Cheukting/mathqa huggingface dataset:
Question (physics): pipe a can fill a tank in 16 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 ) 21
Rationale: "let the pipe b be closed after x minutes . 30 / 16 - x / 24 = 1 = > x / 24 = 30 / 16 - 1 = 14 / 16 = > x = 14 / 16 * 24 = 21 . answer : e"
Answer: e
Question (general): what is the units digit of ( 147 ^ 25 ) ^ 50 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 25 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 50 has the form 4 n + 2 , so the units digit is 9 . the answer is e .
Answer: e
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 33 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 65 %
Rationale: "x discount on pony jeans , ( 0.33 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.33 - x ) + 2 * 18 x = 9 - - > x = 0.65 = 65 % answer : e ."
Answer: e
Question (physics): a train travelling at a speed of 75 mph enters a tunnel 31 / 2 miles long . the train is 1 / 4 mile long . how long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 2.5 min , b ) 3 min , c ) 3.2 min , d ) 3.5 min , e ) 4 min
Rationale: total distance = ( 7 / 2 + 1 / 4 ) miles = 15 / 4 miles time taken = 15 / 4 * 75 hrs = 1 / 20 hrs = 3 min answer b
Answer: b
Question (other): the value of log 343 7 is
Options: a ) 1 / 3 , b ) - 3 , c ) - 1 / 3 , d ) 3 , e ) 0.3
Rationale: "solution let log 3437 = n . then , 343 n = 7 = ( 73 ) n = 7 . ‹ = › 3 n = 1 ‹ = › n = 1 / 3 . log 343 7 = 1 / 3 . answer a"
Answer: a
Question (gain): a watch was sold at a loss of 16 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 700 , b ) 882 , c ) 799 , d ) 778 , e ) 901
Rationale: "84 % 104 % - - - - - - - - 20 % - - - - 140 100 % - - - - ? = > rs . 700 answer : a"
Answer: a
Question (general): robin ' s average ( arithmetic mean ) test score on 9 tests is 82 . what must be robin ' s score on a 10 th test for his average score on the 10 tests to be 83 ?
Options: a ) 92 , b ) 82 , c ) 72 , d ) 62 , e ) 52
Rationale: ( 9 * 82 + x ) / 10 = 83 x = ( 10 * 83 ) - ( 9 * 82 ) x = 830 - 738 total score required 830 - 738 = 92 correct answer is a
Answer: a
Question (other): the simple form of the ratio 9 / 8 : 3 / 4 is ?
Options: a ) 5 : 8 , b ) 5 : 5 , c ) 5 : 9 , d ) 3 : 2 , e ) 5 : 1
Rationale: "9 / 8 : 3 / 4 = 3 : 2 answer : d"
Answer: d
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 210 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 782 , c ) 278 , d ) 310 , e ) 881
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 210 ) / 26 = 20 x = 310 m . answer : d"
Answer: d
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 220 , what were her original savings ?
Options: a ) $ 900 , b ) $ 880 , c ) $ 1000 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 220 . so 1 / 4 of her savings is $ 220 . so her original savings are 4 times $ 220 = $ 880 correct answer b"
Answer: b
Question (general): i have only 1 $ and 2 $ note . i want to give 95 $ to john . how many maximum number of 2 $ note i need ?
Options: a ) 39 , b ) 95 , c ) 47 , d ) 55 , e ) 76
Rationale: check whether 95 is divisible by 2 then that is maximum no of 2 $ note else check next maximum term before 95 so 94 / 2 = 47 ans is c
Answer: c
Question (general): if 10,000 microns = 1 decimeter , and 10,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 0.01 , b ) 1 , 000,000 , c ) 0.001 , d ) 1,000 , e ) 1.0 e - 05
Rationale: given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b
Answer: b
Question (physics): a train 125 m long crosses a platform 125 m long in 14 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 64 kmph , c ) 54 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 125 + 125 = 250 t = 14 s = 250 / 14 * 18 / 5 = 64 kmph answer : b"
Answer: b
Question (gain): salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 12 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 50 % , b ) 40 % , c ) 30 % , d ) 20 % , e ) 10 %
Rationale: let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.12 0.2 x = 0.02 x = 0.1 = 10 % the answer is e .
Answer: e
Question (gain): what is the compound interest paid on a sum of rs . 3500 for the period of 2 years at 10 % per annum .
