Cheukting/mathqa huggingface dataset:
Question (gain): at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 55 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 55 = 25 + b + 25 b / 100 b = 24 answer ( a )"
Answer: a
Question (other): a marketing firm determined that , of 200 households surveyed , 80 used neither brand e nor brand b soap , 60 used only brand e soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap e and soap b ( d ) 40
Answer: d
Question (general): two employees x and y are paid a total of rs . 570 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 259 , b ) s . 289 , c ) s . 299 , d ) s . 300 , e ) s . 389
Rationale: let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 570 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 570 ⇒ y [ 12 / 10 + 1 ] = 570 ⇒ 22 y / 10 = 570 ⇒ 22 y = 5700 ⇒ y = 5700 / 22 = rs . 259 a )
Answer: a
Question (physics): a train 390 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 52 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 390 × 2 / 15 ) sec = 52 sec answer : e"
Answer: e
Question (general): if 90 % of a = 30 % of b and b = x % of a , then the value of x is ?
Options: a ) 800 , b ) 300 , c ) 700 , d ) 400 , e ) none of these
Rationale: "0.9 a = 0.3 b so b = 3 a means 300 % of a answer : b"
Answer: b
Question (gain): data sufficiency question : if solution ( x ) with alcohol ( 14 % ) and solution ( y ) with alcohol ( 20 % ) mixed together to form 24 liters of mixture .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 3
Rationale: explanation : let a liters of first solution , and ' b ' liters of second solution has been taken . so using weighted average formula = n 1 × a 1 + n 2 × a 2 n 1 + n 2 n 1 × a 1 + n 2 × a 2 n 1 + n 2 = n 1 × 14 + n 2 × 20 n 1 + n 2 = 15 n 1 × 14 + n 2 × 20 n 1 + n 2 = 15 ⇒ n 1 = 5 n 2 ⇒ n 1 n 2 = 51 ⇒ n 1 = 5 n 2 ⇒ n 1 n 2 = 51 as total volume was given as 24 liters , first solution = 16 × 24 = 416 × 24 = 4 so statement 1 is sufficient . answer : a
Answer: a
Question (general): the average of 6 number is 3.95 . the average of two of them is 3.8 , while the average of the other two is 3.85 . what is the average of the remaining two number ?
Options: a ) 4.5 , b ) 4.2 , c ) 4.7 , d ) 4.8 , e ) none of these
Rationale: solution : sum of the remaining two numbers = ( 3.95 × 6 ) - [ ( 3.8 × 2 ) + ( 3.85 × 2 ) ] = 23.70 - ( 7.6 + 7.7 ) = 23.70 - 15.3 = 8.4 . ∴ required average = 8.4 / 2 = 4.2 answer b
Answer: b
Question (general): a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points q that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points q for 12 th player is 100 - 77 = 23 . answer : e .
Answer: e
Question (general): jill has 7 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 14
Rationale: let the number of each size of jar = w then 1 / 4 w + 1 / 2 w + w = 7 1 3 / 4 w = 7 w = 4 the total number of jars = 3 w = 12 answer : d
Answer: d
Question (general): the sum of ages of 5 children born 2 years different each is 50 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 14 , c ) 16 , d ) 17 , e ) 18
Rationale: let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 30 x = 6 x + 8 = 6 + 8 = 14 answer : b
Answer: b
Question (gain): vijay sells a cupboard at 14 % below cost price . had he got rs . 2086 more , he would have made a profit of 14 % . what is the cost price of the cupboard ?
Options: a ) 7458 , b ) 7456 , c ) 7450 , d ) 7454 , e ) 7453
Rationale: "explanation : cost price = 2086 / ( 0.14 + 0.14 ) = 2086 / 0.28 = rs . 7450 answer : c"
Answer: c
Question (general): we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "m + h = 80 h = 80 - m 4 m + 5 h = 390 4 m + 5 * ( 80 - m ) = 390 m = 10 the answer is a ."
