regisss/math_qa huggingface dataset:
Problem: product of two co - prime numbers is 117 . their l . c . m should be
Options: a ) 222 , b ) 117 , c ) 278 , d ) 767 , e ) 298
Rationale: h . c . f of co - prime numbers is 1 . so , l . c . m = \ inline \ fn _ jvn \ frac { 117 } { 1 } = 117 answer : b
Answer: b
Problem: if to a certain number , 720 be added , and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462 . what is that number ?
Options: a ) 1280 , b ) 1270 , c ) 1260 , d ) 1250 , e ) none
Rationale: solution let x = the number required . a = 720 d = 7392 b = 125 h = 462 then by the conditions of the problem ( x + a ) / b = d / h therefore x = ( bd - ah ) / h restoring the numbers , x = [ ( 125.7392 ) - ( 720.462 ) ] / 462 = 1280 . answer a
Answer: a
Problem: 10 women can complete a work in 9 days and 10 children take 12 days to complete the work . how many days will 6 women and 7 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 2
Rationale: "1 women ' s 1 day work = 1 / 90 1 child ' s 1 day work = 1 / 120 ( 6 women + 7 children ) ' s 1 day work = ( 6 / 90 + 7 / 120 ) = 1 / 8 6 women and 7 children will complete the work in 8 days . d"
Answer: d
Problem: a cricket player whose bowling average was 22.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 121 , d ) 984 , e ) 108
Rationale: average = total runs / total wickets total runs after last match = 22.5 w + 52 total wickets after last match = w + 5 ( 22.5 w + 52 ) / ( w + 5 ) = 22.5 - 0.5 = 22 w = 116 so total wickets aftr last match = w + 5 = 121 answer : c
Answer: c
Problem: the radius of the wheel of a bus is 35 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 200 , b ) 250 , c ) 300 , d ) 500 , e ) none of these
Rationale: radius of the wheel of bus = 35 cm . then , circumference of wheel = 2 ï € r = 70 ï € = 220 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 220 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 220 = 500 answer d
Answer: d
Problem: a furniture manufacturer has two machines , but only one can be used at a time . machine e is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine e can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
Options: a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7
Rationale: machine e finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of e = 5 shifts / day rate of b = 4 shifts / day rate of ( e + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d
Answer: d
Problem: a train 110 m long is running with a speed of 84 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4.4 sec , e ) 2 sec
Rationale: "speed of train relative to man = 84 + 6 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . time taken to pass the men = 110 / 25 = 4.4 sec . answer : d"
Answer: d
Problem: a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 25 payments is to be $ 500 ; each of the remaining payments is to be $ 100 more than each of the first 25 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 500 , b ) 450 , c ) 552 , d ) 600 , e ) 400
Rationale: "total = 500 ( 25 ) + 600 ( 27 ) number of installments = 52 average = total / number of installments = 552 approximately answer : c"
Answer: c
Problem: there are 6 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 225 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 6 c 2 number of ways of selecting 2 non fiction books = 6 c 2 6 c 2 * 6 c 2 = 15 * 15 = 225 answer : c"
Answer: c
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 4 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 ) 48 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 4 books / month = 48 books a year total number of books = 48 cs"
Answer: c
Problem: in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 340 points , how many points is the third question worth ?
Options: a ) 39 , b ) 24 , c ) 28 , d ) 26 , e ) 30
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 340 10 x = 160 x = 16 3 rd question = x + 8 = 16 + 8 = 24 answer b"
Answer: b
Problem: how many natural numbers are there between 43 and 200 which are exactly divisible by 6 ?
