regisss/math_qa huggingface dataset:
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 10.5 and 1 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 6 , b ) 8.5 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "mean = 10.5 two standard deviations is 1 + 1 = 2 there could be two calues for this . mean + two standard deviations = 12.5 mean - two standard deviations = 8.5 answer choice has 8.5 and so b is the answer ."
Answer: b
Problem: what is the measure of the angle e made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30
b ) 45
c ) 60
d ) 75
e ) 90
Rationale: c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . . c
Answer: c
Problem: if albert ’ s monthly earnings rise by 20 % , he would earn $ 560 . if , instead , his earnings rise by only 21 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 660 , d ) 564 , e ) 693
Rationale: "= 560 / 1.2 ∗ 1.21 = 564 = 564 answer is d"
Answer: d
Problem: a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 30 % . their gross income from sales for one month increases by what percent ?
Options: a ) 9 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 17 %
Rationale: let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.3 x = 1.17 * ( p * x ) , an increase of 17 % . the answer is e .
Answer: e
Problem: 324 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 36 , d ) 39 , e ) 43
Rationale: "explanation : 324 ã · ? ã — 15 = 405 - 270 = 135 ( 324 ã — 15 ) / ? = 135 ? = ( 324 ã — 15 ) / 135 = 36 answer : option c"
Answer: c
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 answer : b"
Answer: b
Problem: lovely shop runs a sale on goldfish and platys . if one customer buys 13 goldfish and 12 platys for $ 5.60 , and another buys 14 goldfish and 21 platys for $ 8.05 , what is the ratio of the price of goldfish to platys ?
Options: a ) 0.8 , b ) 0.75 , c ) c ) 8 / 9 , d ) 5 / 7 , e ) 6 / 8
Rationale: the approach of plugging in the numbers is a fine approach . but , in this case , the answer was the first option and thus , by plugging in a number in the ration given , we arrived at the answer quickly ! however , what if the correct ratio was option d or c ? in any case , the algebraic solution is n ' t that complex if you realize a key concept : the number 7 can be factored out of the second equation ! here ' s the working : lovely shop runs a sale on goldfish and platys . 13 x + 12 y = 5.60 < < < < < equation 1 14 x + 21 y = 8.05 < < < < < equation 2 2 x + 3 y = 1.15 [ factor out 7 from equation 2 ] < < < < < equation 3 8 x + 12 y = 4.6 [ multiply equation 3 with 4 ] 5 x = 1.0 [ equation 1 - equation 2 ] x = 0.2 3 y = 1.15 - 0.4 = 0.75 [ substitute for x in equation 1 ] y = 0.25 x / y = 0.2 / 0.25 = 20 / 25 = 4 / 5 = 0.8 [ answer a ] the whole thing must have taken me about 45 s : d
Answer: d
Problem: a football team lost 5 yards and then gained 9 . what is the team ' s progress ?
Options: a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 9 = 4 yards correct answer is d ) 4"
Answer: d
Problem: in expressing a length 810472 km as nearly as possible with 3 significant digits , find the percentage error .
Options: a ) 0.034 , b ) 0.024 , c ) 0.352 , d ) 0.063 , e ) 0.026
Rationale: error = ( 81.5 – 81.472 ) km = 0.028 . required percentage = [ ( 0.028 / 81.472 ) * 100 ] % = 0.034 % . answer a .
Answer: a
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 450,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 40000 * 2 = 80000 80000 * 2 = 160000 160000 * 2 = 320000 hence , the answer is b ."
Answer: b
Problem: 140 college students were asked in a survey if they preferred windows or mac brand computers . 80 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 50 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 10 , c ) 50 , d ) 60 , e ) 75
Rationale: "140 = 80 ( mac ) + x ( window ) + 50 ( both ) = > x = 10 answer : b"
Answer: b
Problem: there are 5 more women than there are men on a local co - ed softball team . if there are a total of 15 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 5 / 10 , d ) 6 / 10 , e ) 4 / 10
Rationale: w = m + 5 w + m = 15 m + 5 + m = 15 2 m = 10 m = 5 w = 10 ratio : 5 : 10 ans : c
Answer: c
Problem: each factor of 210 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 8 . answer : c ."
