regisss/math_qa huggingface dataset:
Problem: the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 65 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 48 , b ) 50 , c ) 54 , d ) 66 , e ) 86
Rationale: "the total sum of the numbers should be increased by 40 . then the average will increase by 40 / 10 = 4 . the correct average is 50 . the answer is b ."
Answer: b
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 w should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked w will be 25 % greater than the original number . the answer is c ."
Answer: c
Problem: john spends $ 320 buying his favorite dolls . if he buys only small monkey dolls , which are $ 4 cheaper than the large monkey dolls , he could buy 40 more dolls than if he were to buy only large monkey dolls . how much does a large monkey doll cost ?
Options: a ) $ 7.2 , b ) $ 7.5 , c ) $ 8 , d ) $ 9 , e ) $ 10
Rationale: a and b is not an integer . so we start with c if large doll costs $ 8 , then he can buy 320 / 8 = 40 large dolls and 320 / 4 = 80 small dolls . difference is 40 , which is we wanted . answer c .
Answer: c
Problem: the number 110 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ?
Options: a ) 10 , b ) 12 , c ) 18 , d ) 14 , e ) 17
Rationale: "sum of the squares of 3 different positive integers = 110 5 ^ 2 + 6 ^ 2 + 7 ^ 2 = 110 now , sum of these 3 different integers = 5 + 6 + 7 = 18 ans - c"
Answer: c
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 12 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 26 km / hr , b ) 40 km / hr , c ) 60 km / hr , d ) 77 km / hr , e ) 46 km / hr
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 12 = 3 x = > x = 50 / 9 . so , speed of the faster train = 100 / 9 = 100 / 9 * 18 / 5 = 40 km / hr . answer : b"
Answer: b
Problem: a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 200 , b ) s . 100 , c ) s . 300 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 1000 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 600 and 400 . difference in profit share = 600 - 400 = 200 answer : a"
Answer: a
Problem: there is a total of 120 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 3 . what is the probability that the marble will be either red or blue ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 2 / 7 , d ) 1 / 3 , e ) 5 / 12
Rationale: "total marbles in the box = 120 white marbles = 120 / 4 = 30 green marbles = 120 / 3 = 40 w + g = 70 red + blue = 50 p ( red or blue ) = 50 / 120 = 5 / 12 answer : e"
Answer: e
Problem: three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in ?
Options: a ) 08 hours , b ) 12 hours , c ) 03 hours , d ) 04 hours , e ) 21 hours
Rationale: "the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b"
Answer: b
Problem: if a 2 + b 2 + c 2 = 941 and ab + bc + ca = 10 , then a + b + c is
Options: a ) 44 , b ) 56 , c ) 16 , d ) 32 , e ) 31
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 941 and ab + bc + ca = 10 , ( a + b + c ) ^ 2 = 941 + 2 ( 10 ) = 961 = 31 ^ 2 therefore : a + b + c = 31 answer : e"
Answer: e
Problem: what is the tens digit of 6 ^ 18 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 18 has the form 5 n + 3 , so the tens digit of 6 ^ 18 is 1 . the answer is a ."
Answer: a
Problem: if dev works alone he will take 20 more hours to complete a task than if he worked with tina to complete the task . if tina works alone , she will take 5 more hours to complete the complete the task , then if she worked with dev to complete the task ? what is the ratio of the time taken by dev to that taken by tina if each of them worked alone to complete the task ?
