Cheukting/mathqa huggingface dataset:
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 8.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 75 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 8 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 8 − 30 / 5 ) + 30 / 2 = 30 ( 8 − 6 ) + 15 = 30 × 2 + 15 = 75 ° answer is d ."
Answer: d
Question (gain): ravi and sunil are partners in a business . ravi invests rs . 10,000 for 8 months and sunil invested rs . 12000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 80000 : 120000 = 2 : 3 answer : b"
Answer: b
Question (physics): dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 3 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "dan can complete 1 / 15 of the job per hour . in 3 hours , dan completes 3 ( 1 / 15 ) = 1 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 4 / 5 / 1 / 10 = 8 hours . the answer is d ."
Answer: d
Question (general): alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,800 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,100 , c ) 1,900 , d ) 2,550 , e ) 3,400
Rationale: assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 3800 therefore x = 2600 / 4 = 650 price of 28 inch + 30 inch = 850 + 1050 = 1900 option c
Answer: c
Question (general): 1 , 3,5 , 7,9 , . 50 find term of sequnce
Options: a ) 1234 , b ) 1367 , c ) 1789 , d ) 1568 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Question (general): how many multiples of 3 are there between 81 and 358 ?
Options: a ) 94 , b ) 95 , c ) 93 , d ) 97 , e ) 98
Rationale: "3 * 27 = 81 3 * 119 = 357 total multiples of 3 = ( 119 - 27 ) + 1 = 93 answer is c ."
Answer: c
Question (gain): a trader bought a car at 10 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 110 , c ) 112 , d ) 126 , e ) 115
Rationale: "original price = 100 cp = 80 s = 80 * ( 140 / 100 ) = 126 100 - 126 = 26 % answer : d"
Answer: d
Question (general): according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 30 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 16.66 , 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 + 30 = 62 - - > c = 5 / 9 * 30 = 16.66 . increase = 16.66 degrees . answer : b ."
Answer: b
Question (physics): a train covers a distance of 18 km in 10 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 120 m , b ) 180 m , c ) 270 m , d ) 220 m , e ) 280 m
Rationale: "speed = ( 18 / 10 * 60 ) km / hr = ( 108 * 5 / 18 ) m / sec = 30 m / sec . length of the train = 30 * 9 = 270 m . answer : c"
Answer: c
Question (general): the smallest value of n , for which n + 1 is not a prime number , is
Options: a ) 5 , b ) 6 , c ) 8 , d ) 3 , e ) 10
Rationale: "( 1 + 1 ) = 2 . ( 2 + 1 ) = 3 . ( 3 + 1 ) = 4 . ( 4 + 1 ) = 5 . which is not prime , n = 3 . answer : d"
Answer: d
Question (general): a number divided by 24 leaves remainder 56 what is the remainder when same number divided by 7
Options: a ) 9 , b ) 7 , c ) 5 , d ) 3 , e ) 1
Rationale: "add 24 + 56 = 80 now 80 divided by 7 so we get 3 as reaminder answer : d"
Answer: d
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 42.5 % , e ) ca n ' t be calculated
Rationale: the owner buys 100 kg but actually gets 114 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 114 - 80 ) / 80 * 100 = ~ 42.5 % answer : d .
Answer: d
Question (general): 9548 + 7314 = 3362 + ( ? )
Options: a ) 8300 , b ) 8400 , c ) 13500 , d ) 8700 , e ) 9000
Rationale: 9548 16862 = 3362 + x + 7314 x = 16862 - 3362 - - - - - = 13500 16862 - - - - - c )
Answer: c
Question (gain): john had a stock of 620 books in his bookshop . he sold 50 on monday , 82 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 54.84 % , b ) 36.5 % , c ) 46.5 % , d ) 56.5 % , e ) 66.5 %
Rationale: "let n be the total number of books sold . hence n = 50 + 82 + 64 + 78 + 135 = 280 let m be the books not sold m = 620 - n = 620 - 280 = 340 percentage books not sold / total number of books = 340 / 620 = 0.55 = 54.84 % correct answer a"
Answer: a
Question (general): a sum of money is distributed among w , x , y , z in the proportion of 1 : 6 : 2 : 4 . if x gets $ 1500 more than y , what is the w ' s share ?