Options: a ) 26 , b ) 25 , c ) 24 , d ) 22 , e ) 23
Rationale: "43 / 6 = 7 , remainder = 1 . hence 5 more should be added to 43 to get the minimum number divisible by 6 between 43 and 200 . = > minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48 200 / 6 = 33 , remainder = 2 . hence 2 should be decreased from 200 to get the maximum number divisible by 6 between 43 and 200 . = > maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198 hence , natural numbers numbers divisible by 6 between 43 and 200 are 48 , 54 , 60 , . . . 198 this is arithmetic progression with a = 48 , d = 6 , l = 198 number of terms = ( l − a ) / d + 1 = ( 198 − 48 ) / 6 + 1 = 150 / 6 + 1 = 25 + 1 = 26 answer is a"
Answer: a
Problem: right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q , and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1,100 , c ) 9,900 , d ) 10,000 , e ) 12,100
Rationale: "p can take a total of 10 * 11 co - ordinates . for a given p , r can take a total of 9 co - ordinates and q can take a total of 10 co - ordinates . hence , total = 110 * 9 * 10 = 9900 ans : c"
Answer: c
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 160 marks , the no of questions he attempts correctly is :
Options: a ) 35 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 160 = > 5 x = 220 = > x = 44 answer : e"
Answer: e
Problem: in the coordinate plane , points ( x , 1 ) and ( 18 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 18 , y ) = ( 18,9 ) - - > x + y = 2 + 9 = 11 . answer : d ."
Answer: d
Problem: find the simple interest on $ 1200 for 5 years at 20 % per annum ?
Options: a ) $ 1200 , b ) $ 1000 , c ) $ 500 , d ) $ 1100 , e ) $ 1500
Rationale: "si = ptr / 100 = 1200 * 5 * 20 / 100 = $ 1200 answer is a"
Answer: a
Problem: a batsman makes a score of 50 runs in the 17 th inning and thus increases his averages by 2 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 18 , c ) 42 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 50 then average run after 17 th inning = ( 16 x + 50 ) / 17 ( 16 x + 50 ) / 17 = x + 2 = > 16 x + 50 = 17 x + 34 = > x = 16 x = 16 ; average after 17 th inning = 16 + 2 = 18 answer : b"
Answer: b
Problem: to produce an annual income of rs . 800 from a 8 % stock at 90 , what is the amount of stock needed ?
Options: a ) 10000 , b ) 11000 , c ) 12000 , d ) 13000 , e ) 14000
Rationale: "since face value is not given , take it as rs . 100 . as it is an 8 % stock , income ( dividend ) per stock = rs . 8 ie , for an income of rs . 8 , amount of stock needed = rs . 100 for an income of rs . 800 , amount of stock needed = 100 × 800 / 8 = 10000 answer is a ."
Answer: a
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 7.5 ) , ( 8 , 0 ) , ( 0 , - 7.5 ) , ( - 8 , 0 ) ?
Options: a ) 56 , b ) 88 , c ) 112 , d ) 116 , e ) 120
Rationale: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 7.5 + 7.5 = 15 area = 1 / 2 * 16 * 15 = 120 e is the answer"
Answer: e
Problem: ramu bought an old car for rs . 40000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) a ) 14 % , b ) b ) 16 % , c ) c ) 18 % , d ) d ) 21.6 % , e ) of these
Rationale: "total cp = rs . 40000 + rs . 13000 = rs . 53000 and sp = rs . 64900 profit ( % ) = ( 64900 - 53000 ) / 55000 * 100 = 21.6 % answer : d"
Answer: d
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 44 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 277 , c ) 288.1 , d ) 296 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 44 cm . : 44 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 44 / ( 3.81 ) = 277 answer will be b ."
Answer: b
Problem: if 0.12 ÷ x 2 = 12 , than x = ?