Answer: c
Problem: a can do a work in 3 days . b can do in 6 days . if both a & b are working together in how many days they can finish the work ?
Options: a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: "1 day work of a = 1 / 3 1 day work of b = 1 / 6 1 day work of a & b = 1 / 3 + 1 / 6 = 1 / 2 a & b finish the work in 2 days answer is c"
Answer: c
Problem: the population of a village is 6000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 5000 , b ) 4860 , c ) 5400 , d ) 4800 , e ) 5120
Rationale: formula : ( after = 100 denominator ago = 100 numerator ) 6000 ã — 90 / 100 ã — 90 / 100 = 4860 b
Answer: b
Problem: what is the value of 3 x ^ 2 − 2 x + 0.3 for x = 0.5 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.05 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 2 x + 0.3 for x = 0.6 = 3 ( 0.5 * 0.5 ) - 4 * 0.5 * ( 0.5 ) + 0.3 = - 0.5 * 0.5 + 0.3 = - 0.25 + 0.3 = 0.05 correct option : c"
Answer: c
Problem: excluding the stoppages , the speed of a bus is 64 km / hr and including the stoppages the speed of the bus is 48 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 10 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 64 km / hr speed of the bus with stoppage = 48 km / hr difference in speed = 16 km / hr so , the time taken in the stoppages = time taken to cover 16 km = ( 16 / 64 ) hr = 1 / 4 hr = 15 min answer : a"
Answer: a
Problem: an analysis of the monthly incentives received by 5 salesmen : the mean and median of the incentives is $ 7000 . the only mode among the observations is $ 12000 . incentives paid to each salesman were in full thousands . what is the difference z between the highest and the lowest incentive received by the 5 salesmen in the month ?
Options: a ) $ 4000 , b ) $ 5000 , c ) $ 9000 , d ) $ 11000 , e ) $ 13000
Rationale: break down the question in to steps : step # 1 : incentives received by 5 salesmen - - > abcde step # 2 : mean and median of the incentives is $ 7000 : via number properties - - > total incentives = 7000 * 5 = 35000 ab 7000 de step # 3 : only mode among the observations is $ 12000 : mode is the value that appears most often in a set of data . therefore 12000 must occur more then once and since 12000 is larger than the mean ( 7000 ) the most it can occur is twice in our list . if we place the numbers in ascending order we haveab 70001200012000 step # 4 : what is the difference z between the highest and the lowest incentive : - the total paid has to equal mean * # of numbers = 7000 * 5 = 35 000 . - the three values we have so far ( 12000 12000 and 7000 ) equal 31000 . - therefore the first two numbers ( ab ) must equal 4000 - there is only one mode which is 12000 , therefore 4000 must be equal to a set of two numbers that are not the and a < b if a = 1000 b = 3000 - - > difference between the highest and the lowest incentive = 12000 - 1000 = 11000 no other options for a or b to fit the criteria final list : 1000300070001200012000 answer d
Answer: d
Problem: 6000 , 1200 , 300 , 60 . . .
Options: a ) 30 , b ) 15 , c ) 20 , d ) 36 , e ) 46
Rationale: "6000 / 5 = 1200 1200 / 4 = 300 300 / 5 = 60 60 / 4 = 15 answer : b"
Answer: b
Problem: the ratio of 2 numbers is 10 : 20 and their h . c . f . is 100 . their l . c . m . is ?
Options: a ) 1100 , b ) 3000 , c ) 2100 , d ) 1000 , e ) 2000
Rationale: "let the numbers be 10 x and 20 x their h . c . f . = 100 so the numbers are 10 * 100 , 20 * 100 = 1000 , 2000 l . c . m = 2000 answer is e"
Answer: e
Problem: if the numbers 1 to 97 are written on 97 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 97 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 71 composite numbers from 1 to 97 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 97 . answer : c"
Answer: c
Problem: 3.5 can be expressed in terms of percentage as ?
