Cheukting/mathqa huggingface dataset:
Question (physics): a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 30 paise per sq . metre
Options: a ) s 255 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 30 = 25500 p in rs = 25500 / 100 = rs 255 answer : a"
Answer: a
Question (physics): john and andrew can finish the work 9 days if they work together . they worked together for 6 days and then andrew left . john finished the remaining work in another 6 days . in how many days john alone can finish the work ?
Options: a ) 30 days , b ) 60 days , c ) 18 days , d ) 80 days , e ) 90 days
Rationale: amount of work done by john and andrew in 1 day = 1 / 9 amount of work done by john and andrew in 6 days = 6 ã — ( 1 / 9 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 6 days amount of work john can do in 1 day = ( 1 / 3 ) / 6 = 1 / 18 = > john can complete the work in 18 days answer : c
Answer: c
Question (general): of the 14,210 employees of the anvil factory , 3 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 14.3 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . a"
Answer: a
Question (gain): what percent is 400 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 10 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 400 / 1000 ã — 100 = 40000 / 1000 = 40 % answer is b"
Answer: b
Question (general): the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 160 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 184 , b ) 367 , c ) 269 , d ) 177 , e ) 191
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 160 x + ( x - 160 ) = 208 2 x = 368 x = 184 runs answer : a"
Answer: a
Question (general): the total age of a and b is 14 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 14 + b + c = > a ? c = 14 + b ? b = 14 = > c is younger than a by 14 years answer : option d"
Answer: d
Question (gain): a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 22,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 3500 net price of the car in 02 = 18700 + 3500 = $ 22200 correct option : c"
Answer: c
Question (geometry): if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m , what is its area ?
Options: a ) 2520
b ) 2510
c ) 2525
d ) 2025
e ) 2020
Rationale: l - b = 23 . . . ( 1 ) perimeter = 206 2 ( l = b ) = 206 l + b = 103 . . . ( 2 ) ( 1 ) + ( 2 ) 2 l = 23 + 103 = 126 l = 126 / 2 = 63 metre substituting the value of l in ( 1 ) , we get 63 - b = 23 b = 63 - 23 = 40 metre area = lb = 63 ã — 40 = 2520 m 2 answer : a
Answer: a
Question (physics): a boat having a length 5 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 5 x 2 x 0.01 ) m 3 = 0.10 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.10 x 1000 ) kg = 100 kg . answer : a"
Answer: a
Question (physics): if 100 cats kill 100 mice in 100 days , then 4 cats would kill 4 mice in how many days ?
Options: a ) 1 day , b ) 4 days , c ) 40 days , d ) 100 days , e ) 50 days
Rationale: as 100 cats kill 100 mice in 100 days 1 cats kill 1 mouse in 100 days then 4 cats kill 4 mice in 100 days answer : d
Answer: d
Question (general): what is the unit digit in 7105 ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "unit digit in 7105 = unit digit in [ ( 74 ) 26 * 7 ] but , unit digit in ( 74 ) 26 = 1 unit digit in 7105 = ( 1 * 7 ) = 7 answer : c"
Answer: c
Question (other): of the 55 cars on a car lot , 40 have air - conditioning , 25 have power windows , and 12 have both air - conditioning and power windows . how many of the cars on the lot have neither air - conditioning nor power windows ?
Options: a ) 15 , b ) 8 , c ) 10 , d ) 2 , e ) 18
Rationale: total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d
Answer: d
Question (general): what is the remainder when 49 ^ 74 - 5 ^ 74 is divided by 24 ?
Options: a ) 2 , b ) 1 , c ) 0 , d ) 3 , e ) none of these
Rationale: "easiest way for me : 49 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 24 * 2 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : c"
Answer: c
Question (gain): a sum of 13,400 amounts to 14,400 in 2 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 6 % , d ) 4 % , e ) 8 %
Rationale: "d 4 % s . i . = ( 14400 - 13400 ) = 1000 . rate = ( 100 x 1000 ) / ( 13400 x 2 ) % = 4 %"
Answer: d
Question (gain): a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 420 less than the sum lent . what was the sum lent ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "p - 420 = ( p * 5 * 8 ) / 100 p = 700 the answer is c ."
Answer: c
Question (physics): 30 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 20 , b ) 77 , c ) 36 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 30 : : 18 : x [ please pay attention , we have written 27 : 30 rather than 30 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 30 \ times 18 } { 27 } } x = 20 so 20 days will be required to get work done by 27 men . answer : a"
Answer: a
Question (general): if n is a positive integer and n ^ 2 is divisible by 200 , then what is the largest positive integer that must divide n ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 36 , e ) 50
Rationale: 200 = 2 ^ 3 * 5 ^ 2 if 200 divides n ^ 2 , then n must be divisible by 2 ^ 2 * 5 = 20 the answer is c .