Options: a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 1 , e ) 0
Rationale: explanation : 0.12 ÷ x 2 = 12 = > 0.12 / x 2 = 12 = > x 2 = 0.12 / 12 = 0.01 = > x = 0.1 answer : option c
Answer: c
Problem: a woman complete a journey in 30 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 672 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 30 - - > x / 21 + x / 24 = 60 - - > x = 672 km . e"
Answer: e
Problem: in a class of 35 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 35 - 29 = 6 play neither answer is a"
Answer: a
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 488 , c ) 882 , d ) 269 , e ) 298
Rationale: 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a
Answer: a
Problem: the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let x be subtracted . then , 6 - x 7 - x < 16 21 21 ( 6 - x ) < 16 ( 7 - x ) 5 x > 14 x > 2.8 least such whole number is 3 . answer : a
Answer: a
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "assume hours worked : 10 hours hourly wage : 10 $ weekly wage : 100 $ after decrease of 20 % in hourly wage would become 8 $ hours worked would have to be 12.5 hours in order to maintain weekly wage of 100 $ % increase in number of hours worked = ( 12.5 - 10 ) / 10 = 0.25 * 100 = 25 % answer is c"
Answer: c
Problem: a and b can do a piece of work in 8 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
Options: a ) 40 days , b ) 20 days , c ) 8 days , d ) 60 days , e ) 40 days
Rationale: "c 8 days c = 1 / 4 – 1 / 8 = 1 / 8 = > 8 days"
Answer: c
Problem: patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 60 pencils is how many times the selling price of 60 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.33 , e ) 1.75
Rationale: "say the cost price of 60 pencils was $ 60 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 60 - 60 p = 20 p - - > p = 3 / 4 . ( cost price ) / ( selling price ) = 1 / ( 3 / 4 ) = 4 / 3 = 1.33 . answer : d ."
Answer: d
Problem: the distance between two cities a and b is 600 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 am , b ) 07 am , c ) 01 pm , d ) 05 pm , e ) 03 pm
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 600 . therefore , 60 x + 75 ( x - 1 ) = 600 . = > x = 5 . so , they meet at ( 8 + 5 ) i . e , 1 p . m . answer : c )"
Answer: c
Problem: in a group of 800 people , 1 / 5 play at least one instrument , 128 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 25
Rationale: "p ( playing 2 or more instruments ) = 128 / 800 = 4 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 4 / 25 = 1 / 25 . answer e ."
Answer: e
Problem: the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is :
Options: a ) 36 , b ) 52 , c ) 66 , d ) 96 , e ) none
Rationale: "sol . t . d . = √ p . w . * b . g . = √ 576 * 16 = 96 . answer d"
Answer: d
Problem: car a runs at the speed of 52 km / hr & reaches its destination in 10 hr . car b runs at the speed of 46 km / h & reaches its destination in 8 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 62 : 25 , b ) 66 : 52 , c ) 68 : 15 , d ) 65 : 41 , e ) 23 : 59
Rationale: "sol . distance travelled by car a = 52 × 10 = 520 km distance travelled by car b = 46 × 8 = 368 km ratio = 520 / 368 = 65 : 41 d"
Answer: d
Problem: the distance from city a to city b is 60 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 60
Rationale: "the time it takes bob to drive to city b is 60 / 40 = 1.5 hours . alice needs to take less than 1 hour for the trip . alice needs to exceed a constant speed of 60 / 1 = 60 miles per hour . the answer is e ."
Answer: e
Problem: if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is ?
Options: a ) 28 , b ) 18 , c ) 24 , d ) 21 , e ) 16
Rationale: "explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x 140 x 30 x x = 100 x 18 x 42 or x = 18 answer : b"
Answer: b
Problem: a pharmaceutical company received $ 7 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 76 %
Rationale: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 7 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 7 / 20 ) x 60 = 21 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 9 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 21 ) / 21 ] x 100 - 1600 / 21 x 100 at this point we can stop and consider the answer choices . since we know that 1600 / 21 is just a bit less than ½ , we know that - 1600 / 21 x 100 is about a 76 % decrease . answer e ."
Answer: e
Problem: the sum of three consecutive even numbers is 93 . find the middle number of the three ?
Options: a ) 14 , b ) 35 , c ) 39 , d ) 31 , e ) 12
Rationale: "middle value = 93 / 3 = 31 ans d"
Answer: d
Problem: an error 6 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 12.36 , b ) 8.36 , c ) 9.36 , d ) 10.36 , e ) 11.36
Rationale: "explanation : 100 cm is read as 106 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 106 × 106 ) cm 2 = 11236 ( a 2 - a 1 ) = 11236 - 10000 = 1236 = > 1236 / 10000 * 100 = 12.36 answer : a"
Answer: a
Problem: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height . find the diameter of each sphere .