Options: a ) 0.35 % , b ) 3.5 % , c ) 35 % , d ) 350 % , e ) 0.0035 %
Rationale: "answer : option d 3.5 = 35 / 10 = ( 35 / 10 * 100 ) = 350 %"
Answer: d
Problem: a rectangular photograph is surrounded by a border that is 2 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 94 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 34 , b ) 36 , c ) 23 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 4 ) ( b + 4 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 94 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 94 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 4 ) ( b + 4 ) = ( l + 8 ) ( b + 8 ) - 94 lb + 4 l + 4 b + 16 = lb + 8 l + 8 b + 64 - 94 simplify 4 l + 4 b = 46 - - - - - - > 2 ( l + b ) = 23 ( check eq ( 1 ) ) answer is c"
Answer: c
Problem: an inspector rejects 15 % of the meters as defective . how many will he examine to reject 10 ?
Options: a ) a ) 100 , b ) b ) 66.7 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 15 ( 15 / 100 ) x = 10 x = ( 10 * 100 * ) / 15 = 66.7 answer is b"
Answer: b
Problem: the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 35 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 16 , b ) 17 , c ) 19 , d ) 22 , e ) 26
Rationale: the total sum of the numbers should be increased by 10 . then the average will increase by 10 / 10 = 1 . the correct average is 17 . the answer is b .
Answer: b
Problem: a gambler bought $ 4,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 3,120 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 4,000 - $ 880 = $ 3,120 . answer : d"
Answer: d
Problem: there are 600 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?
Options: a ) 100 , b ) 200 , c ) 250 , d ) 300 , e ) 400
Rationale: "there are 594 managers and 6 others . the 6 others would compose 2 % of the total number of people if there were 300 people in the room . thus 300 managers must leave . the answer is d ."
Answer: d
Problem: when 3 fair coins are tossed together , what is the probability of getting 2 tails ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 3 / 4 , e ) 2 / 3
Rationale: we can get 2 tails in 3 c 2 ways . we can get 3 tails in exactly one way . also , there are a total out 8 possible outcomes . thus , the required probability = ( 3 + 1 ) / 8 = 1 / 2 answer : a
Answer: a
Problem: the ratio of two cow a , b milk is 5 : 3.3 kg milk of cow a get distributed and 1 kg milk of cow b get distributed . now , 8 kg milk of cow b left . now what is the ratio of cow a and b left milk ?
Options: a ) 3 : 2 , b ) 4 : 3 , c ) 5 : 4 , d ) 6 : 5 , e ) 5 : 3
Rationale: left milk of cow b = 3 x - 1 = 8,3 x = 9 , x = 3 . left milk of cow a = 15 - 3 = 12 12 / 8 = 3 : 2 . answer a
Answer: a
Problem: a tank is filled by 3 pipes a , b , c in 8 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 56 hr , d ) 20 hr , e ) 50 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 8 7 / x = 1 / 8 x = 56 hours answer is c"
Answer: c
Problem: a car travels at a speed of 75 miles per hour . how far will it travel in 5 hours ?
