Cheukting/mathqa huggingface dataset:
Question (general): in the number 10,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d
Answer: d
Question (physics): a clock shows the time as 7 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 40 minutes
Rationale: "there are 11 hours in between 7 a . m . to 6 p . m . 11 * 5 = 55 minutes . answer : b"
Answer: b
Question (general): if mn ≠ 0 and 25 percent of n equals 37 1 / 2 percent of m , what is the value of 12 n / m ?
Options: a ) 18 , b ) 323323 , c ) 8 , d ) 3 , e ) 98
Rationale: given : 25 percent of n equals 37 ( 1 / 2 ) percent of m = > ( 25 / 100 ) * n = ( 75 / 200 ) * m = > 2 n = 3 m . 12 n / m = 6 * 2 n / m = 6 * 3 m / m = 18 . hence a .
Answer: a
Question (gain): if the cost price of 18 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 12.5 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 18 articles = rs . 18 . selling price of 16 articles = rs . 18 therefore , selling price of 18 articles is : - = > 18 / 16 ã — 18 = > 20.25 . therefore , profit = selling price - cost price . = > 20.25 â ˆ ’ 18 = 2.25 . hence , the percentage of profit = profit x 100 / c . p . = > 2.25 / 18 ã — 100 . = > 12.5 % profit . answer : b"
Answer: b
Question (general): the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 22 years , b ) 24 years , c ) 26 years , d ) 28 years , e ) 30 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 240 - 214 ) = 26 years . answer : c"
Answer: c
Question (geometry): if the length of an edge of cube p is thrice the length of an edge of cube q , what is the ratio of the volume of cube q to the volume of cube p ?
Options: a ) 1 / 4
b ) 1 / 5
c ) 1 / 6
d ) 1 / 27
e ) 1 / 9
Rationale: the length of cube q = 1 ; the length of cube p = 3 ; the ratio of the volume of cube q to the volume of cube p = 1 ^ 3 / 3 ^ 3 = 1 / 27 answer : d
Answer: d
Question (general): si on a certain sum of money for 3 yrs at 8 percent / annum is 1 / 2 the ci on rs . 4000 for 2 yrs at 10 percent / annum . the sum placed on si is ?
Options: a ) rs . 1700 , b ) rs . 1720 , c ) rs . 1750 , d ) rs . 1850 , e ) rs . 2000
Rationale: c . i . = rs . 4000 x 1 + 10 2 - 4000 100 = rs . 4000 x 11 x 11 - 4000 10 10 = rs . 840 . sum = rs . 420 x 100 = rs . 1750 . 3 x 8 c
Answer: c
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 22 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 2 , e ) 8
Rationale: "# of red marbles in bag a can be either 2 or 6 . no 2 in the choices , so 6 . d . bag a : r : w : b = 2 : 6 : 9 bag b r : w = 1 : 4 6 x + 4 y = 22 i . e 3 x + 2 y = 11 x has to be odd to make an odd sum from the eq . x = 1 , y = 4 or x = 3 , y = 1 so r can be 2 x i . e 2 or 6 . answer d"
Answer: d
Question (general): what is the sum of the first 23 natural numbers ( starting from 1 ) ?
Options: a ) 256 , b ) 266 , c ) 276 , d ) 286 , e ) 296
Rationale: the sum of n natural numbers = n * ( n + 1 ) / 2 = 23 * 24 / 2 = 276 the answer is c .
Answer: c
Question (physics): in a garden , 26 trees are planted at equal distances along a yard 700 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 28 , c ) 12 , d ) 14 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 700 / 25 = 28 i . e . , distance between two consecutive trees = 28 answer is b ."
Answer: b
Question (general): a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find b ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 7 / 24 ) ã — 8640 ] = rs . 2520 answer : option b"
Answer: b
Question (geometry): what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 20 % ?
