Cheukting/mathqa huggingface dataset:
Question (other): on multiplying a number f by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number f is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Question (gain): at an election 2 candidates are participated a candidate got 30 % of votes and defeated by 5000 votes . 100 votes are invalid . find the total polled votes ?
Options: a ) 11520 , b ) 12600 , c ) 15000 , d ) 13560 , e ) 12560
Rationale: winners votes = 100 - 30 = 70 % invalid votes = 100 polled votes = [ ( 100 * 5000 ) / ( 2 * 70 - 100 ) ] + 100 = 12600 answer is b
Answer: b
Question (other): the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 6 : 8 , b ) 6 : 2 , c ) 6 : 5 , d ) 6 : 4 , e ) 6 : 2
Rationale: "4 : 5 3 : 2 - - - - - - - 12 : 15 : 10 12 : 10 6 : 5 answer : c"
Answer: c
Question (gain): if a large pizza has a radius that is 10 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 15 % , b ) 21 % , c ) 25 % , d ) 30 % , e ) 36 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.1 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.1 * r ) ^ 2 = 1.21 * pi * r ^ 2 , an increase of 21 % . the answer is b ."
Answer: b
Question (probability): if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ?
Options: a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Answer: b
Question (other): 60 kg of an alloy a is mixed with 100 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 2 and alloy b has tin and copper in the ratio 1 : 4 , then the amount of tin in the new alloy is ?
Options: a ) 24 kg , b ) 44 kg , c ) 20 kg , d ) 30 kg , e ) 52 kg
Rationale: quantity of tin in 60 kg of a = 60 * 2 / 5 = 24 kg quantity of tin in 100 kg of b = 100 * 1 / 5 = 20 kg quantity of tin in the new alloy = 24 + 20 = 44 kg answer is b
Answer: b
Question (general): what is the sum of all possible solutions to the equation √ 2 x ^ 2 − x − 9 = x + 1 ?
Options: a ) - 2 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "first of all notice that since lhs is the square root of a number , it must be non - negative ( the square root function can not give negative result ) , then the rhs must also be non - negative : x + 1 ≥ 0 - - > x ≥ − 1 square the equation : 2 x ^ 2 − x − 9 = x ^ 2 + 2 x + 1 - - > x ^ 2 − 3 x − 10 = 0 - - > x = - 2 or x = 5 . discard x = - 2 because it ' s not > = - 1 . we are left with only one root : 5 . answer : d"
Answer: d
Question (physics): pipe a can fill a tank in 10 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 48
Rationale: "let the pipe b be closed after x minutes . 30 / 10 - x / 24 = 1 = > x / 24 = 30 / 10 - 1 = 2 = > x = 2 * 24 = 48 . answer : e"
Answer: e
Question (gain): if price of t . v set is reduced by 18 % , then its sale increases by 88 % , find net effect on sale value
Options: a ) 44 , b ) 54 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 18 + 88 + ( - 18 * 88 ) / 100 = - 18 + 88 - 16 = 54 answer : b"
Answer: b
Question (general): a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was :
Options: a ) 14 , b ) 19 , c ) 33 , d ) 38 , e ) 56
Rationale: "explanation : let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years . answer : a"
Answer: a
Question (physics): 20 machines can do a work in 5 days . how many machines are needed to complete the work in 10 days ?
Options: a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20
Rationale: "required number of machines = 20 * 5 / 10 = 10 answer is a"
Answer: a
Question (general): in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 225 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 180 , c ) 24 , d ) 28 , e ) 40
Rationale: "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 225 ^ 2 16 x ^ 2 + 9 x ^ 2 = 225 ^ 2 25 x ^ 2 = 225 ^ 2 x ^ 2 = 25 * 9 ^ 2 x = 45 therefore ab = 45 * 4 = 180 answer : b"
Answer: b
Question (general): at company x , senior sales representatives visit the home office once every 18 days , and junior sales representatives visit the home office once every 12 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 36 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Question (general): set a of 8 positive integers may have the same element and have 36 . and set b of 8 positive integers must have different elements and have 36 . when m and n are the greatest possible differences between 36 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 36 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 29 and 36 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 8 . so , 29 - 8 = 21 . the correct answer is b .