Options: a ) 425 miles , b ) 625 miles , c ) 325 miles , d ) 375 miles , e ) 625 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 75 + 75 + 75 + 75 + 75 = 5 * 65 = 375 miles correct answer d"
Answer: d
Problem: angelina walked 150 meters from her home to the grocery at a constant speed . she then walked 200 meters to the gym at double the speed . she spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 10 , e ) 12
Rationale: let the speed be x . . . so time taken from home to grocery = 150 / x . . the speed to gym = 2 x . . so time taken = 200 / 2 x = 100 / x . . its given 150 / x - 100 / x = 10 50 / x = 10 x = 5 m / secs . . so grocery to gym = 2 * 5 = 10 m / s . . . answer : d
Answer: d
Problem: a cylinder of height h is 5 / 6 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 60 % , d ) 72 % , e ) 100 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 5 / 6 new cylinder 3 / 5 so 3 / 5 / 5 / 6 = 3 / 5 * 6 / 5 = 0.72 or 72 % . answer d"
Answer: d
Problem: a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 285 , b ) 227 , c ) 271 , d ) 187 , e ) 199
Rationale: "since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a"
Answer: a
Problem: a train running at the speed of 30 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 75 , b ) 65 , c ) 25 , d ) 288 , e ) 212
Rationale: "speed = 30 * ( 5 / 18 ) m / sec = 25 / 3 m / sec length of train ( distance ) = speed * time ( 25 / 3 ) * 9 = 75 meter answer : a"
Answer: a
Problem: if 8 men or 12 women can do a piece of work in 15 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 9 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 17 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 15 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 15 = 1 / 180 so , 20 women work = 20 / 180 = 1 / 9 ans : 9 days answer : a"
Answer: a
Problem: a train 200 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 443 m , b ) 354 m , c ) 450 m , d ) 350 m , e ) 300 m
Rationale: "e 300 e = 72 * 5 / 18 = 25 = 500 â € “ 200 = 300"
Answer: e
Problem: what is the rate percent when the simple interest on rs . 9100 amount to rs . 455 in 3 years ?
Options: a ) 3.7 % , b ) 5.7 % , c ) 6.7 % , d ) 8.7 % , e ) 9.7 %
Rationale: "455 = ( 4100 * 3 * r ) / 100 r = 3.7 % answer : a"
Answer: a
Problem: the length of a train and that of a platform are equal . if with a speed of 126 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 227 , b ) 299 , c ) 1050 , d ) 750 , e ) 211
Rationale: "speed = [ 126 * 5 / 18 ] m / sec = 35 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 35 è x = 35 * 60 / 2 = 1050 answer : c"
Answer: c
Problem: laura took out a charge account at the general store and agreed to pay 7 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.45 , d ) $ 38.10 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 7 % interest = ( 7 / 100 ) * 35 = 2.45 $ total amount that laura owes a year later = 35 + 2.45 = 37.45 $ answer c"
Answer: c
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 852 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 17.37 % , d ) 99 % , e ) 12 %
Rationale: "852 - - - 148 100 - - - ? = > 17.37 % answer : c"
Answer: c
Problem: a man walks at a rate of 10 mph . after every ten miles , he rests for 6 minutes . how much time does he take to walk 60 miles ?
Options: a ) 300 , b ) 318 , c ) 322 , d ) 324 , e ) 390
Rationale: "to cover 60 miles the man needs ( time ) = ( distance ) / ( rate ) = 60 / 10 = 6 hours = 360 minutes . he will also rest 5 times ( after 10 , 20 , 30,40 and 50 miles ) , so total resting time = 5 * 6 = 30 minutes . total time = 360 + 30 = 390 minutes . answer : e ."
Answer: e
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 15 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 6000 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 15 , the sum = 400 × 15 = 6000 answer d"
Answer: d
Problem: r is the set of positive odd integers less than 40 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) three , c ) four , d ) five , e ) seven
Rationale: "squares < 40 { 1,4 , 9,16 , 25,36 } s = { 1 , 9,25 } r = { 1,3 , . . . . . 40 } hence b ."
Answer: b
Problem: a square and an equilateral triangle have the same perimeter . what is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle ?
