Cheukting/mathqa huggingface dataset:
Question (general): the simple interest on a sum of money will be rs . 600 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732
Rationale: "p - - - 10 - - - - 600 p - - - 5 - - - - - 300 3 p - - - 5 - - - - - 900 - - - - - - = > 1200 answer : c"
Answer: c
Question (geometry): a rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters . if the carpet squares cost $ 24 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200
b ) $ 576
c ) $ 480
d ) $ 960
e ) $ 1,920
Rationale: the width of the rectangular floor ( 24 m ) is a multiple of one side of the square ( 8 m ) , and the length of the floor ( 64 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 24 / 8 ) * ( 64 / 8 ) = 24 . the total cost is 24 * 24 = $ 576 . the answer is , therefore , b .
Answer: b
Question (general): what least number must be subtracted from 427751 so that remaining no . is divisible by 10
Options: a ) 3 , b ) 1 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 427751 by 10 we get the remainder 1 , so 1 should be subtracted option b"
Answer: b
Question (gain): jim is able to sell a hand - carved statue for $ 660 which was a 20 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 512.40 , c ) $ 550 , d ) $ 574.90 , e ) $ 588.20
Rationale: "cost price = 660 / 120 * 100 = 550 answer : c"
Answer: c
Question (physics): the minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time . how much does the clock gain or lose in 12 hours ?
Options: a ) 27.273 seconds , b ) 29.273 seconds , c ) 37.273 seconds , d ) 47.273 seconds , e ) 17.273 seconds
Rationale: after 60 minute rotation the minute hand will make an angle of 30 degree with hour hand . after that let the time required to make an overtake is t minute in this time angle covered by minute hand = ( 360 / 60 ) t = 6 t similarly angle covered by hour hand = ( 30 / 60 ) t = t / 2 so for overtake 6 t = 30 + t / 2 or t = 60 / 11 min = 5 min and 5 / 11 min = 5 min and 300 / 11 sec = 5 min and 27.273 sec so clock loses 27.273 seconds answer : a
Answer: a
Question (general): students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio f of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) f = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Question (general): average monthly income of a family of 3 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 905 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 3 - 650 x 2 rs . = 905 rs . correct option : b"
Answer: b
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 52000 , then the share of b is ?
Options: a ) 2888 , b ) 24000 , c ) 27777 , d ) 29997 , e ) 27712
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 52000 share of b = 6 / 13 ( 52000 ) = rs . 24000 answer : b"
Answer: b
Question (physics): a tank can supply water to a village for 20 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 15 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "losing 10 liters per day results in a loss of 150 liters in 15 days . so , those 150 liters were for 5 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 20 = 600 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 600 / 50 = 12 days . the answer is d ."
Answer: d
Question (physics): 31 of the scientists that attended a certain workshop were wolf prize laureates , and 14 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 25 , d ) d ) 29 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 14 = 25 . . c"
Answer: c
Question (general): a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction x of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose x = 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Question (general): if the average ( arithmetic mean ) of x + 1 , x + 4 , and x + 7 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 1 + x + 4 + x + 7 ) / 3 = 0 = > 3 x + 12 = 0 = > x = - 4 answer a"
Answer: a
Question (general): for how many integers pair ( x , y ) satisfies the result ( 1 / x ) + ( ( 1 / y ) = 1 / 16
Options: a ) a ) 12 , b ) b ) 6 , c ) c ) 10 , d ) d ) 16 , e ) e ) 19
Rationale: it seems that the accepted answer is wrong , according to wolframalpha . the answer should be 31 , which is n ' t even listed as a selectable answer . e
Answer: e
Question (general): of the female students at barkely university , 3 / 5 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 5 / 9 of the students are female , what fraction of all the students are on the honor roll ?
Options: a ) 5 / 9 , b ) 3 / 15 , c ) 23 / 45 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 45 given 5 / 9 of the students are females = 25 then males = 4 / 9 = 20 3 / 5 of the females are on honor roll = 15 males on the honor roll = 2 / 5 = 8 total students on honor roll = 15 + 8 = 23 fraction = 23 / 45 c"
Answer: c
Question (geometry): abcd is a square . e and f are the midpoints of sides cd and bc , respectively . what is the ratio of the shaded region area to the unshaded region ?
Options: a ) 1 : 1
b ) 2 : 1
c ) 3 : 1
d ) 5 : 3
e ) 8 : 3
Rationale: let ' s join the midpoints as shown in the figure then we ' ll get four small squares . . . aodx be 1 and similarly all squares . . and we can split the unit 1 into half and half as per the mid points . . . then shaded will be 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 and unshaded is 1 / 2 + 1 / 2 + 1 / 2 = 3 / 2 . . shaded : unshaded is 5 : 3 . . ans option d .