Answer: c
Question (gain): john paid a sum of money for purchasing 20 pens , which he recovered in full when he sold 10 of them . what was his percentage of profit or loss per pen ?
Options: a ) 100 % , b ) 150 % , c ) 90 % , d ) 80 % , e ) 95 %
Rationale: a 100 % if the sum he paid whilst purchasing 20 pens = a , then the cost price of each pen = a / 20 . since the amount he got whilst selling 10 pens is also = a then the selling price of each pen = a / 10 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 10 - a / 20 = a / 20 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 20 ) / ( a / 20 ) x 100 = 100 %
Answer: a
Question (general): if x is a positive number and 1 / 3 the square root of x is equal to 3 x , then x =
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 81 , d ) 1 , e ) 81
Rationale: "1 / 3 of sqrt ( x ) = 3 x , which means that sqrt ( x ) = 9 x or x = 81 x ^ 2 - > divide by x 1 = 81 x x = 1 / 81 c ."
Answer: c
Question (general): find the smallest number of 6 digits exactly divisible by 25 , 3545 and 15 .
Options: a ) 100555 , b ) 100775 , c ) 100885 , d ) 100995 , e ) 100665
Rationale: smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 â € “ 800 ) = 100775 . answer is b .
Answer: b
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 21 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 3 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 21 s = ( 27 x + 17 y ) / ( x + y ) = 21 = ( 27 x + 17 y ) / = 21 ( x + y ) = 6 x = 4 y = x / y = 4 / 6 = 2 / 3 i . e 2 : 3 answer : c"
Answer: c
Question (general): in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 %
Rationale: ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a
Answer: a
Question (physics): if two - third of a bucket is filled in 6 minute then the time taken to fill the bucket completely will be .
Options: a ) 90 seconds , b ) 70 seconds , c ) 60 seconds , d ) 9 minutes , e ) 120 seconds
Rationale: "2 / 3 filled in 6 mint 1 / 3 filled in 3 mint thn 2 / 3 + 1 / 3 = 6 + 3 = 9 minutes answer : d"
Answer: d
Question (general): a batsman makes a score of 76 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 36 , b ) 28 , c ) 42 , d ) 45 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 76 = 17 x or x = ( 76 – 48 ) = 28 . answer b"
Answer: b
Question (general): find the remainder of the division ( 2 ^ 14 ) / 7 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "find the pattern of the remainders after each power : ( 2 ^ 1 ) / 7 remainder 2 ( 2 ^ 2 ) / 7 remainder 4 ( 2 ^ 3 ) / 7 remainder 1 - - > this is where the cycle ends ( 2 ^ 4 ) / 7 remainder 2 - - > this is where the cycle begins again ( 2 ^ 5 ) / 7 remainder 4 continuing the pattern to ( 2 ^ 14 ) / 7 gives us a remainder of 4 final answer : d ) 4"
Answer: d
Question (physics): a can do a job in 18 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 12 ½ days , e ) none of these
Rationale: "1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 45 / 4 = 11 ¼ * 2 = 22 ½ days answer : b"
Answer: b
Question (general): barbata invests $ 2600 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1300 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2600 + 0.05 * 2600 + x + 0.08 x = 2600 + x + 0.06 ( 2600 + x ) 0.05 * 2600 + 0.08 x = 0.06 x + 0.06 * 2600 0.02 x = 2600 ( 0.06 - 0.05 ) x = 2600 * 0.01 / 0.02 = 1300 ans : ` ` c ' '"
Answer: c
Question (general): at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses w at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) w = 256 , d ) w = 384 , e ) w = 480
Rationale: "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Question (general): if x is equal to the sum of the integers from 40 to 50 , inclusive , and y is the number of even integers from 40 to 50 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 391 , d ) 501 , e ) 613
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 40 + ( 11 - 1 ) * 1 } = 11 * 45 = 495 = x number of even number = ( 50 - 40 ) / 2 + 1 = 6 = y x + y = 495 + 6 = 501 d"
Answer: d
Question (physics): a man swims downstream 28 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 6.5 , b ) 8.6 , c ) 7.5 , d ) 9.2 , e ) 5.5
Rationale: "28 - - - 4 ds = 7 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 7 + 4 ) / 2 = 5.5 answer : e"
Answer: e
Question (physics): alice and bob drive at constant speeds toward each other on a highway . alice drives at a constant speed of 30 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if alice is 100 km away from bob at 7 am , and also 100 km away from bob at 11 am , then how fast is bob driving ( in kilometers per hour ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: alice and bob complete 200 km / 4 hours = 50 km / hour bob ' s speed is 50 - 30 = 20 km / hour the answer is a .