Options: a ) 9 : 8
b ) 15 : 8
c ) 27 : 8
d ) 8 : 9
e ) 8 : 15
Rationale: let x be side of square perimeter of square = 4 x = perimeter of triangle = 3 * side of triangle so side of eq . triangle = ( 4 / 3 ) * x diameter of circle circumscribing the square = sqrt ( 2 ) * x area of circle circumscribing the square = pi * ( sqrt ( 2 ) * x ) ^ 2 / 4 = ( pi / 2 ) * x ^ 2 - - - - ( 1 ) to find radius of the circle inscribed in the triangle area of triangle = r * s = sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 now s = ( 4 / 3 ) * x + ( 4 / 3 ) * x + ( 4 / 3 ) * x / 2 = 2 x so sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 = r * 2 x gives r = { 2 / 3 * ( 3 ^ 1 / 2 ) } * x area of the circle inscribed in the triangle = pi * [ { 2 / 3 * ( 3 ^ 1 / 2 ) } * x ] ^ 2 = pi * ( 4 / 27 ) * x ^ 2 - - - - - - - ( 2 ) so reqd ratio = eqn ( 1 ) / eqn ( 2 ) = [ ( pi / 2 ) * x ^ 2 ] / [ pi * ( 4 / 27 ) * x ^ 2 ] = 27 / 8 so reqd ratio = 27 : 8 answer : c
Answer: c
Problem: 10 is subtracted from 50 % of a number , the result is 25 . find the number ?
Options: a ) 75 , b ) 70 , c ) 35 , d ) 170 , e ) 50
Rationale: "( 50 / 100 ) * x â € “ 10 = 25 5 x = 350 x = 70 answer : b"
Answer: b
Problem: a bag holds 3 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 3 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 3 red and 3 green marbles after one red has been picked , we need to pick 1 red from a total of 2 red and 3 green marbles . p ( both red ) = ( 3 / 6 ) * ( 2 / 5 ) = 1 / 5 option b"
Answer: b
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 7.5 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 5 ) = 2 / 15 the cistern will be filled in 15 / 2 hrs i . e . , 7.5 hrs . answer : d"
Answer: d
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 24,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 277768 , e ) 188871
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 24,000 is made = 96,000 + 24,000 = rs . 1 , 20,000 answer : b"
Answer: b
Problem: a tank can supply water to a village for 100 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 75 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 50 , b ) 60 , c ) 65 , d ) 70 , e ) 72
Rationale: "losing 10 liters per day results in a loss of 750 liters in 75 days . so , those 750 liters were for 25 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 100 = 3000 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 3000 / 50 = 60 days . the answer is b ."
Answer: b
Problem: if x + y = 2 x + 2 z , x - 2 y = 2 z and x + y + z = 21 , what is the value of y / z ?
Options: a ) - 4 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 2.5 .
Rationale: x + y = 2 x + 2 z y = x + 2 z - - - - - - - - - - 1 x - 2 y = 2 z x - 2 z = 2 y - - - - - - - - - 2 subtracting equation 1 from equation 2 - 4 z = y y / z = - 4 a is the answer
Answer: a
Problem: a 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 300 m , b ) 278 m , c ) 350 m , d ) 228 m , e ) 282 m
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 36 = 50 / 3 3 ( x + 300 ) = 1800 è x = 300 m . answer : a"
Answer: a
Problem: the ratio of pens to pencils is 5 to 6 . there are 9 more pencils than pens . how many pencils are there ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 9 x = 9 the number of pencils is 54 . the answer is d .
Answer: d
Problem: the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c"
Answer: c
Problem: if the average of 10 digits is 80 and the average of 6 of them is 58 , calculate the average of the remaining 4 numbers ?
Options: a ) 119 , b ) 117 , c ) 116 , d ) 113 , e ) 115
Rationale: "explanation : total of the 10 digits - 10 * 80 = 800 total of the 6 digits - 6 * 58 = 348 total of the remaining 4 digits - 800 - 348 = 452 average of the remaining 4 numbers = 452 / 4 = 113 answer : d"
Answer: d
Problem: 1 / 2 is what percent of 1 / 3
Options: a ) 150 % , b ) 200 % , c ) 250 % , d ) 300 % , e ) 400 %
Rationale: "explanation : 1 / 2 / 1 / 3 * 100 = 1 / 2 * 3 / 1 * 100 = 150 % answer : option a"
Answer: a
Problem: 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 14
Rationale: "first codition = total hours to complete the work = 39 persons * 12 days * 5 hr second codition = total hours to complete the work = 30 persons * x days * 6 hr since the work is still the same so 39 * 12 * 5 = 30 * x * 6 x = 13 answer : c"
Answer: c
Problem: 2 : 3 : : 23 : ?