Options: a ) 4 : 1 , b ) 2 : 1 , c ) 10 : 1 , d ) 3 : 1 , e ) 1 : 2
Rationale: let time taken by dev to complete the work alone be x days and that by tina be y days work done by dev in 1 day = 1 / x work done by tina in 1 day = 1 / y work done by devtina in 1 day = 1 / x + 1 / y = ( x + y ) / xy thus working together they will complete the work in xy / ( x + y ) days acc . to the ques : 1 ) if dev works alone he will take 20 more hours to complete a task than if he worked with tina ' x - xy / ( x + y ) = 20 = > ( x ^ 2 ) / ( x + y ) = 20 . . . . . . . . . . . . . ( i ) 2 ) if tina works alone , she will take 5 more hours to complete the complete the task , then if she worked with dev y - xy / ( x + y ) = 5 = > ( y ^ 2 ) / ( x + y ) = 5 . . . . . . . . . . . . . . ( ii ) dividing ( i ) by ( ii ) x ^ 2 / y ^ 2 = 4 = > x / y = 2 ans : b hope it helps
Answer: b
Problem: a train 140 m long is running with a speed of 50 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 8.1 , b ) 7.0 , c ) 9.33 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 50 + 4 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . time taken to pass the men = 140 * 1 / 15 = 9.33 sec . answer : option c"
Answer: c
Problem: a train 110 m long is running with a speed of 40 km / hr . in what time will it pass a man who is running at 5 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7.5 , d ) 8.8 , e ) 9
Rationale: "speed of train relative to man = 40 + 5 = 45 km / hr . = 45 * 5 / 18 = 25 / 2 m / sec . time taken to pass the men = 110 * 2 / 25 = 8.8 sec . answer : option d"
Answer: d
Problem: john and steve are speed walkers in a race . john is 15 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.8 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 42.5 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.8 t + 15 + 2 - - - > 0.4 t = 17 - - - > t = 42.5 seconds . e is the correct answer ."
Answer: e
Problem: an error 2.5 % 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 ) 6.04 % , b ) 5.14 % , c ) 5.23 % , d ) 5.0625 % , e ) 5.5 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102.5 x 102.5 ) cm 2 . ( a 2 - a 1 ) = [ ( 102.5 ) 2 - ( 100 ) 2 ] = ( 102.5 + 100 ) x ( 102.5 - 100 ) = 506.25 cm 2 . percentage error = 5.0625 d"
Answer: d
Problem: the average of 10 consecutive integers is 20 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 14 , b ) 14.5 , c ) 15 , d ) 15.5 , e ) 16
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d ."
Answer: d
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 10 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 90
Rationale: "200 men do the rest of the work in 100 - 10 = 90 days 100 men can do the rest of the work in 90 * 200 / 100 = 180 days required number of days = 180 - 90 = 90 days answer is e"
Answer: e
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 30 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 — 30 = 12 hours answer d"
Answer: d
Problem: if a rectangular room measures 10 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000 , b ) 240,000 , c ) 2 , 400,000 , d ) 200 , 000,000 , e ) 240 , 000,000
Rationale: "d . 200 , 000,000 10 * 100 * 5 * 100 * 4 * 100 = 200 , 000,000"
Answer: d
Problem: only a single rail track exists between stations a and b on a railway line . one hour after the north bound super fast train n leaves station a for station b , a south - bound passenger train s reaches station a from station b . the speed of the super fast train is twice that of a normal express train e , while the speed of a passenger train s is half that of e . on a particular day , n leaves for b from a , 20 min behind the normal schedule . in order to maintain the schedule , both n and s increased their speeds . if the super fast train doubles its speed , what should be the ratio ( approximately ) of the speeds of passenger train to that of the super fast train so that the passenger train s reaches exactly at the scheduled time at a on that day ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 1 : 6 , e ) 1 : 7
Rationale: explanation : if speed of n = 4 , speed of s = 1 . = > average speed = ( 2 x 4 x 1 ) / ( 4 + 1 ) = 1.6 . because time available is 2 / 3 , speed = 3 / 2 . now average speed = 2.4 now speed of n = 8 . speed of s = y . = > ( 2 x 8 x y ) / ( 8 + y ) = 2.4 = > y = 1.3 the required ratio is 1.3 : 8 i . e 1 : 6 . answer : d
Answer: d
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 15 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 30
Rationale: a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 15 days , b can do 1 / 2 of the project . thus a and b must complete 1 / 2 of the project , which takes 6 days . the total number of days is 6 + 15 = 21 . the answer is b .
Answer: b
Problem: 2.2 cubic dm of lead is to be drawn into a cylindrical wire 0.50 cm diameter . find the length of the wire in meters .
Options: a ) 110
b ) 111
c ) 113
d ) 112
e ) none of them
Rationale: let the length of the wire be h meters . then , ∏ ( 0.50 / ( 2 x 100 ) ) ^ 2 x h = 2.2 / 1000 = h = ( ( 2.2 / 1000 ) x ( 100 x 100 ) / ( 0.25 x 0.25 ) x ( 7 / 22 ) ) = 112 m . answer is d .