Answer: a
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 132 mins , e ) 130 mins
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 36 = > 4 / x = 1 / 36 x = 36 â ˆ — 4 = 144 mins answer is a"
Answer: a
Question (physics): a hall 36 m long and 15 m broad is to be paved with stones , each measuring 6 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 60 * 50 ) therefore , number of stones = ( 3600 * 1500 / 60 * 50 ) = 1800 answer : b"
Answer: b
Question (physics): walking with 4 / 5 of my usual speed , i arrive at the bus stop 10 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "let t = usual time = distance / usual speed t + 10 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 40 the answer is c ."
Answer: c
Question (physics): eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 480 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 32 / 15 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 5 / 3
Rationale: "distance traveled by eddy = 480 km time taken by eddy = 3 hours average speed of eddy = 480 / 3 = 160 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 160 / 75 = 32 / 15 answer a"
Answer: a
Question (general): a pharmaceutical company received $ 2 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 108 ) / ( 2 / 20 ) = 30 / 54 = 55,5 % it means that 9 / 108 represents only 83,3 % . therefore a decrease of 15 % . answer b"
Answer: b
Question (physics): ram , who is half as efficient as krish , will take 24 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "answer ram takes 24 days to complete the task , if he works alone . krish is twice as efficient as ram is . so , working alone , krish will take half the time to complete the task . i . e . , 12 days . ram will complete 1 / 24 th of the task in a day . krish will complete 1 / 12 th of the task in a day . when they work together , they will complete 1 / 24 + 1 / 12 = 1 / 8 th of the task in a day . therefore , when they work together they will complete the task in 8 days . choice c"
Answer: c
Question (gain): i bought two books ; for rs . 540 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 280 , c ) 189 , d ) 278 , e ) 315
Rationale: "x * ( 85 / 100 ) = ( 540 - x ) 119 / 100 x = 315 answer : e"
Answer: e
Question (gain): a sum of money deposited at c . i . amounts to rs . 1980 in 3 years and to rs . 2492 in 4 years . find the rate percent ?
Options: a ) 30 % , b ) 10 % , c ) 25 % , d ) 19 % , e ) 50 %
Rationale: "1980 - - - 512 100 - - - ? = > 25 % answer : c"
Answer: c
Question (physics): what is the greatest possible length which can be used to measure exactly the lengths 10 m , 14 m 50 cm and 20 m 40 cm cm ?
Options: a ) 20 cm , b ) 10 cm , c ) 25 cm , d ) 50 cm , e ) 28 cm
Rationale: "required length = hcf of 1000 cm , 1450 cm , 2040 cm = 10 cm answer is b"
Answer: b
Question (gain): an alloy weighing 18 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 90 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 18 * ( 70 / 100 ) = 12.6 ounces . now we add x ounces of pure gold to make it 90 % gold . so 12.6 + x = ( 24 + x ) * 90 / 100 = > x = 90 . answer is b ."
Answer: b
Question (physics): john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 55 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 55 = > v = 50 ( option c ) ."
Answer: c
Question (physics): a train 400 m long can cross an electric pole in 40 sec and then find the speed of the train ?
Options: a ) 36 kmph , b ) 40 kmph , c ) 42 kmph , d ) 45 kmph , e ) 38 kmph
Rationale: "length = speed * time speed = l / t s = 400 / 40 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : a"
Answer: a
Question (physics): a train 220 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is :
Options: a ) 41 , b ) 40.6 , c ) 40.8 , d ) 42 , e ) 42.6
Rationale: "speed of the train relative to man = 220 / 20 = 11 m / sec . = 11 x 18 / 5 km / hr = 198 / 5 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 198 / 540.6 km / hr . answer : b"
Answer: b
Question (general): the price of a certain painting increased by 10 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 95 % , d ) 93.5 % , e ) 90 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 10 = 110 price at the end of year 2 = 110 - 110 * 0.15 = 110 * 0.85 = 93.5 hence required answer = ( 93.5 / 100 ) * 100 % = 93.5 % answer is d ."