Options: a ) 25 , b ) 28 , c ) 22 , d ) 29 , e ) 30
Rationale: "d 29 3 is the next prime number after 2 . similarly , 29 is the next prime number after 23 ."
Answer: d
Problem: the product of two numbers is 220 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 220 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 220 ) = 729 x + y = 27 . option c"
Answer: c
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 300 resolutions .
Options: a ) 421 m , b ) 422 m , c ) 423 m , d ) 424 m , e ) 425 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 300 resolutions . = 300 * 2 * 22 / 7 * 22.4 = 42200 cm = 422 m answer : b"
Answer: b
Problem: the ratio between x and y is 7 / 9 ; x is increased by 4 and y is decreased by 4 , what is the ratio between the new values of x and y ?
Options: a ) 7 / 9 , b ) 14 / 9 , c ) 7 / 18 , d ) 11 / 13 , e ) it can not be determined
Rationale: "ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . x is increased by 4 and y is decreased by 4 - - > ( 7 k + 4 ) / ( 9 k - 4 ) new ratio can be 11 / 15 , 18 / 14 , etc . answer : e"
Answer: e
Problem: an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets liquid in at the rate of 8 litres / min then outlet pipe would take 6 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 12800 litres , c ) 12100 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 10 hours = ( x - 480 ) * ( 10 + 6 ) hours 10 x = ( x - 480 ) * 16 - - > x = 1280 - - > capacity = 10 x = 12800 liters . answer : b"
Answer: b
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many y miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him y : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Problem: ( 3108 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 331 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9268 ) / 28 = 331 option c"
Answer: c
Problem: for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 8 and the price of a student ticket was $ 4 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 20960 , b ) $ 21920 , c ) $ 22680 , d ) $ 28500 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 4 + 27 * 90 * 8 = $ 22,680 . answer : c ."
Answer: c
Problem: a train ride from two p to town q costs $ 6.85 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 ) $ 1.50 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20
Rationale: "let x be the cost of a bus ride . x + ( x + 685 ) = 985 2 x = 300 x = $ 1.50 the answer is a ."
Answer: a
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 222 grams of compound x ?
Options: a ) 54 , b ) 185 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 222 gms of x have 222 * 10 / 12 = 185 gms of b and 222 - 185 = 37 gms of a . cross check : - a / b = 37 / 185 = 2 / 10 ( as given ) ans b"
Answer: b
Problem: a train 100 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 6 sec , b ) 9 sec , c ) 12 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 100 m at 50 / 3 m / sec = 100 * 3 / 50 sec = 6 sec answer : a"
Answer: a
Problem: how many multiples of 8 are less than 1600 , and also multiples of 64 ?
Options: a ) 25 , b ) 28 , c ) 62 , d ) 83 , e ) 89
Rationale: the lcm of 8 and 64 is 64 . divide 1600 / 64 = 25 . xxx . so a is your answer .
Answer: a
Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 50 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 50 = 3 ^ 100 * 2 ^ 100 the answer is a ."
Answer: a
Problem: find k if 32 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 32 / k = 4 and 32 / 8 = 4 , then k = 8 correct answer c"
Answer: c
Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 14 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 42 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 14 ( in order 3 / 7 and 5 / 14 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 14 , which is 98 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 98 people in the room . therefore there are 3 / 7 * 98 = 42 people in the room under the age of 21 . answer : d ."
Answer: d
Problem: in a group of ducks and cows , the total number of legs are 36 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 36 more than twice the number of heads = > 2 ( d + 2 c ) = 36 + 2 ( c + d ) = > d + 2 c = 18 + c + d = > 2 c = 18 + c = > c = 18 i . e . , total number of cows = 18 answer is d ."