Answer: d
Problem: how many positive integers less than 200 are there such that they are multiples of 13 or multiples of 14 ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "200 / 13 = 15 ( plus remainder ) so there are 15 multiples of 13 200 / 14 = 14 ( plus remainder ) so there are 14 multiples of 14 we need to subtract 1 because 13 * 14 is a multiple of both so it was counted twice . the total is 15 + 14 - 1 = 28 the answer is d ."
Answer: d
Problem: there are 2 sections a and b in a class , consisting of 36 and 24 students respectively . if the average weight of section a is 30 kg and that of section b is 30 kg , find the average of the whole class ?
Options: a ) 30 kg , b ) 37 kg , c ) 42 kg , d ) 55.12 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 36 * 30 + 24 * 30 = 1800 average weight of the class is = 1800 / 60 = 30 kg answer is a"
Answer: a
Problem: sarah is driving to the airport . after driving at 25 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 50 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 100 , b ) 175 , c ) 210 , d ) 245 , e ) 280
Rationale: "after driving at 25 miles per hourfor one hour , this distance left to cover is d - 25 . say this distance is x miles . now , we know that the difference in time between covering this distance at 25 miles per hour and 50 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 25 - x / 50 = 3 / 2 - - > 2 x / 50 - x / 50 = 3 / 2 - - > x / 50 = 3 / 2 - - > x = 75 . total distance = x + 25 = 100 miles . answer : a"
Answer: a
Problem: two trains start from p and q respectively and travel towards each other at a speed of 50 km / hr and 40 km / hr respectively . by the time they meet , the first train has travelled 100 km more than the second . the distance between p and q is :
Options: a ) 500 km , b ) 630 km , c ) 900 km , d ) 660 km , e ) none
Rationale: "sol . at the time of meeting , let the distane travelled byb the second train be x km . then , distance covered by the first train is ( x + 100 ) km ∴ x / 40 = ( x + 100 ) / 50 ⇔ 50 x = 40 x 4000 ⇔ x = 400 . so , distance between p and q = ( x + x + 100 ) km = 900 km . answer c"
Answer: c
Problem: a is thrice as good a workman as b and takes 10 days less to do a piece of work than b takes . b alone can do the whole work in
Options: a ) 15 days , b ) 10 days , c ) 9 days , d ) 8 days , e ) 7 days
Rationale: explanation : ratio of times taken by a and b = 1 : 3 means b will take 3 times which a will do in 1 time if difference of time is 2 days , b takes 3 days if difference of time is 10 days , b takes ( 3 / 2 ) * 10 = 15 days option a
Answer: a
Problem: the difference between simple and compound interest on rs . 1500 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) 8.0 , b ) 3.0 , c ) 9.5 , d ) 3.75 , e ) 2.15
Rationale: "s . i . = ( 1500 * 10 * 1 ) / 100 = rs . 150 c . i . = [ 1500 * ( 1 + 5 / 100 ) 2 - 1500 ] = rs . 153.75 difference = ( 153.75 - 150 ) = rs . 3.75 answer : d"
Answer: d
Problem: in a class , 12 students like to play basketball and 8 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) 18 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 12 + 8 - 3 = 17 c )"
Answer: c
Problem: in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if one - sevenths of the male students are married , what fraction of the female students is single ?
Options: a ) 1 / 3 , b ) 1 / 7 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 1 / 7 of 70 = 10 males are married if 30 is the total number of students who are married and out of that 10 are males then the remaining 20 will be females who are married . total females = 30 married females = 20 then single females = 30 - 20 = 10 we need to find the fraction of female students who are single i . e single female students / total female student = 10 / 30 = 1 / 3 [ a ]
Answer: a
Problem: a train ride from two p to town q costs $ 6.35 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?
Options: a ) $ 1.75 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20
Rationale: "let x be the cost of a bus ride . x + ( x + 635 ) = 985 2 x = 350 x = $ 1.75 the answer is a ."
Answer: a
Problem: a drink vendor has 10 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 261 , c ) 422 , d ) 430 , e ) 438
Rationale: "the number of liters in each can = hcf of 10 , 144 and 368 = 2 liters . number of cans of maaza = 10 / 2 = 5 number of cans of pepsi = 144 / 2 = 72 number of cans of sprite = 368 / 2 = 184 the total number of cans required = 5 + 72 + 184 = 261 cans . answer : b"
Answer: b
Problem: if 40 % of a certain number is 160 , then what is 30 % of that number ?