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "explanation : in this type of question , just equate the two volumes to get the answer as , volume of cylinder = π r 2 h volume of sphere = 43 π r 3 = > 12 ∗ 4 / 3 π r 3 = π r 2 h = > 12 ∗ 4 / 3 π r 3 = π ∗ 8 ∗ 8 ∗ 2 = > r 3 = 8 ∗ 8 ∗ 2 ∗ 3 / 12 ∗ 4 = > r 3 = 8 = > r = 2 cm = > diameter = 2 ∗ 2 = 4 cm option a"
Answer: a
Problem: what is the decimal equivalent of ( 1 / 9 ) ^ 2 ?
Options: a ) 0.0123 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 9 ) ² = ( 1 / 9 ) ( 1 / 9 ) = 1 / 81 approach # 1 : use long division to divide 81 into 1 to get 1 / 81 = 0.0123 a"
Answer: a
Problem: 7589 - ? = 3434
Options: a ) 4242 , b ) 4155 , c ) 1123 , d ) 11023 , e ) none of them
Rationale: "let 7589 - x = 3434 then x = 7589 - 3434 = 4155 answer is b"
Answer: b
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 30 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 8.3 , e ) 6.2
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 30 run rate needed = 250 / 30 = 8.3 answer : option d"
Answer: d
Problem: with a slope of 4 , with a straight line in the xy - plane which has a point with x - coordinate of the point 14 and y - coordinate 19 , find the y - intercept .
Options: a ) - 19 , b ) 18 , c ) - 37 , d ) 50 , e ) 37
Rationale: eq of line = y = mx + c m = 4 x = 14 y = 19 c = y - mx substitute given : c = 19 - ( 4 ) ( 14 ) c = - 37 correct option is c
Answer: c
Problem: elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 16
Rationale: "number of cups flour needed for 3 ounces of butter = 4 number of cups flour needed for 1 ounce of butter = 4 / 3 number of cups flour needed for 12 ounces of butter = 4 / 3 * 12 = 16 answer e"
Answer: e
Problem: excluding stoppages , the speed of a bus is 52 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 6 min , c ) 9 min , d ) 8 min , e ) 11 min
Rationale: "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( 7 / 52 ) x 60 = 8 min answer : d"
Answer: d
Problem: what is the smallest positive integer x , such that √ 392 x is an integer ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 14
Rationale: "for a perfect square , the powers of prime factors should be even . 392 can be broken up as 2 ^ 3 * 7 ^ 2 . you just need 2 to be multiplied to this number so that the number finally becomes 2 ^ 4 * 7 ^ 2 which is a perfect square . therefore x = 2 . answer : a"
Answer: a
Problem: the cost of an article is decreased by 10 % . if the original cost is $ 60 , find the decrease cost .