Answer: d
Problem: the radius of a semi circle is 6.6 cm then its perimeter is ?
Options: a ) 32.7 , b ) 32.4 , c ) 22.4 , d ) 33.9 , e ) 32.1
Rationale: "36 / 7 r = 6.6 = 33.9 answer : d"
Answer: d
Problem: the total age of a and b is 12 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 20 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 12 a - c = 12 answer is b"
Answer: b
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party w . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( w and b ) = 35 only w = 20 ( w and b ) / b = 1 / 2 let ( w and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Problem: pipe a fills a tank in 6 minutes . pipe b can fill the same tank 2 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5
Rationale: "a ' s rate is 1 / 6 and b ' s rate is 1 / 3 . the combined rate is 1 / 6 + 1 / 3 = 1 / 2 the pipes will fill the tank in 2 minutes . the answer is d ."
Answer: d
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8600 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 4100 , b ) s . 4270 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8600 = 34400 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2400 salary of may is rs . 6500 salary of january = rs . 4100 answer : a"
Answer: a
Problem: what is the tens digit of 7 ^ 545 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 0
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 546 = 4 * 136 + 1 the ten ' s digit will be 0 . answer e"
Answer: e
Problem: set a consists of all the prime numbers between 6 and 42 . what is the range of set a ?
Options: a ) 16 , b ) 34 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 41 lowest number = 7 range = highest - lowest = 41 - 7 = 34 option b"
Answer: b
Problem: a certain elevator has a safe weight limit of 2000 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2000 so 200 * x + 230 * x = 2000 = > 430 x = 2000 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 we are not taking 10 as answer because say 10 th person has minimum of 200 weight then 200 * 5 + 230 * 5 = 2150 ( which is more than 2000 ) answer c .
Answer: c
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3360 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 420 , d ) s . 400 , e ) s . 480
Rationale: explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3360 × ( 1 / 8 ) = 420 answer : option c
Answer: c
Problem: 90 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 135 , d ) 140 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 90 + 50 % ( 90 ) = 90 + 45 = 135 . answer c"
Answer: c
Problem: rahim bought 55 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 16 , d ) s . 11 , e ) s . 10
Rationale: "average price per book = ( 1500 + 340 ) / ( 55 + 60 ) = 1840 / 115 = rs . 16 answer : c"
Answer: c
Problem: the average of 10 numbers was calculated as 16 . it is discovered later on that while calculating the average , one number , namely 46 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "10 * 16 - 26 + 46 = 180 180 / 10 = 18 the answer is a ."
Answer: a
Problem: a taxi company charges $ 1.25 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 3 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.25 for the first quarter - mile , we will have $ 3.65 left to spend on quarter - mile intervals . since $ 3.65 / $ 0.15 = 24.33 we can buy 24.33 more quarter - miles , and will travel 25.33 quarter miles in all : 25.33 × 1 / 4 = 6 1 / 3 miles . the correct answer is choice ( e ) ."