Options: a ) $ 1500 , b ) $ 150 , c ) $ 375 , d ) $ 200 , e ) $ 450
Rationale: let the shares of w , x , y , z are 1 a , 6 a , 2 a , 4 a 6 a - 2 a = 1500 4 a = $ 1500 , a = 375 w ' s share = 1 a = $ 375 answer is c
Answer: c
Question (general): a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are :
Options: a ) 500 , b ) 387 , c ) 298 , d ) 267 , e ) 191
Rationale: "explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark answer : a ) 500"
Answer: a
Question (gain): what is 15 percent of 58 ?
Options: a ) 6.9 , b ) 7.4 , c ) 8.7 , d ) 9.3 , e ) 10.4
Rationale: "( 15 / 100 ) * 58 = 8.7 the answer is c ."
Answer: c
Question (general): if equation | x / 4 | + | y / 4 | = 2.5 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 50 , c ) 100 , d ) 400 , e ) 200
Rationale: the equation can be reduced to intercept form as | x / 10 | + | y / 10 | = 1 , so these are lines in four quadrants with x and y intercept as 10 , so it is a rhombus with diagonals of 20 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 20 * 20 = 200 . answer e .
Answer: e
Question (physics): if 60 honey bees make 60 grams of honey in 60 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 60
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 60 : : 60 : x honey 60 : 1 = > 1 x 60 x x = 60 x 1 x 60 = > x = 60 . answer : e"
Answer: e
Question (probability): what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 7 - sided polygon ) ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 7
Rationale: "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 4 = 1 / 2 . the answer is a ."
Answer: a
Question (general): find the remainder when 3 ^ 27 is divided by 5 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5
Rationale: "solution : 3 ^ 27 = ( ( 3 ^ 4 ) ^ 6 ) * ( 3 ^ 3 ) = ( 81 ^ 6 ) * 27 then unit digit of ( 81 ^ 6 ) is 1 so on multiplying with 27 , unit digit in the result will be 7 . now , 7 when divided by 5 gives 2 as remainder . answer b"
Answer: b
Question (physics): a is twice as good a work man as b and together they finish a piece of work in 16 days . the number of days taken by a alone to finish the work is :
Options: a ) 36 days , b ) 24 days , c ) 46 days , d ) 16 days , e ) 14 days
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 16 divide 1 / 14 in the ratio 2 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 14 x 2 / 3 ) = 1 / 24 hence , a alone can finish the work in 24 days . answer b"
Answer: b
Question (geometry): a cube of edge 15 cm is imersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in waer level .
Options: a ) 11.25 cm .
b ) 12.25 cm
c ) 13.25 cm
d ) 14.25 cm
e ) none of these
Rationale: sol . increase in volume = volume of the cube = ( 15 * 15 * 15 ) cm ³ . ∴ rise in water level = [ volume / area ] = [ 15 * 15 * 15 / 20 * 15 ] cm = 11.25 cm . answer a
Answer: a
Question (general): a volunteer organization is recruiting new members . in the fall they manage to increase their number by 7 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.55 % , c ) 14.44 % , d ) 13.33 % , e ) 12.22 %
Rationale: "( 100 % + 7 % ) * ( 100 % - 19 % ) = 1.07 * . 81 = 0.8667 1 - 0.8667 = 13.33 % lost = - 13.33 % the answer is d the organization has lost 13.33 % of its total volunteers from fall to spring ."