Answer: b
Question (general): how many times digit 6 is used while writing numbers from 100 to 1100 ?
Options: a ) 648 , b ) 320 , c ) 252 , d ) 225 , e ) 26
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 320 . hence b ."
Answer: b
Question (general): what is the total cost of 2 sandwiches at $ 3.49 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.46 , e ) $ 11.85
Rationale: "answer = d 2 * 3.49 + 4 * 0.87 = 2 ( 3.50 - 0.01 ) + 4 ( 1.00 - 0.13 ) = 7 + 4 - 0.02 - 0.52 = 11 - 0.54 = 10.46"
Answer: d
Question (general): gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 7 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 3 : 1 , d ) 5 : 2 , e ) 2 : 3
Rationale: "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 7 w 10 + 5 x = 7 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is e"
Answer: e
Question (other): find the ratio in which rice at rs . 7.00 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 6 : 7 , e ) none of these
Rationale: "solution required ratio = 60 : 70 = 6 : 7 answer d"
Answer: d
Question (general): the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 6 ) and ( 9 , 6 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 3 , b ) 2 , c ) 1 / 4 , d ) 3 / 5 , e ) 5 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 3 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 3 ) is 3 / 5 . the answer is d ."
Answer: d
Question (gain): calculate how many seconds it will take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 5 , 6 , 10 and 12 seconds . ?
Options: a ) 61 , b ) 60 , c ) 79 , d ) 70 , e ) 78
Rationale: "lcm of 5 , 6 , 10 and 12 is 60 lcm = 60 answer : b"
Answer: b
Question (physics): a water tank is one - fifth full . pipe a can fill a tank in 15 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the combined rate of filling / emptying the tank = 1 / 15 - 1 / 6 = - 1 / 10 since the rate is negative , the tank will be emptied . a full tank would take 10 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 10 = 2 minutes the answer is a ."
Answer: a
Question (probability): a jar contains 4 black and 3 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
Rationale: "p ( 1 st black , 2 nd white ) = 4 / 7 * 3 / 6 = 4 / 14 ; p ( 1 st white , 2 nd black ) = 3 / 7 * 4 / 6 = 4 / 14 . p = 4 / 14 + 4 / 14 = 4 / 7 . answer : c ."
Answer: c
Question (physics): a can do a work in 3 days . b can do the same work in 6 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 3 b rate = 1 / 6 ( a + b ) rate = ( 1 / 3 ) + ( 1 / 6 ) = 1 / 2 a & b finish the work in 2 days correct option is d"
Answer: d
Question (general): in an it company , there are a total of 100 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 65
Rationale: "you could pick 50 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 55 . c"
Answer: c
Question (other): in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 390 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 84 , b ) 96 , c ) 104 , d ) 112 , e ) 120
Rationale: "the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 390 = 104 the answer is c ."
Answer: c
Question (physics): a train 280 m long , running with a speed of 36 km / hr will pass a tree in
Options: a ) 12 sec , b ) 15 sec , c ) 16 sec , d ) 28 sec , e ) none
Rationale: "sol . speed = ( 36 x 5 / 18 ) m / sec . = 10 m / sec . time taken = ( 280 x 1 / 10 ) sec = 28 sec answer d"
Answer: d
Question (general): for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 4 , then v =
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 4 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 9 the answer is b ."
Answer: b
Question (gain): a person buys an article at rs . 340 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 600 , b ) 882 , c ) 374 , d ) 356 , e ) 521
Rationale: "cost price = rs . 340 profit = 10 % of 340 = rs . 34 selling price = cost price + profit = 340 + 34 = 374 answer : c"
Answer: c
Question (general): on dividing 12401 by a certain number , we get 76 as quotient and 13 as remainder . what is the divisor ?