Answer: e
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 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "answer a can complete a project in 20 days . so , a will complete 1 / 20 th of the project in a day . b can complete a project in 30 days . so , b will complete 1 / 30 th of the project in a day . let the total number of days taken to complete the project be x days . b worked for all x days . however , a worked for ( x - 10 ) days because a quits 10 days before the project is completed . in a day , a completes 1 / 20 th of the project . therefore , a would have completed x − 10 / 20 th of the project in ( x - 10 ) days . in a day , b completes 130130 th of the project . therefore , b would have completed x / 30 h of the project in x days . ∴ x − 10 / 20 + x / 30 = 1 or x = 18 . choice a"
Answer: a
Problem: 60 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 60 = 80 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 80 = 120 litres . answer c
Answer: c
Problem: what is the remainder when 8 ^ 714 is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 1 , d ) 0 , e ) 4
Rationale: "8 ^ 0 = 1 8 ^ 1 = 8 8 ^ 2 = 64 8 ^ 3 = 512 8 ^ 4 = 4096 8 ^ 5 = . . . . . 8 and so on after ignoring the first last - digit of 8 ^ 0 = 1 , in a recurring last - digit pattern of 8,4 , 2,6 , 8,4 , 2,6 . . . . 715 / 4 = 178 ( with a remainder 2 ) so the last number is a 4 . so when 8 ^ 714 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Problem: 20.20 / 2000 is equal to :
Options: a ) 1.01252677 , b ) 0.013466667 , c ) 0.125266677 , d ) 0.126256677 , e ) 0.12725776
Rationale: "20.20 / 2000 = 2525 / 200000 = 0.013466667 answer : b"
Answer: b
Problem: a bus trip of 450 miles would have taken 1 hour less if the average speed s for the trip had been greater by 5 miles per hour . what was the average speed s , in miles per hour , for the trip ?
Options: a ) 10 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "( s + 5 ) ( t - 1 ) = 450 s * t = 450 solving both the equations , we get : s = 45 or - 50 since speed should be positive , s = 45 hence , option c"
Answer: c
Problem: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters w long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1
Answer: b
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 72 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 91 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 110 mph + 72 mph ) / 2 = 91 mph correct answer is : b"
Answer: b
Problem: a starts business with rs . 35000 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 22378 , b ) 279889 , c ) 2788 , d ) 9000 , e ) 2882
Rationale: explanation : ratio in which profit is to be divided = 2 : 3 assume that b ' s contribution to the capital = b ⇒ 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 / 7 b = 2 / 3 ⇒ b = ( 3500 × 12 × 3 ) / ( 2 × 7 ) = 500 × 6 × 3 = 9000 answer : d
Answer: d
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 16 , d ) 29 , e ) 39
Rationale: 45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 = > 45 - [ 28 - { 37 - 15 + * } ] = 55 45 - [ 28 - 37 + 15 - * ] = 55 = > 45 [ 43 - 37 - * ] = 55 45 - [ 6 - * ] = 55 = > 45 - 6 + * = 55 39 + * = 55 = > * = 55 - 39 = 16 answer : c
Answer: c
Problem: what is the remainder of q = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , q = when divided by 10 , the remainder must be 7 . d"
Answer: d
Problem: find the fraction which has the same ratio to 2 / 5 that 3 / 8 has to 1 / 5
Options: a ) 1 / 15 , b ) 3 / 4 , c ) 5 / 8 , d ) 9 / 6 , e ) 8 / 7
Rationale: "p : 2 / 5 = 3 / 8 : 1 / 5 as the product of the means is equal to the product of the extremes . p * 1 / 5 = 2 / 5 * 3 / 8 p * 1 / 5 = 6 / 40 p = 3 / 4 = > p = 3 / 4 answer : b"
Answer: b
Problem: what is the remainder when 1271 * 1275 * 1277 * 1289 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 9 , d ) 11 , e ) 7
Rationale: "1271 * 1275 * 1277 * 1285 = ( 1272 - 1 ) ( 1272 + 3 ) ( 1284 - 7 ) ( 1284 + 5 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( - 1 ) ( 3 ) ( - 7 ) ( 5 ) = 105 . thus the question becomes : what is the remainder upon division of 105 by 12 ? the answer to this question is 9 . answer : c ."
Answer: c
Problem: in a class of 27 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.3
Rationale: explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 19 * 45 = 1330 average marks of whole class = 1330 / 27 = 49.3 answer : option e
Answer: e
Problem: a man sitting in a train which is traveling at 56 kmph observes that a goods train , traveling in opposite direction , takes 15 seconds to pass him . if the goods train is 410 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 42 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 410 / 15 m / sec = ( ( 410 / 15 ) × ( 18 / 5 ) ) kmph = 98 kmph . speed of goods train = ( 98 - 56 ) kmph = 42 kmph answer : option d"
Answer: d