Options: a ) 270 , b ) 380 , c ) 120 , d ) 360 , e ) 180
Rationale: "explanation : 40 % = 40 * 4 = 160 30 % = 30 * 4 = 120 answer : option c"
Answer: c
Problem: if the sum of two numbers is 45 and the l . c . m and sum of the reciprocal of the numbers are 120 and 11 / 120 then hcf of numbers is equal to :
Options: a ) 55 , b ) 5 , c ) 10 , d ) 45 , e ) 4
Rationale: let the numbers be a and b and hcf is x , then , a + b = 45 and ab = x * 120 = 120 x required sum = 1 / a + 1 / b = ( a + b ) / ab = 45 / 120 x = 11 / 120 . x = 5 . answer : b
Answer: b
Problem: find the missing figures : 0.1 % of ? = 0.24
Options: a ) 12 , b ) 120 , c ) 24 , d ) 240 , e ) 36
Rationale: "let 0.1 % of x = 0.24 . then , 0.1 * x / 100 = 0.24 x = [ ( 0.24 * 100 ) / 0.1 ] = 240 . answer is d ."
Answer: d
Problem: there has been successive increases of 25 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 23 % , b ) 27 % , c ) 31 % , d ) 35 % , e ) 39 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.25 * p = x * p y = x / ( 1.1 * 1.25 ) which is about 0.73 x which is a decrease of about 27 % . the answer is b ."
Answer: b
Problem: pipe a can fill a tank in 60 min . there is a second pipe in the bottom of the cistern to empty it . if all the two pipes are simultaneously opened , then the cistern is full in 180 min . in how much time , the second pipe alone can empty the cistern ?
Options: a ) 60 min , b ) 45 min , c ) 90 min , d ) 70 min , e ) 30 min
Rationale: work done by the third pipe in 1 min = 1 / 180 - ( 1 / 60 ) = - 1 / 45 . [ - ve sign means emptying ] the third pipe alone can empty the cistern in 45 min . answer : b
Answer: b
Problem: a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 35 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 44 % , b ) 40 % , c ) 68.75 % , d ) 56.25 % , e ) 36 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 35 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.75 . so his profit is $ 6.75 - $ 4 = $ 2 and his profit percent is ( 2.75 / 4 ) * 100 = 68.75 % answer : - c"
Answer: c
Problem: nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 2 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 48
Rationale: e its is . let price = x ( x - 2 ) 8 = 6 x x = 8 hence total money = 6 * 8 = 48
Answer: e
Problem: according to a recent student poll , 3 / 4 out of 20 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 1 / 14 , b ) 4 / 49 , c ) 18 / 19 , d ) 45 / 49 , e ) 13 / 14
Rationale: "15 students are interested , 5 are not interested prob = 1 - 5 c 2 / 20 c 2 = 1 - ( 5 * 4 / ( 20 * 19 ) ) = 1 - 1 / 19 = 18 / 19 answer : c"
Answer: c
Problem: there are 4 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 3 , b ) 1 / 14 , c ) 3 / 14 , d ) 1 / 15 , e ) 1 / 16
Rationale: "taking 2 red shoe the probability is 4 c 2 from 8 shoes probability of taking 2 red shoes is 4 c 2 / 8 c 2 = 3 / 14 answer : c"
Answer: c
Problem: ram , who is half as efficient as krish , will take 30 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 10 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 30 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 30 days is 30 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 30 w / 3 w = 10 days answer b"
Answer: b
Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 5 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 100 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 5 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 5 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 100 = 20 t 19 t + 100 = 20 t 100 = t there are a total of 100 students in the math class . answer is d ."
Answer: d
Problem: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 11 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 23 years , b ) 24 years , c ) 25 years , d ) 26 years , e ) 27 years
Rationale: "explanation let the average age of the whole team by x years . 11 x â € “ ( 26 + 40 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 54 2 x = 54 x = 27 . so , average age of the team is 27 years . answer e"
Answer: e
Problem: the area of one square is x ^ 2 + 12 x + 36 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 64 , what is the value of x ?