Options: a ) 33 % , b ) 44 % , c ) 55 % , d ) 56 % , e ) 73 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 20 % increase a surface = 6 * ( ( 1.2 a ) ^ 2 ) = 6 * 1.44 * a ^ 2 the increase in the surface area = ( 6 * 1.44 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.44 - 1 ) ) / ( 6 * a ^ 2 ) = 1.44 - 1 = 0.44 = 44 % answer : b"
Answer: b
Question (physics): two pipes a and b can separately fill a tank in 12 and 15 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 399 , b ) 540 , c ) 772 , d ) 272 , e ) 121
Rationale: "1 / 12 + 1 / 15 - 1 / x = 1 / 15 x = 12 12 * 45 = 540 answer : b"
Answer: b
Question (geometry): what is the diagonal of a square field whose perimeter is 64 m ?
Options: a ) 15 m , b ) 16 √ 2 m , c ) 20 m , d ) 25 m , e ) 18 m
Rationale: "sol : let the side of the square be xm . therefore , 4 x = 64 x = 16 diagonal of the square is = √ 2 * ( 16 ) ^ 2 = 16 √ 2 answer : b"
Answer: b
Question (gain): the difference between simple interest and compound interest on rs . 1400 for one year at 20 % per annum reckoned half - yearly is :
Options: a ) $ 185.63 , b ) $ 852.36 , c ) $ 875.5 , d ) $ 989.9 , e ) $ 875.8
Rationale: "s . i = [ ( 1400 * 20 * 1 ) / 100 ] = $ 280 . c . i = [ 1400 * ( 1 + ( 5 / 100 ) ^ 2 ) - 1400 ] = $ 1269.8 . difference = ( 1269.8 - 280 ) = $ 989.8 answer ( d )"
Answer: d
Question (geometry): a semicircular shaped window has diameter of 63 cm . its perimeter equals
Options: a ) 162
b ) 766
c ) 298
d ) 277
e ) 198
Rationale: explanation : perimeter of window = { \ color { blue } \ pi } r + 2 r = [ { ( 22 / 7 ) * ( 63 / 2 ) } + 63 ] = 99 + 63 = 162 cm answer : a ) 162
Answer: a
Question (gain): by selling 100 pens , a trader gains the cost of 30 pens . find his gain percentage ?
Options: a ) 30 % , b ) 33 % , c ) 31 % , d ) 32 % , e ) 34 %
Rationale: "let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 30 pens = rs . 30 profit % = 30 / 100 * 100 = 30 % answer : a"
Answer: a
Question (general): out of 3 consecutive odd numbers 11 times the first number is equal to addition of thrice the third number and adding 16 to 4 times the second . what is the first number ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: description : = > 11 x = 4 ( x + 2 ) + 16 + 3 ( x + 4 ) = > 11 x = 7 x + 36 = > 4 x = 36 x = 9 answer e
Answer: e
Question (gain): working together at their respective constant rates , machine a and machine b can produce 1600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1600 unit total would it produce ?
Options: a ) 25 , b ) 33 , c ) 50 , d ) 67 , e ) 75
Rationale: 1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1600 units in 24 hrs , so it can produce 1600 * 8 / 24 = 533.33 units is 8 hrs . 533.33 is 33.33 % of 1600 . b is the answer
Answer: b
Question (general): according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 26 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 14.44 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 26 = 58 - - > c = 5 / 9 * 26 = 14.44 . increase = 14.44 degrees . answer : b ."
Answer: b
Question (gain): if price of t . v set is reduced by 20 % , then its sale increases by 80 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 20 + 80 + ( - 20 * 80 ) / 100 = - 20 + 80 - 16 = 44 answer : a"
Answer: a
Question (physics): 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 8 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 9
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 16 m / h - - > 8 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 8 ^ 2 d ^ 2 = 80 = ~ 9 answer option e"
Answer: e
Question (general): the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?
