inches ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter q must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"
Answer: b
Problem: pipes a and b can fill a tank in 3 and 4 hours . pipe c can empty it in 4 hours . if all pipes are opened together , then the tank will be filled in ?
Options: a ) 3 hr , b ) 1 / 2 hr , c ) 1 hr , d ) 9 / 7 hr , e ) 5 / 3 hr
Rationale: "net part filled in 1 hour = 1 / 3 + 1 / 4 - 1 / 4 = 1 / 3 the tank will be full in 3 hr answer is a"
Answer: a
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 5 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 20 : 9 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 5 - - > e : l = 3 : 5 = 12 : 20 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 12 : 9 . thus , l : s = 20 : 9 . answer : d ."
Answer: d
Problem: in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students r in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Problem: if 10 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 11.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "a for me 9 people with 1 $ each - > maximum = 11"
Answer: a
Problem: the average salary of workers in an industry is rs . 200 the average salary of technicians being rs . 400 and that of non - technicians being rs . 125 . what is the total number of workers ?
Options: a ) 277 , b ) 665 , c ) 662 , d ) 552 , e ) 281
Rationale: "8 * 84 = 672 – 7 = 665 answer : b"
Answer: b
Problem: two trains of equal lengths take 10 sec and 8 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 12 , c ) 9 , d ) 99 , e ) 21
Rationale: speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 8 = 15 m / sec . relative speed = 12 + 15 = 27 m / sec . required time = ( 120 + 120 ) / 27 = 9 sec . answer : c
Answer: c