Options: a ) 0 , b ) 4.3 , c ) 2.5 , d ) 4.67 , e ) 10
Rationale: spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 6 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 6 l 2 = 2 x - 3 p 1 = 4 ( x + 6 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 64 4 ( x + 6 ) + 4 ( 2 x - 3 ) = 64 . . . . . . . . . . . . . . > x = 4.3 answer : b
Answer: b
Problem: in one hour , a boat goes 6 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 4 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 6 + 2 ) km / hr = 4 kmph . answer a"
Answer: a
Problem: on the first day of her vacation , louisa traveled 200 miles . on the second day , traveling at the same average speed , she traveled 350 miles . if the 200 - mile trip took 3 hours less than the 350 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 45 , b ) 55 , c ) 60 , d ) 65 , e ) 50
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 200 / t = 350 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 200 / 4 = 50 answer : e"
Answer: e
Problem: while working alone at their respective constant rates , server g uploads 480 files in 4 hours and server y uploads 480 files in 8 hours . if all files uploaded by these servers are the same size , how long would it take the two servers , working at the same time and at their respective constant rates , to process a total of 480 files ?
Options: a ) 2 hr , b ) 2 hr 20 min , c ) 2 hr 40 min , d ) 5 hr 40 min , e ) 6 hr
Rationale: server g processes 480 / 4 files per hour = 120 per hour server y processes 180 / 8 files per hour = 60 per hour total files processed per hour when g and y work together = 120 + 60 per hour = 180 files per hour 480 / 180 = 2 2 / 3 hours = c
Answer: c
Problem: two numbers are respectively 40 % and 60 % more than a third number . what percentage is the first of the second ?
Options: a ) 72 % , b ) 87.5 % , c ) 63.7 % , d ) 56.9 % , e ) 90 %
Rationale: "required answer = ( 100 + x ) / ( 100 + y ) * 100 = 140 * 100 / 160 = 87.5 % answer is b"
Answer: b
Problem: if rs . 578 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 408 , c ) s . 389 , d ) s . 368 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 578 * 2 / 17 = rs . 68 b ' s share = 578 * 3 / 17 = rs . 102 c ' s share = 578 * 12 / 17 = rs . 408 . answer : b"
Answer: b
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 6 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 28 , c ) 32 , d ) 48 , e ) 58
Rationale: "et no of sheep and horses are 6 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 6 * 8 ) = 48 answer : d"
Answer: d
Problem: a man swims downstream 40 km and upstream 56 km taking 8 hours each time , what is the speed of the man in still water ?
Options: a ) 6 , b ) 24 , c ) 8 , d ) 12 , e ) 44
Rationale: "40 - - - 8 ds = 5 ? - - - - 1 56 - - - - 8 us = 7 ? - - - - 1 m = ? m = ( 5 + 7 ) / 2 = 6 answer : a"
Answer: a
Problem: 4 / 6 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 41 % , c ) 45 % , d ) 64 % , e ) 78 %
Rationale: "total population = 60 ( assume ) . 4 / 6 * 60 = 40 people from montague . 2 / 6 * 60 = 20 people from capulet . 0.2 * 40 = 8 people from montague support juliet . 0.7 * 20 = 14 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 14 / ( 8 + 14 ) = ~ 64 . answer : d"
Answer: d
Problem: if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 3 is divided by 41 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 16 , e ) 18
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 3 = 82 k + 5 + 3 = 82 k + 8 or x + 3 = 8 , 90,172 etc . when divided by 41 , we will get the remainder 8 . e"
Answer: e
Problem: alfred buys an old scooter for $ 4400 and spends $ 800 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 7 % , d ) 8.12 % , e ) 11.5 %
Rationale: "c . p . = 4400 + 800 = $ 5200 s . p . = $ 5800 gain = 5800 - 5200 = $ 600 gain % = 600 / 5200 * 100 = 11.5 % answer is e"
Answer: e
Problem: a 1100 m long train crosses a tree in 110 sec , how much time will it take to pass a platform 700 m long ?