Answer: d
Question (general): a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 7 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 26 , b ) 29 , c ) 19 , d ) 30 , e ) 40
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 7 strikes , there would be 6 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 7 ' o clock , the 7 strikes and 6 intervals will take 2 * ( 7 + 6 ) = 26 secs a"
Answer: a
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg , what is his percent ?
Options: a ) 28 % , b ) 66.7 % , c ) 55 % , d ) 28 % , e ) 55 %
Rationale: "600 - - - 400 100 - - - ? = > 66.7 % answer : b"
Answer: b
Question (physics): 15 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 18.75 days , c ) 20 days , d ) 88 days , e ) 44 days
Rationale: "15 * 25 = 20 * x = > x = 18.75 days answer : b"
Answer: b
Question (general): if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 23 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 23 . n = 5 - - > n ^ 2 = 49 - - > remainder upon division 49 by 23 is 3 . answer : d ."
Answer: d
Question (general): the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 2 | + 5 is equal to :
Options: a ) – 7 , b ) 7 , c ) 10 , d ) 12 , e ) 18
Rationale: "x ^ 2 - 8 x + 16 = | x - 2 | rhs can be - ve or + ve x ^ 2 - 9 x + 18 = 0 x ^ 2 - 7 x + 14 = 0 x = 7,6 , 3,2 we test all 3 values in original equation , all ok . thus , sum = 7 + 6 + 3 + 2 = 18 ans ( e )"
Answer: e
Question (gain): 80 is what percent of 160 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 80 / 160 × 100 = 50 % answer : d
Answer: d
Question (general): the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 40 cents more than the commodity y ?
Options: a ) 2007 , b ) 2008 , c ) 2009 , d ) 2010 , e ) 2011
Rationale: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 40 = 60 cents on commodity y , which will take 6 years . the answer is a ."
Answer: a
Question (physics): a 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds . what is the length of the platform ?
Options: a ) 150 m , b ) 350 m , c ) 420 m , d ) 600 m , e ) 700 m
Rationale: explanation : length of the train = distance covered in crossing the post = speed × time = speed × 18 speed of the train = 300 / 18 m / s = 50 / 3 m / s time taken to cross the platform = 39 s ( 300 + x ) / ( 50 / 3 ) = 39 s where x is the length of the platform 300 + x = ( 39 × 50 ) / 3 = 650 meter x = 650 - 300 = 350 meter answer : option b
Answer: b
Question (general): what is the remainder when 1034 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 0 , b ) 27 , c ) 30 , d ) 21 , e ) 18
Rationale: "take the remainder from each of 1034 / 33 , 1047 / 33 and so on . . 1034 / 33 gives remainder = 11 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 11 * 24 * 27 * 30 break them into pairs 11 * 24 / 33 gives remainder 0 and 27 * 30 / 33 gives remainder 18 so 0 * 18 / 33 gives remainder 0 . a"
Answer: a
Question (physics): 39 persons can repair a road in 24 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 26
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 39 x 5 x 24 x = ( 39 x 5 x 24 ) / ( 30 x 6 ) x = 26 . answer : e"
Answer: e
Question (physics): two boats are heading towards each other at constant speeds of 4 miles / hr and 20 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 6 / 15 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 5
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 4 + 20 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 24 * 1 / 60 = 6 / 15 miles apart . answer : b ."
Answer: b
Question (general): 1 / 0.04 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 25 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.04 = ( 1 * 100 ) / 4 = 100 / 4 = 25 option c"
Answer: c
Question (gain): a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 30 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 216 , c ) $ 220 , d ) $ 230 , e ) $ 168
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 30 emlpoyee paid = . 7 * 240 = 168 $ answer e"
Answer: e
Question (general): if an integer n is to be chosen at random from the integers 1 to 92 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 29 / 46 , e ) 3 / 4
Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 46 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 46 + 12 ) / 92 = 58 / 96 = 29 / 46 ans is d"
Answer: d
Question (general): on dividing a number by 56 , we get 27 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 56 x + 27 ( ∵ since the number gives 27 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 3 hence , if the number is divided by 8 , we will get 3 as remainder . answer : b"
Answer: b
Question (gain): what sum of money will produce rs . 90 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 263 , b ) 500 , c ) 367 , d ) 642.9 , e ) 339
Rationale: "90 = ( p * 4 * 7 / 2 ) / 100 p = 642.9 answer : d"
Answer: d
Question (gain): a and b enter into a partnership . a contributed rs . 5000 for 8 months and b rs . 6000 for 5 months . find a ' s share in a total profit of rs . 8400 .
Options: a ) rs . 4800 , b ) rs . 2400 , c ) rs . 3600 , d ) rs . 5600 , e ) none of these
Rationale: explanation : ratio of capitals of a and b = ratio of their investments = 5000 × 8 : 6000 × 5 = 40000 : 30000 = 4 : 3 . : a ' s share = rs . [ ( 4 / 7 ) × 8400 ] = rs . 4800 answer : option a
Answer: a
Question (other): two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixtures be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8 : 5 ?