Options: a ) 630 , b ) 735 , c ) 825 , d ) 600 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3500 = 3500 * ( 21 / 100 ) = 735 answer b"
Answer: b
Question (general): a grand father has 3 grand children . age difference of two children among them is 3 . eldest child age is 3 times the youngest child ’ s age and the eldest child age is two year more than the sum of age of other two children . what is the age of the eldest child ?
Options: a ) 22 , b ) 15 , c ) 28 , d ) 26 , e ) 9
Rationale: as the eldest son ' s age is 3 times that of the youngest , eldest son ' s age should be a multiple of 3 . from the given options take 15 as the eldest son ' s age . then youngest son ' s age becomes 5 . but eldest sons age is 2 more than the sum of the remaining two sons . so sum of the remaining two sons is 13 . so the age of the middle son is 13 - 5 = 8 . which satisfies another condition in the question that the difference between the two sons age is 3 . so answer is 15 . answer : b
Answer: b
Question (gain): rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 87 . how much was lent at 5 % ?
Options: a ) 228 , b ) 299 , c ) 300 , d ) 500 , e ) 188
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 87 5 x / 100 + 90 â € “ 6 x / 100 = 87 x / 100 = 3 = > x = 300 answer : c"
Answer: c
Question (general): what is the lowest positive integer that is divisible by 4 through 7 , inclusive ?
Options: a ) 77 , b ) 270 , c ) 1600 , d ) 840 , e ) 980
Rationale: "the integer should be divisible by : 4 , 5 , 6 and 7 . the least common multiple of these integers is lcm = 4 * 5 * 6 * 7 = 840 answer : d"
Answer: d
Question (other): of the people who responded to a market survey , 60 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 3 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 150 , c ) 240 , d ) 360 , e ) 480
Rationale: "ratio = 3 : 1 = > 3 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 60 = > 3 x = 60 = > x = 20 hence total no . of respondents = 60 + 20 = 80 hence a is the answer ."
Answer: a
Question (general): the average of 50 numbers id 38 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 11.3 , e ) 37.5
Rationale: "explanation : total of 50 numbers = ( 50 × 38 ) = 1900 ( 50 × 38 ) = 1900 total of 48 numbers = ( 1900 - ( 45 + 55 ) ] = 1800 required average = 180048 = 2256 = 37.5 answer : e"
Answer: e
Question (probability): when fair coin is tossed 9 times find the probability of getting head at least once .
Options: a ) 1 / 512 , b ) 511 / 512 , c ) 9 / 512 , d ) 503 / 51 , e ) 503 / 510
Rationale: 1 - 1 / 2 ^ 9 = 1 - 1 / 512 = 511 / 512 answer : b
Answer: b
Question (physics): an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets water in at the rate of 16 litres / min then outlet pipe would take 8 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 21600 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 16 litres / min , or 16 * 60 = 960 liters / hour ; net outflow rate when both pipes operate would be x - 960 liters / hour . capacity of the tank = x * 10 hours = ( x - 960 ) * ( 10 + 8 ) hours 10 x = ( x - 960 ) * 18 - - > x = 2160 - - > capacity = 10 x = 21600 liters . answer : c ."
Answer: c
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 50 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 156 , e ) 210
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,5 * 1 / 3 * x 120 = 13 / 30 x x = 276 276 - 120 = 156 answer d"
Answer: d
Question (general): which number need to add to 1782452 to get a number exactly divisible by 92 ?
Options: a ) 44 , b ) 43 , c ) 42 , d ) 41 , e ) 48
Rationale: "1782452 / 92 = 19374 and reminder = 44 . 92 - 44 = 48 so , the next number divisible by 92 is 48 places in front of 1782452 which means 48 + 1782452 = 1782500 48 should be added to 1782452 e"
Answer: e
Question (physics): a boat takes 19 hours for travelling downstream fro poin a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 180 km , b ) 190 km , c ) 220 km , d ) 230 km , e ) none
Rationale: sol . speed downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed upstream = ( 14 - 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 ⇔ x / 18 + x / 20 = 19 ⇒ x = 180 km . answer a
Answer: a
Question (general): city x has a population 7 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 14 : 1 , e ) 18 : 1
Rationale: x = 7 y , y = 2 * z x : y , y : z 7 : 1 , 2 : 1 14 : 2 , 2 : 1 so , x : z = 14 : 1 ( d )
Answer: d
Question (general): in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the sixth row ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 6 th row is 1 + 3 ( 5 ) = 16 the answer is b ."