Options: a ) 163 , b ) 785 , c ) 852 , d ) 456 , e ) 852
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 12401 - 13 ) / 76 = 163 answer ( a )"
Answer: a
Question (general): the average of the marks of 10 students in a class is 40 . if the marks of each student are doubled , find the new average ?
Options: a ) 78 , b ) 56 , c ) 80 , d ) 27 , e ) 40
Rationale: "sum of the marks for the 10 students = 10 * 40 = 400 . the marks of each student are doubled , the sum also will be doubled . the new sum = 400 * 2 = 800 . so , the new average = 800 / 10 = 80 . answer : c"
Answer: c
Question (gain): how much interest will $ 10,000 earn in 9 months at an annual rate of 6 % ?
Options: a ) $ 250 , b ) $ 350 , c ) $ 450 , d ) $ 550 , e ) $ 650
Rationale: "soln : - 9 months = 3 / 4 of year ; 6 % = 6 / 100 = 3 / 50 ; $ 10,000 ( principal ) * 3 / 50 ( interest rate ) * 3 / 4 ( time ) = $ 450 . answer : c"
Answer: c
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 72 and 36 ?
Options: a ) 120 , b ) 150 , c ) 145 , d ) 108 , e ) 112
Rationale: "prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 72 = 2 x 2 x 2 x 3 x 3 gcf = 36 lcm = 72 sum = 108 ans : d"
Answer: d
Question (general): at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 19.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 13.7 , b ) 14.0 , c ) 14.3 , d ) 14.6 , e ) 14.9
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 19.6 x ^ 2 = 1.96 x = 1.4 at 4 : 00 pm , the amount of bacteria was 10 ( 1.4 ) = 14 grams . the answer is b ."
Answer: b
Question (gain): a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 350 . find the total worth of the stock ?
Options: a ) 20029 , b ) 20000 , c ) 20289 , d ) 17500 , e ) 20026
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 350 = > x = 17500 answer : d"
Answer: d
Question (general): farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( e ) ."
Answer: e
Question (physics): if 3 spiders make 3 webs in 3 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 3 webs 3 : 1 1 x 3 x x = 3 x 1 x 3 = > x = 3 answer is e"
Answer: e
Question (physics): three machines , each working at the same constant rate , together can complete a certain job in 18 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 9 days ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 8
Rationale: "rate of one machine = 1 job / ( 18 * 3 ) days let x = number of machines needed to complete the job in 9 days 1 / ( 3 * 18 ) * 9 * x = 1 job x = 6 6 - 3 = 3 answer : a"
Answer: a
Question (general): light glows for every 30 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 142 times , c ) 382 times , d ) 392 times , e ) 165 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 30 ) = 165 times . answer : e"
Answer: e
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 2 : 5 . the first number is :
Options: a ) a ) 33 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 2 : 5 x = 11 = > 3 x = 33 answer : a"
Answer: a
Question (general): a man is 35 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 33 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 35 ) + 2 = 2 ( x + 2 ) x + 37 = 2 x + 4 x = 33 . answer : e"
Answer: e
Question (gain): p and q invested in a business . the profit earned was divided in the ratio 4 : 6 . if p invested rs 60000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 90000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 60000 : q = 4 : 6 ⇒ 60000 × 6 = 4 q ⇒ q = ( 60000 × 6 ) / 4 = 90000 answer is c ."
Answer: c
Question (general): on charlie ' s cell phone plan , he signed up for 8 gb of data per 4 week period . if he went over the 8 gb per month , it would cost him an extra $ 10.00 per gb . in the first week , he used 2 gb ; in the 2 nd week , he used 3 gb ; in the 3 rd week , he used 5 gb ; and in the 4 th week , he used a whopping 10 gb . how much extra did charlie need to pay on his cell phone bill ?