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 9 : 7 , d ) 7 : 9 , e ) 8 : 1
Rationale: "explanation : let cost price ( cp ) of 1 litre spirit be rs . 1 quantity of spirit in 1 litre mixture from vessel a = 5 / 7 cost price ( cp ) of 1 litre mixture from vessel a = rs . = 5 / 7 quantity of spirit in 1 litre mixture from vessel b = 7 / 13 cost price ( cp ) of 1 litre mixture from vessel b = rs . = 7 / 13 quantity of spirit to be obtained in 1 litre mixture from vessel c = 8 / 13 cost price ( cp ) of 1 litre mixture from vessel c ( mean price ) = rs . = 8 / 13 = > mixture from vessel a : mixture from vessel b = 1 / 13 : 9 / 91 = 7 : 9 answer is d"
Answer: d
Question (gain): company a imported 10,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 20 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?
Options: a ) 420 , b ) 840 , c ) 800 , d ) 1680 , e ) 2100
Rationale: "answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 20 % brass widgets leads to 8 % blue brass widgets out of the total 10,550 widgets . 10,000 / 100 * 8 = 800 . answer c ."
Answer: c
Question (physics): a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 6 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 6 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 3 m / s a"
Answer: a
Question (geometry): a rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) 2288 , b ) 2779 , c ) 3300 , d ) 3900 , e ) 2781
Rationale: "area = ( l + b â € “ d ) d ( 80 + 40 â € “ 10 ) 10 = > 1100 m 2 1100 * 3 = rs . 3300 answer : c"
Answer: c
Question (physics): there is enough provisions for 1200 girls in a hostel for 50 days . if there were 600 girls less , how long will the provision last ?
Options: a ) 75 , b ) 80 , c ) 90 , d ) 95 , e ) 100
Rationale: "we have , m 1 d 1 = m 2 d 2 1200 * 50 = 600 * d 2 d 2 = 1200 * 50 / 600 = 100 days . answer : e"
Answer: e
Question (other): a 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 5 kg when 50 kg alloy is immersed . this is a loss of ( 5 / 50 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Question (general): a , b and c have rs . 300 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 250 , b ) b ) 249 , c ) c ) 248 , d ) d ) 247 , e ) e ) 246
Rationale: "a + b + c = 300 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 300 - - - - - - - - - - - - - - - - c = 250 answer : a"
Answer: a
Question (general): united telephone charges a base rate of $ 7.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 200 minutes , b ) 100 minutes , c ) 120 minutes , d ) 140 minutes , e ) 160 minutes
Rationale: "lets take number of minutesx . given that , 7 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 100 minutes ans b"
Answer: b
Question (gain): there are 50 students in a class . if 12 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 28 , d ) 129 , e ) 44
Rationale: "number of students absent on a particular day = 12 % of 50 i . e . , 12 / 100 × 50 = 6 therefore , the number of students present = 50 - 6 = 44 students . answer : e"
Answer: e
Question (general): how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 24 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.5 * 8 = 0.2 ( x + 8 ) - - > x = 24 . answer : d ."
Answer: d
Question (geometry): can c and can в are both right circular cylinders . the radius of can c is twice the radius of can b , while the height of can c is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can c with the same brand of gasoline ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 4 , d ) $ 8 , e ) $ 16
Rationale: let x be the radius of b and 2 h be the height of b . therefore , radius of c = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
Answer: e
Question (general): a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 3 years ago ?
Options: a ) 11 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 3 years ago ? i . e . d - 4 = 14 - 3 = 11 years answer : a"
Answer: a
Question (other): 6 years ago , the ratio of the ages of vimal and saroj was 6 : 5 . 4 years hence , the ratio of their ages will be 11 : 10 . what is saroj ' s age at present ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 15
Rationale: given that , six years ago , the ratio of the ages of vimal and saroj = 6 : 5 hence we can assume that age of vimal six years ago = 6 x age of saroj six years ago = 5 x after 4 years , the ratio of their ages = 11 : 10 ⇒ ( 6 x + 10 ) : ( 5 x + 10 ) = 11 : 10 ⇒ 10 ( 6 x + 10 ) = 11 ( 5 x + 10 ) ⇒ 5 x = 10 ⇒ x = 105 = 2 saroj ' s present age = ( 5 x + 6 ) = 5 × 2 + 6 = 16 answer is c .
Answer: c
Question (physics): a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 70 km downstream .
Options: a ) 4.25 hr , b ) 3.8 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 13 km / hr speed of the stream = 5 km / hr speed downstream = ( 13 + 5 ) = 18 km / hr time taken to travel 70 km downstream = 70 â  „ 18 = 3.8 hours answer is b"
Answer: b