Options: a ) 288 , b ) 190 , c ) 188 , d ) 180 , e ) 12
Rationale: l = s * t s = 1100 / 110 s = 10 m / sec . total length ( d ) = 1800 m t = d / s t = 1800 / 10 t = 180 sec answer : d
Answer: d
Problem: if rs . 440 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 580 , e ) s . 585
Rationale: "80 = ( 440 * 4 * r ) / 100 r = 5.68 % i = ( 440 * 6 * 5.68 ) / 100 = 150 440 + 150 = 590 answer : c"
Answer: c
Problem: what is the remainder when 43 ^ 92 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 92 has the form 4 k so the units digit of 43 ^ 92 is 1 . the remainder when dividing by 5 is 1 . the answer is b ."
Answer: b
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.8 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) 23 kg
Rationale: "the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.8 weight of the new student = ( 30 * 27.8 – 29 * 28 ) = 834 - 812 = 22 answer : a"
Answer: a
Problem: in the quadratic equation ax 2 - x - 12 = 0 , if the sum of two roots is 1 , what is the product of the two roots ?
Options: a ) - 12 , b ) - 6 , c ) 12 , d ) 6 , e ) 24
Rationale: explanation : the sum of the roots of the quadratic equation ax 2 + bx + c = 0 are ( - b / a ) and the product of the roots are ( c / a ) . thus , in the equation ax 2 - 11 x + 40 = 0 , where a = a , b = - 1 and c = - 12 . we get , sum of the roots = 1 / a = 1 a = 1 product of the roots = - 12 / 1 = - 12 answer : a
Answer: a
Problem: a book is bought for $ 60 and sold for $ 63 . what is the profit in percentage ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "63 / 60 = 1.05 the answer is b ."
Answer: b
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers e are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes e in this range . answer : a ."
Answer: a
Problem: in the science city , kolkata the rate of the ticket is increased by 50 % to increased the revenue but simultaneously 20 % of the visitor decreased . what is percentage change in the revenue . if it is known that the science city collects one revenue only from the visitors and it has no other financial supports :
Options: a ) + 20 % , b ) - 25 % , c ) + 305 , d ) - 30 % , e ) can not determined
Rationale: solution : let the initial revenue be 100 . 100 - - - - - 50 % ↑ ( ticket up ) - - - - - > 150 - - - - - 20 % ↓ ( visitors down ) - - - - - > 120 . there is 20 % increase in the revenue . answer : option a
Answer: a
Problem: 81 * 82 * 83 * 84 * 85 * 86 * 87 * 89 . what should be in the unit place in this product ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: it should be zero in the unit place in this product . 85 * 82 will give zero in unit place . answer : a
Answer: a
Problem: how many zeros does 500 ! end with ?
Options: a ) 201 , b ) 240 , c ) 124 , d ) 125 , e ) 180
Rationale: "according to above 500 ! has 500 / 5 + 500 / 25 + 500 / 125 = 100 + 20 + 4 = 124 trailing zeros . answer : c ."
Answer: c
Problem: if the sum of two positive integers is 12 and the difference of their squares is 48 , what is the product of the two integers ?
Options: a ) 32 , b ) 119 , c ) 128 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 12 - - 1 x ^ 2 - y ^ 2 = 48 = > ( x + y ) ( x - y ) = 48 - - 2 using equation 1 in 2 , we get = > x - y = 4 - - 3 solving equation 1 and 3 , we get x = 8 y = 4 product = 8 * 4 = 32 answer a"
Answer: a
Problem: john makes $ 50 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.9 % , d ) 18.12 % , e ) 60 %
Rationale: "increase = ( 30 / 50 ) * 100 = ( 3 / 5 ) * 100 = 60 % . e"
Answer: e
Problem: a man can row downstream at 16 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 16 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 26 = > x = 13 , y = 3 . answer : a"
Answer: a
Problem: a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 45.00 ?
Options: a ) $ 10.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 25.20 , e ) $ 18.00
Rationale: "for retail price = $ 45 first maximum discounted price = 45 - 30 % of 45 = 45 - 13.5 = 31.5 price after additional discount of 20 % = 31.5 - 20 % of 31.5 = 31.5 - 6.3 = 25.2 answer : option d"
Answer: d
Problem: in a group of 150 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.4 , b ) 0.5 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: "number of people whose age is less than 20 is given by 150 - 90 = 60 probability p that a person selected at random from the group is less than 20 is given by 60 / 150 = 0.4 correct answer a"
Answer: a
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 202 to 300 inclusive ?