Options: a ) $ 120 , b ) $ 40 , c ) $ 80 , d ) $ 100 , e ) $ 140
Rationale: to determine how much extra he would need to pay , you have to add all 4 weeks of gb usage ( 2 + 3 + 5 + 10 = 20 ) . to determine the extra amount of gb usage , you have to subtract the the original amount of gb ( 8 ) allowed on his plan . 20 - 8 = 12 to determine the extra cost on his cell phone plan , you have to multiply $ 10.00 per extra usage ( 12 ) for a total of $ 120.00 . the correct answer is a
Answer: a
Question (physics): a pipe can fill a cistern in 44 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 4 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 44 minutes 1 / 11 part filled in = 44 * 1 / 11 = 4 minutes answer is a"
Answer: a
Question (general): 0.0003 x 0.3 = ?
Options: a ) 0.0009 , b ) 9.0 e - 05 , c ) 0.09 , d ) 0.009 , e ) 9.0
Rationale: "3 x 3 = 9 . sum of decimal places = 5 0.0003 x 0.3 = 0.00009 answer : option b"
Answer: b
Question (geometry): the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams e ?
Options: a ) e = 16 , b ) e = 32 , c ) e = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Question (physics): a train running at the speed of 54 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 150 meter , b ) 105 meter , c ) 140 meter , d ) 135 meter , e ) none of these
Rationale: "explanation : speed = 54 * ( 5 / 18 ) m / sec = 15 m / sec length of train ( distance ) = speed * time = 15 * 7 = 105 meter option b"
Answer: b
Question (gain): what will be the fraction of 25 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 11 , e ) none of above
Rationale: "explanation : it will 25 * 1 / 100 = 1 / 4 option a"
Answer: a
Question (general): what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 4
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 12 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 4 = 1.25 so biggest is 5 / 4 and smallest is 2 / 3 their difference is 5 / 4 - 2 / 3 = 7 / 12 option c"
Answer: c
Question (geometry): an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 5 : 8
b ) 3 : 2
c ) 6 : 1
d ) 8 : 7
e ) 5 : 6
Rationale: let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 4 y and y . 2 ( 3 x + 2 x ) = 2 ( 4 y + y ) 5 x = 5 y x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 4 y * y = 6 x ^ 2 : 4 y ^ 2 = 6 x ^ 2 : 4 x ^ 2 = 6 : 4 = 3 : 2 the answer is b .
Answer: b
Question (geometry): if the sides of a triangle are 26 cm , 24 cm and 20 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 288 , d ) 266 , e ) 240
Rationale: "the triangle with sides 26 cm , 24 cm and 20 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 20 = 240 cm 2 answer : e"
Answer: e
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 38 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5632 , c ) 6420 , d ) 7500 , e ) 8960
Rationale: "l = ( 48 - 16 ) m = 32 m , b = ( 38 - 16 ) m = 22 m , h = 8 m . volume of the box = ( 32 x 22 x 8 ) m 3 = 5632 m 3 . answer : option b"
Answer: b
Question (physics): it takes 40 identical printing presses 9 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "40 printing presses can do 1 / 9 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 9 = 1 / 12 of the job each hour . the answer is d ."
Answer: d
Question (general): the average age of 15 students of a class is 16 years . out of these , the average age of 6 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 10 years , b ) 11 years , c ) 12 years , d ) 13 years , e ) 14 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 6 + 16 * 9 ) ] = ( 240 - 228 ) = 12 years . answer : c"
Answer: c
Question (geometry): a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 6 inches wide on each side , the total area would have been ( m + 200 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 12 ) ( y + 12 ) = m and so ( 2 ) xy + 12 x + 12 y + 144 = m + 200 let ' s subtract equation ( 1 ) from equation ( 2 ) . 10 x + 10 y + 140 = 200 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."
Answer: b