Answer: a
Question (gain): the calendar of the year 2040 can be used again in the year ?
Options: a ) 2063 , b ) 2061 , c ) 2111 , d ) 2191 , e ) 2068
Rationale: "explanation : given year 2040 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2040 + 28 = 2068 answer : e"
Answer: e
Question (general): how many integers from 1 to 100 exist such that each is divisible by 5 and also has 5 as a digit ?
Options: a ) 10 , b ) 12 , c ) 11 , d ) 20 , e ) 25
Rationale: "5 , 15,25 , 35,40 , 50,55 , 65,75 , 85,95 so there are total 11 such type of numbers . answer : c"
Answer: c
Question (physics): in what time will a train 100 metres long cross an electic pole , if its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) none
Rationale: "sol . speed = [ 144 x 5 / 18 ] m / sec = 40 m / sec . time taken = ( 100 / 40 ) sec = 2.5 sec . answer a"
Answer: a
Question (physics): a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 48 km , d ) 120 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 25 2 x + 3 x = 600 x = 120 km answer is d"
Answer: d
Question (probability): from a group of 4 boys and 4 girls , 4 children are to be randomly selected . what is the probability that 2 boys and 2 girls will be selected ?
Options: a ) 12 / 29 , b ) 14 / 31 , c ) 16 / 33 , d ) 18 / 35 , e ) 20 / 37
Rationale: "the total number of ways to choose 4 children from 8 is 8 c 4 = 70 the number of ways to choose 2 boys and 2 girls is 4 c 2 * 4 c 2 = 6 * 6 = 36 p ( 2 boys and 2 girls ) = 36 / 70 = 18 / 35 the answer is d ."
Answer: d
Question (physics): a wooden box of dimensions 8 m x 3 m x 6 m is to carry rectangularboxes of dimensions 8 cm x 3 cm x 2 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 3000000 , e ) none of these
Rationale: explanation : number = ( 800 * 300 * 600 ) / 8 * 3 * 2 = 3000000 answer : d
Answer: d
Question (physics): a can do a work in 8 days . b can do the same work in 24 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 / 8 b rate = 1 / 24 ( a + b ) rate = ( 1 / 8 ) + ( 1 / 24 ) = 1 / 6 a & b finish the work in 6 days correct option is e"
Answer: e
Question (general): what is the remainder when 50 ! is divided by 16 ^ 8 ? ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "16 raise to 8 = 2 raise to 32 , now highest power of 2 divisible by 50 ! is 25 + 12 + 6 + 3 + 1 = 47 since 2 raise to 47 is divisible , 2 raise to 32 also will be divisible answer : a"
Answer: a
Question (physics): two goods trains each 1250 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 228 , b ) 278 , c ) 48 , d ) 27 , e ) 120
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 1250 + 1250 = 2500 m . required time = 2500 * 6 / 125 = 120 sec . answer : e"
Answer: e
Question (gain): if the cost price of 140 pencils is equal to the selling price of 100 pencils , the gain percent is
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "let c . p . of each pencil be re . 1 . then , c . p . of 100 pencils = rs . 100 ; s . p . of 100 pencils = rs . 140 . gain % = 40 / 100 * 100 = 40 % answer : e"
Answer: e
Question (general): mother , her daughter and her grand child weighs 140 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 44 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 140 kg daughter + child = 60 kg mother = 140 - 60 = 80 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 80 = 16 kg so now daughter = 140 - ( mother + child ) = 140 - ( 80 + 16 ) = 44 kg answer : a"
Answer: a
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 5 : 2 . the first number is :
Options: a ) a ) 3 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 5 : 2 x = 1 = > 3 x = 3 answer : a"
Answer: a
Question (general): a mixture of sand and cement contains , 3 parts of sand and 5 parts of cement . how much of the mixture must be substituted with sand to make the mixture half sand and half cement ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 1 / 8
Rationale: we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c .
Answer: c
Question (general): the sum of ages of 5 children born 3 years different each is 65 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 65 5 x = 35 x = 7 . x + 12 = 7 + 12 = 19 b"
Answer: b
Question (gain): a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 24.00 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 10.00 , d ) $ 9.60 , e ) $ 20.00
Rationale: let the cost price of book = x selling price of book = 24 $ markup % = 20 ( 120 / 100 ) x = 24 = > x = 20 answer e
Answer: e