Options: a ) 5,150 , b ) 7,550 , c ) 10,150 , d ) 12,550 , e ) 20,150
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 202 + 204 + . . . + 300 = 50 ( 200 ) + ( 2 + 4 + . . . + 100 ) = 10,000 + 2550 = 12,550 the answer is d ."
Answer: d
Problem: the average weight of 8 person ' s increases by 3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 60 kg , b ) 70 kg , c ) 80 kg , d ) 89 kg , e ) 95 kg
Rationale: "total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 65 + 24 ) kg = 89 kg . d )"
Answer: d
Problem: a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 15 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 46.85 % , b ) 43.75 % , c ) 50 % , d ) 56.25 % , e ) 36 %
Rationale: the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 20 % impurities to the product . it means that he is selling $ 5 worth of product for $ 5.75 . so his profit is $ 5.75 - $ 4 = $ 1.75 and his profit percent is ( 1.75 / 4 ) * 100 = 43.75 % answer : - b
Answer: b
Problem: if it is assumed that 65 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 420 , c ) 461.5 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 65 % = 300 / 0.65 = 461.5 option c"
Answer: c
Problem: if the length , breadth and the height of a cuboid are in the ratio 6 : 5 : 4 and if the total surface area is 33300 cm 2 cm 2 , then the length , breadth and height in cms , are respectively .
Options: a ) 90 , 85,60
b ) 85 , 75,60
c ) 90 , 75,70
d ) 90 , 75,60
e ) none
Rationale: explanation : let length = 6 x , breadth = 5 x and height = 4 x in cm 2 ( 6 x × 5 x + 5 x × 4 x + 6 x × 4 x ) = 33300 148 x 2 = 33300 ⇒ x 2 = 33300 / 148 = 225 ⇒ x = 15 length = 90 cm , breadth = 75 cm and height = 60 cm correct option : d
Answer: d
Problem: a train covers a distance of 14 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) m , b ) m , c ) m , d ) m , e ) m
Rationale: "speed = ( 14 / 10 * 60 ) km / hr = ( 84 * 5 / 18 ) m / sec = 70 / 3 m / sec . length of the train = 70 / 3 * 6 = 140 m . answer : c"
Answer: c
Problem: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 2 hours ?
Options: a ) 450 , b ) 750 , c ) 1,800 , d ) 5,900 , e ) 7,500
Rationale: "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 2 hours ) = 450 cans . the answer is a ."
Answer: a
Problem: one hour after yolanda started walking from x to y , a distance of 31 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 16
Rationale: "when b started walking y already has covered 3 miles out of 31 , hence the distance at that time between them was 31 - 3 = 28 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 28 / 7 = 4 hours . in 6 hours b walked 4 * 4 = 16 miles . answer : e ."
Answer: e
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 5 days ?
Options: a ) 5 / 18 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 5 days = 5 ( 1 / 18 ) = 5 / 18 . answer a"
Answer: a
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 25 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 216 , c ) $ 220 , d ) $ 180 , e ) $ 240
Rationale: wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 25 emlpoyee paid = . 75 * 240 = 180 $ answer d
Answer: d
Problem: 789.009 - ? + 56.84 = 215.943
Options: a ) 899.015 , b ) 752.804 , c ) 714.642 , d ) 629.906 , e ) none of these
Rationale: "explanation : 629.906 answer : option d"
Answer: d
Problem: an seller earns an income of re 3 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 15 th day of business , he earns an income of :
Options: a ) 19 , b ) 22 , c ) 25 , d ) 20 , e ) 36
Rationale: 2 nd day he earns = 3 ( 2 – 3 ) 3 rd day he earns = 3 ( 3 – 3 ) on 15 th day he earns 3 ( 15 - 3 ) = 36 rupees answer : e
Answer: e
Problem: how much 80 % of 40 is greater than 10 % of 15 ?