Options: a ) 33 , b ) 12 , c ) 68 , d ) 36 , e ) 54
Rationale: "original cost = $ 60 decrease in it = 10 % of $ 60 = 10 / 100 ã — 60 = 600 / 100 = $ 6 therefore , decrease cost = $ 60 - $ 6 = $ 54 answer : e"
Answer: e
Problem: if 4 people are selected from a group of 5 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 8 / 21
Rationale: "if we are to select 4 people from 5 couples without any restriction , how many ways can we make the selection ? 10 ! / 4 ! 6 ! = 210 if we are to select 4 people from 5 couples with restriction that no married couple can both make it to the group , only a representative ? 5 ! / 4 ! 1 ! = 5 but we know that to select a person from each couple , take 2 possibilities 5 * 2 * 2 * 2 * 2 = 80 probability = desired / all possibilities = 80 / 210 = 8 / 21 answer : e"
Answer: e
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 2.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 2889 , d ) 3600 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 2.5 = 3600 . answer : d"
Answer: d
Problem: the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 96 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c"
Answer: c
Problem: find the simple interest on $ 2500 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 750 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 2500 * 3 * 10 / 100 = $ 750 answer is c"
Answer: c
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 4.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 40 = 10 * 3 / 2 = 15 time difference = 4.1 ans : b"
Answer: b
Problem: p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 25 days
Rationale: "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 16 days = 16 ã — ( 1 / 40 ) = 2 / 5 remaining work = 1 â € “ 2 / 5 = 3 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 3 / 5 ) / ( 1 / 15 ) = 9 total days = 16 + 9 = 25 answer : option e"
Answer: e
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 360 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 700 , c ) 900 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c"
Answer: c
Problem: if the price of petrol increases by 25 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 25 ) i . e 125 . now , his consumption should be reduced to : - = 125 − 100125 ∗ 100 . hence , the consumption should be reduced to 20 % . answer : b"
Answer: b
Problem: an association of mathematics teachers has 1,260 members . only 640 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 30.47 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 640 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 640 = 384 percent of total membership that voted for winning candidate = ( 384 / 1260 ) * 100 = 30.47 % answer a"
Answer: a
Problem: there are 10 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 10 c 2 = 10 * 9 / 2 = 45 so option c is correct"
Answer: c
Problem: by selling 24 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 6 , e ) 4
Rationale: "80 % - - - 24 120 % - - - ? 80 / 120 * 24 = 16 answer : c"
Answer: c
Problem: ramesh purchased a refrigerator for rs . 13500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 2899 , d ) 18975 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 13,500 discount offered = 20 % marked price = 13500 * 100 / 80 = rs . 16875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 17250 * 110 / 100 = rs . 18975 answer : d"
Answer: d
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 15 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 15 = 6 hours answer c"
Answer: c
Problem: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 4 meters . what is value of the radius ?
Options: a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5
Rationale: "10 * 0.31 = 3.1 m ^ 3 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 4 ) which is about 1 / 4 r = 1 / 2 the answer is a ."
Answer: a
Problem: in a family 4 people eat only vegetarian , 3 people eat only non veg . , 2 people eat both veg and non veg . . how many people are in the family ?
Options: a ) 4 , b ) 3 , c ) 10 , d ) 2 , e ) 9
Rationale: "total number of people in family = veg + non veg + ( both veg and non veg ) total = 4 + 3 + 2 = 9 answer is e"
Answer: e
Problem: how many of the positive factors of 36 are not factors of 72
Options: a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 1
Rationale: "factors of 36 - 1 , 2,3 , 4,6 , 9,12 , 18,36 , factors of 72 - 1,2 , 3,4 , 6,8 , 9,12 , 18,24 , 36,72 , comparing both , we have no factors of 36 which are not factors of 72 - 0 answer ( a )"
Answer: a
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 1 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 1 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 31 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 2 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 31 c"
Answer: c
Problem: noelle walks from point a to point b at an average speed of 4 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 6 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 6 = 2 * 4 * x / 4 + x x = 12 d is the answer"
Answer: d
Problem: the sum of all two digit numbers divisible by 4 is
Options: a ) 1242 , b ) 1542 , c ) 1742 , d ) 1610 , e ) 1842
Rationale: "required numbers are 12 , 16,20 . . . . . 96 this is an a . p . in which a = 12 , d = 4 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 12 + ( n - 1 ) * 6 = 96 , 12 + 4 n - 4 = 96 4 + 4 n = 96 4 n = 96 - 4 n = 92 / 4 then n = 23 . required sum = n / 2 ( a + l ) = 23 / 2 ( 12 + 96 ) = 1242 answer is a"
Answer: a
Problem: the profits of qrs company rose 35 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 %
Rationale: assume 100 in march , then 135 in april as 35 % increase , then 108 in may as 20 % decrease from april , and then 162 in june which is 150 % of 108 . so overall increase is from 100 to 162 is 62 % answer d
Answer: d
Problem: find the area of a parallelogram with base 36 cm and height 24 cm ?