Answer: d
Question (physics): two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 16 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 16 ) m = 360 m . answer e"
Answer: e
Question (gain): a and b began business with rs . 7000 and rs . 15000 after 6 months , a advances rs . 3000 and b withdraws rs . 5000 . at the end of the year , their profits amounted to rs . 2940 find the share of a and b respectively .
Options: a ) 1100 , 1750 , b ) 1140 , 1800 , c ) 940 , 2000 , d ) 1190 , 1750 , e ) 1000 : 1690
Rationale: "7 * 6 + 10 * 6 ) : ( 15 * 6 + 10 * 6 ) = 102 : 150 = 51 : 75 = 17 : 25 17 : 25 a ' s share = 17 / 42 * 2940 = 1190 . b ' s share = 25 / 42 * 2940 = 1750 . a and b shares respectively 1190 and 1750 . answer : d"
Answer: d
Question (gain): in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 15 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 39 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 40 % not job of choice with diploma = . 15 x not job of choice w / o diploma = . 85 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 15 % of 60 % = 9 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 10 % = 30 % ) . 30 % + 9 % = 39 % . therefore 39 % of the people in country z have a diploma . ans a"
Answer: a
Question (gain): the present worth of rs . 676 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 625 , e ) none
Rationale: solution present worth = rs . [ 676 / ( 1 + 4 / 100 ) ² ] = rs . ( 676 x 25 / 26 x 25 / 26 ) = rs . 625 answer d
Answer: d
Question (gain): a shopkeeper sold an article for rs 2591.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: "explanation : gain % = ( 191.36 * 100 / 2400 ) = 7.97 % = 8 % approx option d"
Answer: d
Question (general): dacid obtained 86 , 89 , 82 , 87 and 81 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 88 , d ) 85 , e ) 75
Rationale: "average = ( 86 + 89 + 82 + 87 + 81 ) / 5 = 425 / 5 = 85 . answer : d"
Answer: d
Question (general): the product of two positive integers is 783 and their difference is 2 . what is the bigger number ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 29 , e ) 31
Rationale: "let ' s use trial and error to find the two numbers . 30 * 28 = 840 ( too high ) 29 * 27 = 783 the answer is d ."
Answer: d
Question (general): matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 700 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 700 = 150 + x i . e . x = 550 i . e . y = 2 new sales = y + 1 = 3 answer : option a"
Answer: a
Question (physics): water is poured into a cylindrical well at the rate of 22 cubic meters per hour , the level of water in the tank rises at a rate of 0.7 meters per hour . which of the following best approximates the diameter of the tank in meters ?
Options: a ) √ 10 / 2
b ) √ 10
c ) 2 √ 10
d ) 5
e ) 10
Rationale: here ' s my re - worked solution : volume = 22 = pi ( r ^ 2 ) ( 0.7 ) 22 = 22 / 7 ( 7 / 10 ) ( r ^ 2 ) 10 = r ^ 2 r = sqrt ( 10 ) diameter = 2 * sqrt ( 10 ) ans : c
Answer: c
Question (general): how many different 3 - digit multiples of 5 can be composed of digits 1 , 2 , 3 , 4 , and 5 if none of the digits is repeated ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 4 possible choices . x can be any of the 3 possible choices . 4 + 3 + 1 = 8 c
Answer: c
Question (general): a student finds the sum 1 + 2 + 3 + . . . as his patience runs out . he found the sum as 575 . when the teacher declared the result wrong , the student realized that he missed a number . what was the number the student missed ?