Options: a ) 18 , b ) 99 , c ) 19 , d ) 18 , e ) 17
Rationale: "( 80 / 100 ) * 40 – ( 10 / 100 ) * 15 32 - 15 = 17 answer : e"
Answer: e
Problem: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 10 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 10 / 50 ) * 100 = 20 % so , x * 20 % = 50 x = 250 ans . c"
Answer: c
Problem: a can finish a work in 12 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 5 days
Rationale: b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done by a in 12 * 5 / 12 = 5 days answer is e
Answer: e
Problem: 75 boys can complete a job in 24 days . how many men need to complete the job twice in 20 days
Options: a ) 160 , b ) 170 , c ) 180 , d ) 190 , e ) 200
Rationale: one man can complete the job in 24 * 75 = 1800 days to complete the job twice he would need 3600 days . thus , to complete the job in 20 days , 3600 / 20 = 180 men are needed . answer : c
Answer: c
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on december 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 44 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 nov 1 = c - 40 dec 1 = c - 44 difference between stock on december 1 than were in stock on january 1 will be - c - ( c - 44 ) = 44 hence answer will be ( d )"
Answer: d
Problem: there are 760 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 425 , d ) 475 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 760 . hence 3 x + 5 x = 760 solve for x 8 x = 760 x = 95 number of boys 3 x = 3 × 95 = 285 number of girls 5 x = 5 × 95 = 475 d"
Answer: d
Problem: a contractor is engaged for 30 days on the condition that he receives rs . 25 for eachday he works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was heabsent ?
Options: a ) 5 , b ) 10 , c ) 17 , d ) 25 , e ) 30
Rationale: "30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b"
Answer: b
Problem: if a dozen of oranges cost $ 5 , what would be the cost of 10 oranges ?
Options: a ) 3.56 , b ) 4.16 , c ) 4.86 , d ) 5.1 , e ) 5.2
Rationale: the cost of one orange = 5 / 12 = 0.416 the cost of ten oranges = 0.416 x 10 = $ 4.16 answer : b
Answer: b
Problem: the perimeter of one square is 48 cm and that of another is 36 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 12 √ 4 , e ) 15 √ 2
Rationale: "4 a = 48 4 a = 36 a = 12 a = 9 a 2 = 144 a 2 = 81 combined area = a 2 = 225 = > a = 15 d = 15 √ 2 answer : e"
Answer: e
Problem: light glows for every 14 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 381 , b ) 382 , c ) 383 , d ) 384 , e ) 355
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 14 = 354 so total 355 times light ll glow answer : e"
Answer: e
Problem: if 36 men can do a piece of work in 20 hours , in how mwny hours will 15 men do it ?
Options: a ) 22 , b ) 48 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 20 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 20 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 20 } { 15 } = 48 hence , 15 men can do it in 48 hours . answer : b ) 48"
Answer: b
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours z will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) z = 4 . , c ) z = 5 . , d ) 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double z = 6 hrs . . so closest to that option is 5 ."
Answer: c
Problem: find the simple interest on rs . 580 for 11 months at 9 paisa per month ?
Options: a ) 574 , b ) 270 , c ) 566 , d ) 266 , e ) 121
Rationale: "i = ( 580 * 11 * 9 ) / 100 = 574 answer : a"
Answer: a
Problem: every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` rat ' ' ?
Options: a ) 108 , b ) 111 , c ) 114 , d ) 117 , e ) 120
Rationale: ` ` rat ' ' = ( 18 + 1 + 20 ) * 3 = 117 . the answer is d .
Answer: d
Problem: a train 100 m long crosses a platform 125 m long in 2 sec ; find the speed of the train ?
Options: a ) 36 , b ) 405 , c ) 200 , d ) 302 , e ) 404
Rationale: "d = 100 + 125 = 225 t = 2 s = 225 / 2 * 18 / 5 = 405 kmph answer : b"
Answer: b
Problem: 0.0015 ÷ ? = 0.003
Options: a ) 0.05 , b ) 0.005 , c ) 0.5 , d ) 5 , e ) 50
Rationale: "let 0.0015 / x = 0.003 x = 0.0015 / 0.003 = 0.5 answer : c"
Answer: c
Problem: √ ( 9 ) ^ 2
Options: a ) 3 , b ) 14 , c ) 9 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 9 ) ^ 2 = ? or , ? = 9 answer c"
Answer: c
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 39,375 , how much profit did the business make ?
Options: a ) $ 54,000 , b ) $ 57,000 , c ) $ 60,000 , d ) $ 63,000 , e ) $ 66,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 39,375 p = $ 63,000 the answer is d ."
Answer: d
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e"
Answer: e