Options: a ) 760 , b ) 284 , c ) 288 , d ) 864 , e ) 820
Rationale: "area of a parallelogram = base * height = 36 * 24 = 864 cm 2 answer : d"
Answer: d
Problem: what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e"
Answer: e
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 26 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 32 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 52 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 32 hence , the correct answer is c"
Answer: c
Problem: a can do a work in 6 days . b can do the same work in 4 days . both a & b together will finish the work and they got $ 2000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,1200 , e ) 550,1450
Rationale: "ratio of their works a : b = 6 : 4 ratio of their wages a : b = 2 : 3 a ' s share = ( 2 / 5 ) 2000 = 800 b ' s share = ( 3 / 5 ) 2000 = 1200 correct option is d"
Answer: d
Problem: 3.00001 unbiased coins are tossed . what is the probability of getting 2 tails ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 2 tails then e = { tth , tht , htt } p ( e ) = n ( e ) / n ( s ) = 3 / 8 answer is c"
Answer: c
Problem: veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 35 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 110 , d ) 75 , e ) 93
Rationale: "total student = 182 failed = 35 paasd student = 182 - 35 = 160 from bottom her rank is = 147 - 73 + 1 = 75 answer : d"
Answer: d
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 20 ?
Options: a ) 30 , b ) 32 , c ) 34 , d ) 36 , e ) 38
Rationale: "$ 20 = 3 * $ 6 + $ 2 the number of doughnuts is 3 * 12 + 2 = 38 the answer is e ."
Answer: e
Problem: a bowl was half full of water . 4 cups of water were then added to the bowl , filling the bowl to 70 % of its capacity . how many cups of water are now in the bowl ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: lets say total volume of the container = v initial water content is half of total volume = v / 2 then 4 cups of water were added . current water content = ( v / 2 ) + 4 cups = ( 70 / 100 ) v = > v = 20 cups = > current water content is equivalent to = v / 2 + 4 cups = 20 / 2 + 4 = 14 cups ; answer : a
Answer: a
Problem: two numbers are in the ratio of 5 : 7 . if 25 be subtracted from each , they are in the ratio of 35 : 59 . find the numbers ?
Options: a ) 60,88 , b ) 60,86 , c ) 60,82 , d ) 60,84 , e ) 60,83
Rationale: "( 5 x - 25 ) : ( 7 x - 25 ) = 35 : 59 x = 12 = > 60,84 answer : d"
Answer: d
Problem: the number 189 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 20 , d ) 27 , e ) 39
Rationale: "4 ^ 3 + 5 ^ 3 = 189 the number is 4 * 5 = 20 c"
Answer: c
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 36000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "0.037 * 10 ^ 5 can be written as 3600 74000 * 10 ^ ( - 3 ) can be written as 36 required = 3600 / 36 = 100 answer : a"
Answer: a
Problem: in 120 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 24 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 120 / 45 x 9 m = 24 m . a beats b by 24 metres . answer : option a"
Answer: a
Problem: how many seconds will a 450 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 20 , b ) 27 , c ) 42 , d ) 32 , e ) 60
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 450 * 3 / 50 = 27 sec . answer : option b"
Answer: b
Problem: fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 40 %
Rationale: "x discount on pony jeans , ( 0.22 - x ) discount on fox jeans . set the equation : 3 * 10 ( 0.22 - x ) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ."
Answer: e
Problem: a taxi leaves point a 3 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 60 , b ) 72 , c ) 48 , d ) 36 , e ) 64
Rationale: let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 3 hrs . hence 6 * ( v - 30 ) = 3 v 6 v - 180 = 3 v 3 v = 180 v = 60 mph a
Answer: a
Problem: a single reservoir supplies the petrol to the whole city , while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume . when the reservoir is full and if 40,000 liters of petrol is used daily , the suply fails in 90 days . if 32,000 liters of petrol is used daily , it fails in 60 days . how much petrol can be used daily with out the supply ever failing ?