Answer: b
Question (geometry): in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 20 feet between each tree . how many trees can be planted if the road is 148 feet long ?
Options: a ) 8
b ) 9
c ) 10
d ) 11
e ) 16
Rationale: let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 20 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 20 feet spaces will be t - 1 . then , the length of sidewalk required for 20 feet spaces will be 20 * ( t - 1 ) it is given that total length of sidewalk is 148 feet . or 20 ( t - 1 ) + t = 148 or 20 t - 20 + t = 148 or 21 t = 168 or t = 8 answer : - a
Answer: a
Question (other): 20 balls are numbered 1 to 20 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 7 / 30 , b ) 3 / 14 , c ) 9 / 38 , d ) 4 / 21 , e ) 5 / 26
Rationale: "p ( 1 st ball is even ) = 10 / 20 p ( 2 nd ball is also even ) = 9 / 19 p ( both balls are even ) = 10 / 20 * 9 / 19 = 9 / 38 the answer is c ."
Answer: c
Question (physics): how long does a train 120 m long travelling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 17.4 sec
Rationale: "e 17.4 sec d = 120 + 170 = 290 m s = 60 * 5 / 18 = 50 / 3 t = 290 * 3 / 50 = 17.4 sec answer is e"
Answer: e
Question (probability): the probability that a number selected at random from first 50 natural numbers is a composite number is
Options: a ) 21 / 25 , b ) 17 / 25 , c ) 4 / 25 , d ) 8 / 25 , e ) 10 / 25
Rationale: "the number of exhaustive events = 50 c 1 = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . therefore , required probability = 34 / 50 = 17 / 25 . answer : b"
Answer: b
Question (physics): the speed of a train is 90 kmph . what is the distance covered by it in 15 minutes ?
Options: a ) 15 , b ) 66 , c ) 22.5 , d ) 52 , e ) 42
Rationale: "90 * 15 / 60 = 22.5 kmph answer : c"
Answer: c
Question (general): 225 , or 15 ^ 2 , is the first perfect square that begins with two 2 s . what is the sum of the digits of the next perfect square to begin with two 2 s ?
Options: a ) 9 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: because 16 ^ 2 = 256 , y the next perfect square to begin with two 2 s can not be 3 - digit . let ' s try 4 - digit . 40 ^ 2 = 1600 and 50 ^ 2 = 2500 . so , if there is a 4 - digit perfect square to begin with two 2 s it must be between 41 ^ 2 and 49 ^ 2 . test the middle number 45 ^ 2 = 2025 . test larger number : 46 ^ 2 = 2116 . test next number : 47 ^ 2 = 2209 . bingo ! the sum of the digits = 2 + 2 + 0 + 9 = 13 . answer : c .
Answer: c
Question (geometry): what is the angle between the two hands of a clock when time is 8 : 30
Options: a ) 15 degree , b ) 45 degree , c ) 55 degree , d ) 75 degree , e ) 65 degree
Rationale: "use the formula i . e 1 / 2 ( 60 h - 11 m ) / / h - hour and m - minute 1 / 2 ( 60 * 8 - 11 * 30 ) 1 / 2 ( 150 ) 75 degree answer : d"
Answer: d
Question (physics): two trains are moving at 80 kmph and 70 kmph in opposite directions . their lengths are 150 m and 100 m respectively . the time they will take to pass each other completely is ?
Options: a ) 6 sec , b ) 7 sec , c ) 7 2 / 2 sec , d ) 8 sec , e ) 9 sec
Rationale: 70 + 80 = 150 * 5 / 18 = 125 / 3 mps d = 150 + 100 = 250 m t = 250 * 3 / 125 = 6 sec answer : a
Answer: a
Question (general): if x > 0 , x / 50 + x / 25 is what percent of x ?
Options: a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 25 = 2 + 4 = 6 6 is 6 % of 100 . answer : a
Answer: a
Question (general): the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) 2012
Rationale: let the commodity p costs 40 paise more than the commodity q after n years . price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 = > n = 2.5 / . 25 = 10 = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 answer : d
Answer: d
Question (physics): a train 110 m long running at 52 kmph crosses a platform in 30 sec . what is the length of the platform ?
Options: a ) 287 , b ) 398 , c ) 323 , d ) 245 , e ) 267
Rationale: "d = 52 * 5 / 18 = 30 = 433 â € “ 110 = 323 answer : c"
Answer: c
Question (geometry): when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 1 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 1 then x = 1 / 1000 = 0.001 . the answer is c"
Answer: c
Question (physics): the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 90 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 2.5 hours for the trip . dan needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour . the answer is d ."