Options: a ) 16 , b ) 18 , c ) 14 , d ) 20 , e ) 22
Rationale: explanation : sum of 1 st 10 natural numbers ( 1 – 10 ) = 1 + 2 + … 10 = 55 . sum of next 10 natural numbers ( 11 – 20 ) = 10 + 11 + 12 + … 20 = 100 + 55 = 155 . sum of next 10 natural numbers ( 31 – 40 ) = 255 . sum of numbers from 31 – 40 = 355 and so on and on . so , we have here 55 + 155 + 255 = 465 . if we add 355 to 465 , it will be way more than 575 . so , we can add one by one . 465 + 31 + 32 + 33 = 561 . 465 + 31 + 32 + 33 + 34 = 595 . thus , the sum should be 595 instead of 575 , and the missing number is 20 . answer : d
Answer: d
Question (general): dhoni spends $ 300 buying his favorite dolls . if he buys only small monkey dolls , which are $ 2 cheaper than the large monkey dolls , he could buy 25 more dolls than if he were to buy only large monkey dolls . how much does a large monkey doll cost ?
Options: a ) $ 6.5 , b ) $ 6 , c ) $ 7 , d ) $ 8 , e ) $ 9
Rationale: a is not an integer . so we start with b . if large doll costs $ 6 , then he can buy 300 / 6 = 50 large dolls and 300 / 4 = 75 small dolls . difference is 25 , which is we wanted . answer b .
Answer: b
Question (general): set x consists of 5 integers and has median of 20 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 20 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 this is possible . hence it is the greatest such number . answer ( a )"
Answer: a
Question (general): find the principle on a certain sum of money at 8 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 939.6 , b ) 928.8 , c ) 927.78 , d ) 926.82 , e ) 902.1
Rationale: "1120 = p [ 1 + ( 8 * 12 / 5 ) / 100 ] p = 939.60 answer : a"
Answer: a
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 21.6 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 28 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 121.60 let marked price be rs . x . then , 95 / 100 x = 121.60 x = 12160 / 95 = rs . 128 now , s . p . = rs . 128 , c . p . = rs . 100 profit % = 28 % . answer : b"
Answer: b
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 10 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 22 , b ) 21 , c ) 88 , d ) 30 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 10 ) + 6000 ( v - 10 ) < = > 2000 v = 60000 < = > v = 30 answer : d ) 30"
Answer: d
Question (physics): in a kilometer race , a beats b by 100 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 90 sec , b ) 190 sec , c ) 290 sec , d ) 490 sec , e ) 390 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 100 = 100 sec . time taken by a = 100 - 10 = 90 sec . answer : a"
Answer: a
Question (physics): a space shuttle orbits the earth at about 4 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 14,400 , c ) 24,200 , d ) 28,800 , e ) 48,000
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 4 * 3600 = 14,400 answer : b"
Answer: b
Question (general): what is the remainder when 14452 × 15652 × 16781 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 2 * 2 * 1 = will give units digit as 4 so , whatever be the number , if it ends in 4 , the remainder after dividing with 5 will be 4 . optione
Answer: e
Question (probability): a jar contains only red , yellow , and orange marbles . if there are 3 red , 3 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 45 ) * ( 2 ) , which indeed is 2 / 45 . c"
Answer: c
Question (general): there are 2 friends peter and paul . peter age is twice as old as paul when peter was as old as paul is now . sum of the present ages of peter and paul is 35 . what is the present age of peter ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: let pauls age be ' a ' and peters be ' e ' e + a = 35 ( given ) e = 35 - a - - - - - - eq 1 when peter was as old as paul that is when peter ' s age was ' a ' pauls age was a - ( e - a ) = 2 a - e now peters age is e = 2 ( 2 a - e ) e = 4 a - 2 e 3 e = 4 a 3 ( 35 - a ) = 4 a 105 - 3 a = 4 a a = 15 hence e = 20 answer : c
Answer: c
Question (geometry): the area of a parallelogram is 162 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 62 , e ) 2
Rationale: "2 x * x = 162 = > x = 9 answer : b"
Answer: b
Question (geometry): 34 . the side surface of a cylinder is rolled with a rectangular plate . if the height of a cylinder tank is 10 feet and the perimeter of the circular base is 4 feet , what is the area of the rectangular plate ?
Options: a ) 24 , b ) 34 , c ) 28 , d ) 40 , e ) 14
Rationale: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both you can multiply them together to find the area , 40 . ( correct answer d )
Answer: d