Options: a ) 23 , b ) 25 , c ) 30 , d ) 22 , e ) 40
Rationale: "let the average of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer a"
Answer: a
Question (probability): tom and marry each have a bag of marbles , each of which contains 4 red marbles , 10 blue marbles , and 6 yellow marbles . if tom and marry each select one marble from their respective bags , what is the probability that either tom or marry select a blue marble ?
Options: a ) 1 / 7 , b ) 2 / 4 , c ) 3 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: probability that either selects a red marble , p ( either ) = 1 - probability that neither selects a blue marble , p ( neither ) probability that tom selects non blue = 10 c 1 / 20 c 1 = 1 / 2 probability that marry selects non blue = 10 c 1 / 20 c 1 = 1 / 2 = > p ( either ) = 1 - ( 1 / 2 * 1 / 2 ) = 1 - 1 / 4 = 3 / 4 . c )
Answer: c
Question (physics): if 7 cats can kill 7 rats in 7 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 7 minutes , d ) 8 minutes , e ) 9 minutes
Rationale: "it will take 7 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 7 minutes , so 100 cats can kill 100 rats in 7 minutes answer c"
Answer: c
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 20.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?
Options: a ) 3,108 , b ) 3,100 , c ) 3,108 , d ) 3,540 , e ) 3,256
Rationale: to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 20.95 * 14 = 293.30 $ amount remaining = 300 - 293.30 = 6.7 $ total number of hot dogs bought in 20 - pack = 3.05 * 2 = 6.10 $ amount remaining = 6.70 - 6.10 = 0.6 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 14 + 20 * 2 = 3,540 answer d
Answer: d
Question (general): a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 200 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 500 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 200 = 500 answer : b
Answer: b
Question (general): the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 76 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 5 % , d ) 17 % , e ) 19 %
Rationale: quantity x rate = price 1 x 1 = 1 0.76 x 1.25 = 0.95 decrease in price = ( 0.05 / 1 ) × 100 = 5 % c )
Answer: c
Question (general): if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability r that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Question (general): 0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance x between any two of the tick marks ?
Options: a ) 1 / 70 , b ) 1 / 35 , c ) 2 / 35 , d ) 1 / 12 , e ) 1 / 7
Rationale: divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . x = 1 / 35 answer is b .
Answer: b
Question (geometry): find the area of a parallelogram with base 21 cm and height 11 cm ?
Options: a ) 231 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2
Rationale: "area of a parallelogram = base * height = 21 * 11 = 231 cm 2 answer : a"
Answer: a
Question (gain): a cycle is bought for rs . 1120 and sold for rs . 1200 , find the gain percent ?
Options: a ) 7 % , b ) 2 % , c ) 6 % , d ) 1 % , e ) 8 %
Rationale: "explanation : 1120 - - - - 80 100 - - - - ? = > 7 % answer : a"
Answer: a
Question (gain): a trader bought a car at 20 % discount on its original price . he sold it at a 70 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 72 % , c ) 12 % , d ) 82 % , e ) 36 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 170 / 100 ) = 136 100 - 136 = 36 % answer : e"
Answer: e
Question (physics): a boat having a length 9 m and breadth 3 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 ) 120 kg , c ) 189 kg , d ) 180 kg , e ) 270 kg
Rationale: "volume of water displaced = ( 9 x 3 x 0.01 ) m 3 = 0.27 m 3 . mass of man = volume of water displaced x density of water = ( 0.27 x 1000 ) kg = 270 kg . answer : e"
Answer: e
Question (gain): what annual payment will discharge a debt of rs . 1030 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 553.94 , b ) 551.25 , c ) 534.33 , d ) 543.33 , e ) 646.33
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1030 820 x + 1030 * 441 x = 553.94 so , value of each installment = rs . 553.94 answer : option a"
Answer: a
Question (gain): in a factory , there are 90 % technicians and 10 % non - technicians . if the 90 % of the technicians and 10 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 82 % , e ) 42 %