Options: a ) 64000 liters
b ) 56000 liters
c ) 78000 liters
d ) 60000 liters
e ) none of these
Rationale: explanation : let x liter be the per day filling and v litr be the capacity of the reservoir , then 90 x + v = 40000 × 90 - - - - - ( 1 ) 60 x + v = 32000 × 60 - - - - - - ( 2 ) solving eq . ( 1 ) and ( 2 ) , we get x = 56000 hence , 56000 liters per day can be used without the failure of supply . answer : b
Answer: b
Problem: a train 100 m long crosses a platform 250 m long in 7 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 180 kmph , e ) 59 kmph
Rationale: "d = 100 + 250 = 350 t = 7 s = 350 / 7 * 18 / 5 = 180 kmph answer : d"
Answer: d
Problem: what is the greatest positive integer x such that 6 ^ x is a factor of 216 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "216 ^ 10 = ( 6 ^ 3 ) ^ 10 = 6 ^ 30 answer : e"
Answer: e
Problem: the length of the bridge , which a train 100 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 10 m , b ) 16 m , c ) 275 m , d ) 19 m , e ) 27 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 100 + x ) / 30 = 25 / 2 = > 2 ( 100 + x ) = 750 = > x = 275 m . answer : c"
Answer: c
Problem: simple interest on a certain sum at a certain annual rate of interest is 1 / 4 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 4 % . , b ) 25 / 4 % . , c ) 5 % , d ) 6 % . , e ) 3 % .
Rationale: "explanation : let sum = x . then , s . i . = x / 4 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 4 ? r ^ 2 = 100 / 4 = 25 r = 5 hence , rate of interest = 5 % . answer : c"
Answer: c
Problem: ravish has to secure 40 % marks to clear his board exam of class 10 th . he got 40 marks and failed by 40 marks . what is the maximum marks ?
Options: a ) 150 , b ) 135 , c ) 160 , d ) 200 , e ) 155
Rationale: d 200 to pass the exam ravish needs 40 + 40 = 80 marks . = > ( 80 / 40 ) * 100 = 200
Answer: d
Problem: there are 172 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 83 , b ) 85 , c ) 87 , d ) 79 , e ) 89
Rationale: "editing my solution : number of switches = 172 number of switches turned on by a : 3 , 6 , . . . 171 = 57 number of switches turned on by b : 5 , 10 , . . . . 170 = 34 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 57 - 6 ) + ( 34 - 6 ) = 79 answer : d"
Answer: d
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 41 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 140 , b ) 175 , c ) 210 , d ) 245 , e ) 280
Rationale: "in 72 minutes , car x travels 42 miles . car y gains 6 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d ."
Answer: d
Problem: a man swims downstream 36 km and upstream 48 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 5 , b ) 24 , c ) 7 , d ) 42 , e ) 6
Rationale: "36 - - - 6 ds = 6 ? - - - - 1 48 - - - - 6 us = 8 ? - - - - 1 m = ? m = ( 6 + 8 ) / 2 = 7 answer : c"
Answer: c
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 17 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 27 / 100 , e ) 9 / 100
Rationale: c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 17 - 2 cmb = 100 b - cb - mb - 2 cmb = 27 hence the probability = 27 / 100 d
Answer: d
Problem: the original price of a suit is $ 150 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 130 , b ) $ 136 , c ) $ 144 , d ) $ 150 , e ) $ 160
Rationale: "0.8 * ( 1.2 * 150 ) = $ 144 the answer is c ."
Answer: c
Problem: convert 350 inches into centimeter ?
Options: a ) 812 cm , b ) 820 cm , c ) 850 cm , d ) 889 cm , e ) 854 cm
Rationale: "1 inch = 2.54 cm 350 inches = 100 * 2.54 = 889 cm answer is d"
Answer: d
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ?
Options: a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ) 22.5 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b"
Answer: b
Problem: a is twice as fast as b . if b alone can do a piece of work in 10 days , in what time can a and b together complete the work ?