Answer: d
Question (gain): a and b began business with rs . 2000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .
Options: a ) 175 , b ) 288 , c ) 277 , d ) 877 , e ) 361
Rationale: "( 2 * 8 + 1 * 4 ) : ( 4 * 8 + 5 * 4 ) 5 : 13 5 / 18 * 630 = 175 answer : a"
Answer: a
Question (probability): a fair coin is tossed 9 times . what is the probability of getting more heads than tails in 9 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Question (physics): if 18 bindres bind 900 books in 10 days , how many binders will be required to bind 660 books in 12 days ?
Options: a ) 71 , b ) 12 , c ) 18 , d ) 11 , e ) 29
Rationale: explanation : let the required no of binders be x . less books , less binders ( direct proportion ) more days , less binders ( indirect proportion ) \ inline \ fn _ jvn \ left . \ begin { matrix } books \ : 900 : 600 \ \ days \ : \ : 12 : 10 \ end { matrix } \ right \ } : : 18 : x \ inline \ fn _ jvn \ therefore \ inline \ fn _ jvn ( 900 \ times 12 \ times x ) = ( 600 \ times 10 \ times 18 ) \ inline \ fn _ jvn \ leftrightarrow x = \ inline \ fn _ jvn \ frac { 600 \ times 10 \ times 18 } { 900 \ times 12 } = 11 answer : d
Answer: d
Question (general): if a ã — b = 2 a - 3 b + ab , then 1 ã — 2 + 2 ã — 1 is equal to :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: explanation : 1 ã — 2 + 2 ã — 1 = ( 2 ã — 1 - 3 ã — 2 + 1 ã — 2 ) + ( 2 ã — 2 - 3 ã — 1 + 2 ã — 1 ) = ( 2 - 6 + 2 + 4 - 3 + 2 ) = 1 . answer : a
Answer: a
Question (physics): when a train travels at a speed of 80 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 25 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: "let x be the time reached with the speed 80 km / h 50 km / h - - - - > x + 15 distance is equal so 80 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 80 x = 50 x + 750 so the would be in km and x = 25 answer : a"
Answer: a
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 4 seconds . find the length of the train .
Options: a ) 66.67 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 4 = 66.67 meter . answer : a"
Answer: a
Question (general): the average marks of a class of 30 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 82.5 , b ) 52.9 , c ) 52.2 , d ) 52.5 , e ) 52.7
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1200 + 3000 = 4200 average marks of all the students = 4200 / 80 = 52.5 answer : d"
Answer: d
Question (physics): 75 men working 8 hours per day dig 50 m deep . how many extra men should be put to dig to a depth of 70 m working 6 hours per day ?
Options: a ) 75 , b ) 45 , c ) 55 , d ) 65 , e ) 35
Rationale: ( 75 * 8 ) / 50 = ( x * 6 ) / 70 = > x = 140 140 â € “ 65 = 65 answer : d
Answer: d
Question (general): on a certain date , pat invested $ 5,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 20,000 , in how many years , the total value of the investment plus interest will increase to $ 30,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 5,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 5 , 000.00 took to double 10 , 000.00 . again , 10 , 000.00 took to double 20 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 20 , 000.00 takes the same ( 72 / x ) no of years to double 30 , 000.00 . 72 / x = 6 years . so altogather : 5,000 - 10,000 = 6 years 10,000 - 20,000 = 6 years 20,000 - 30,000 = 3 years answer a 15 years .
Answer: a
Question (general): a clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 50 percent of what the collector had paid . the shop then sold the clock again at a profit of 80 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 100 , for how much did the shop sell the clock the second time ?
Options: a ) $ 270 , b ) $ 250 , c ) $ 240 , d ) $ 220 , e ) $ 200
Rationale: original price = x sold to collector at 1.2 x re - buy price = 1.2 x * 0.5 = 0.6 x therefore , x - 0.6 x = 100 ; x = 250 second selling price = 1.8 * 0.6 * 250 = 270 answer : a
Answer: a
Question (general): the average of first six prime numbers greater than 3 is ?
Options: a ) 16 , b ) 10 , c ) 12 , d ) 19 , e ) 17.8
Rationale: "5 + 7 + 11 + 13 + 17 + 19 = 72 / 6 = 12 answer : c"
Answer: c