Rationale: "total = 100 t = 90 nt = 10 90 * ( 10 / 100 ) = 910 * ( 90 / 100 ) = 9 9 + 9 = 18 = > 100 - 18 = 82 % answer : d"
Answer: d
Question (physics): how many seconds will a 450 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 60 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 60
Rationale: explanation : speed of train relatively to man = ( 60 - 6 ) km / hr = 54 km / hr = ( 54 x 5 / 18 ) m / sec = 15 m / sec time taken to pass the man = ( 450 / 15 ) sec = 30 sec . answer : b
Answer: b
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 20 percent on food , and 20 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 25 , e ) 15
Rationale: "assume she has $ 200 to spend . tax clothing = 60 % = $ 120 = $ 12.00 food = 20 % = $ 40 = $ 0.00 items = 20 % = $ 40 = $ 8.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer a"
Answer: a
Question (other): 90 kg of an alloy a is mixed with 140 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 4 and alloy b has tin and copper in the ratio 2 : 5 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 95.4 kg , c ) 117.5 kg , d ) 91.4 kg , e ) 92 kg
Rationale: "quantity of tin in 90 kg of a = 90 * 4 / 7 = 51.4 kg quantity of tin in 140 kg of b = 140 * 2 / 7 = 40 kg quantity of tin in the new alloy = 51.4 + 40 = 91.4 kg answer is d"
Answer: d
Question (geometry): a rectangular garden is to be twice as long as it is wide . if 180 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 180 so , 2 ( l + b ) = 180 or , l + b = 90 now use the answer options ( given length ; breath will be half the length ) ( a ) 60 l = 60 ; b = 30 l + b = 90 ( b ) 70 l = 70 ; b = 35 l + b = 105 ( c ) 80 l = 80 ; b = 40 l + b = 120 ( d ) 90 l = 90 ; b = 45 l + b = 135 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( a )"
Answer: a
Question (general): what is the value of 3 x ^ 2 − 1.8 x + 0.3 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.3 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.3 = 0 + 0.3 = 0.3 answer : c"
Answer: c
Question (physics): three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 20 minutes . if a , b & c are kept open successively for 1.5 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 2 hours 15 min , e ) 3 hours
Rationale: "in three minute 1 / 20 + 1 / 30 - 1 / 20 = 2 / 60 = 1 / 30 part is filled 4.5 min - - - - - - - - 1 / 30 parts x min - - - - - - - - - 1 part ( full ) x = 135 min = 2 hours 15 min answer : d"
Answer: d
Question (physics): a train passes a station platform in 30 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 120 m , b ) 240 m , c ) 168 m , d ) 75 m , e ) 60 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 30 = 15 = > x = 60 m answer : e"
Answer: e
Question (geometry): if the sides of a cube are in the ratio 9 : 7 . what is the ratio of their diagonals ?
Options: a ) 4 : 3 , b ) 16 : 9 , c ) 9 : 7 , d ) 3 : 4 , e ) 3 : 8
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 7 d 1 : d 2 = 9 : 7 where √ 3 cancelled both side answer : c"
Answer: c
Question (gain): last year elaine spent 20 % of her annual earnings on rent . this year she earned 20 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 185.5 , b ) 180.0 , c ) 167.5 , d ) 172.5 , e ) 177.5
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 20 % more , or $ 120 she would ' ve spent 30 % of this on rent , or $ 36 do $ 36 / $ 20 this will give you 180 % b is the correct answer ."
Answer: b
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is c ' s share ?
Options: a ) $ 1200 , b ) $ 1600 , c ) $ 1800 , d ) $ 2000 , e ) $ 2400
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 c ' s share = 4 x = 4 * $ 500 = $ 2000 the answer is d ."
Answer: d
Question (physics): two bullet train s 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.24 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 200 ) m = 340 m . required time = 340 x 9 / 250 = 54 / 5 = 12.24 sec . answer b
Answer: b
Question (general): in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.5 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 2000
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 2000 : ri = 60 , ro = 90 thus ans : e"
Answer: e