Options: a ) 10 / 3 , b ) 8 , c ) 9 , d ) 7 / 3 , e ) 12
Rationale: "a can do the work in 10 / 2 i . e . , 5 days . a and b ' s one day ' s work = 1 / 5 + 1 / 10 = ( 2 + 1 ) / 10 = 10 / 3 so a and b together can do the work in 10 / 3 days . answer : 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 0.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 36 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.4 = 1.5 km = 1500 m . required time = 1500 * 3 / 125 = 36 sec . answer : b"
Answer: b
Problem: how much time does a train 225 metres long running at 90 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 9 s , e ) 7.4 s
Rationale: "explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 225 / t t = 9 s answer : d"
Answer: d
Problem: of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1000 , b ) 1200 , c ) 1400 , d ) 1600 , e ) 1800
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 3 ) x = 120 ( 6 / 60 ) x = 120 x = 1200 the answer is b ."
Answer: b
Problem: the price of lunch for 20 people was $ 300 including a 20 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12.5 , c ) 13.8 , d ) 14 , e ) 15.87
Rationale: "clearly b is the answer i used poe here lets consider option ( b ) 20 * 12.5 = 250 now 250 ( 120 / 100 ) = 300 = > possible answer imo b"
Answer: b
Problem: the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 28 - inch flat - screen television than a square 25 - inch flat - screen television ?
Options: a ) 79.5
b ) 89.3
c ) 85.5
d ) 75.4
e ) 72.5
Rationale: if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 28 - inch flat - screen television the diagonal ( hypotenuse ) = 28 so , we can apply the pythagorean theorem to get x ² + x ² = 28 ² simplify : 2 x ² = 28 ² divide both sides by 2 to get : x ² = 28 ² / 2 since the area of the square = x ² , we can see that the area of this square is 28 ² / 2 square 25 - inch flat - screen television the diagonal ( hypotenuse ) = 25 so , we can apply the pythagorean theorem to get x ² + x ² = 25 ² simplify : 2 x ² = 25 ² divide both sides by 2 to get : x ² = 25 ² / 2 since the area of the square = x ² , we can see that the area of this square is 25 ² / 2 difference in areas = 28 ² / 2 - 25 ² / 2 = ( 28 ² - 25 ² ) / 2 = ( 784 - 625 ) / 2 = 159 / 2 = 79.5 a
Answer: a
Problem: the sector of a circle has radius of 14 cm and central angle 144 o . find its perimeter ?
Options: a ) 60 cm , b ) 63.2 cm , c ) 70 cm , d ) 80 cm , e ) 90 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 144 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 35.2 + 28 = 63.2 cm answer : b"
Answer: b
Problem: a number is doubled and 4 is added . if the resultant is divided by 5 , it becomes 25 . what is that number ?
Options: a ) 73.5 , b ) 68 , c ) 60.5 , d ) none of these , e ) can not be determined
Rationale: "solution let the number be x . then , ( 2 x + 4 ) / 5 ‹ = › 25 ‹ = › 2 x + 4 = 125 ‹ = › 2 x = 121 x = 60.5 answer c"
Answer: c
Problem: chris mixed 4 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 4 lbs of raisin = $ 4 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 4 = 16 fraction of the value of raisin = 4 / 16 = 1 / 4 ans : c"
Answer: c
Problem: how many 3 digit numbers are divisible by 6 in all ?
Options: a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) 172
Rationale: "explanation : required numbers are 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then , a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 . answer is b"
Answer: b
Problem: 1907 x 1907 = ?
Options: a ) a ) 3623216 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3636649 , e ) e ) 3625216
Rationale: "1907 x 1907 = ( 1907 ) 2 = ( 1900 + 7 ) 2 = ( 1900 ) 2 + ( 7 ) 2 + ( 2 x 1900 x 7 ) = 3610000 + 49 + 26600 . = 3636649 . d )"
Answer: d
Problem: an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) 720 , b ) 360 , c ) 250 , d ) 280 , e ) 290
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 3120 = rs . 720 answer : a"
Answer: a