Answer: d
Question (general): in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many e cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer e = 44 . d"
Answer: d
Question (other): half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 150 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 7
Rationale: "there are total 150 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 75 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 150 = 25 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 75 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 150 = 75 + 25 - b + ( 75 - b - 1 ) b = 12 answer ( b )"
Answer: b
Question (general): if 144 / 0.144 = 14.4 / x , then the value of x is :
Options: a ) 0.0414 , b ) 0.144 , c ) 0.0144 , d ) 0.414 , e ) none of them
Rationale: = 144 / 0.144 = 14.4 / x = 144 x 1000 / 144 = 14.4 / x = x = 14.4 / 1000 = 0.0144 answer is c .
Answer: c
Question (gain): ravi and kavi start a business by investing â ‚ ¹ 6000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .
Options: a ) 2 : 12 , b ) 5 : 12 , c ) 7 : 12 , d ) 1 : 12 , e ) 3 : 12
Rationale: "ratio of profit = ratio of investments = 6000 : 72000 = 1 : 12 answer : d"
Answer: d
Question (general): john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 40 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 40 = 60 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 60 / 100 ) * 100 = ( 0.6 ) * 100 = 60 % . e"
Answer: e
Question (physics): it takes joey the postman 1 hours to run a 7 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 8 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 8 , e ) 15
Rationale: "let his speed for one half of the journey be 7 miles an hour let the other half be x miles an hour now , avg speed = 8 mile an hour 2 * 7 * x / 7 + x = 8 14 x = 8 x + 56 = > x = 8 d"
Answer: d
Question (gain): a man buys rs . 20 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is ?
Options: a ) 14 , b ) 15 , c ) 61 , d ) 17 , e ) 18
Rationale: "dividend on rs . 20 = rs . ( 9 / 100 ) x 20 = rs . 9 / 5 . rs . 12 is an income on rs . 100 . rs . 9 / 5 is an income on rs . [ ( 100 / 12 ) x ( 9 / 5 ) ] = rs . 15 ? answer : b"
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 6 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 110 meters ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 52 , e ) 56
Rationale: "the speed of the boat downstream = 6 + 3 = 9 km / hr 9 km / hr * 5 / 18 = 2.5 m / s the time taken to cover 110 meters = 110 / 2.5 = 44 seconds . the answer is b ."
Answer: b
Question (physics): 24 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 36 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 24 ã — 13.5 = 324 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 324 â  „ 9 = 36 answer b"
Answer: b
Question (general): in a room filled with 7 people , 4 people have exactly 1 sibling in the room and 3 people have exactly 1 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 2 / 7
Rationale: "there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 3 people who have exactly 1 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 1 people out of 7 is 7 c 1 = 7 first sibling pair - - - - ( a and b ) - - selecting 1 people - - 1 c 1 = 1 second sibling pair ( c and d ) - - selecting 1 people - - 1 c 1 = 1 third sibling pair ( e f g ) - - selecting 1 out of 3 - - 3 c 1 = 3 total = 1 + 1 + 3 = 5 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 1 people who are siblings = 5 / 7 ( 7 is 7 c 1 ) = 1 - 5 / 7 = 2 / 7 ans e"
Answer: e
Question (general): a mixture of 150 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 7 liters , b ) 15 liters , c ) 10 liters , d ) 9 liters , e ) none of these
Rationale: "explanation : number of liters of water in 150 liters of the mixture = 20 % of 150 = 20 / 100 * 150 = 30 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 30 + p ) and total volume of mixture is ( 150 + p ) . ( 30 + p ) = 25 / 100 * ( 150 + p ) 120 + 4 p = 150 + p = > p = 10 liters . answer is c"
Answer: c
Question (general): a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 126 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 4 , c ) 1 , d ) 5 , e ) 3
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 126 / 25 = 5 . . . . so the max is 5 126 / 20 = 6 . . . so the max is 6 126 - 125 = 1 ( 5 big box or 5 small box + 1 big box ) answer : c"
Answer: c
Question (physics): how many seconds will a 900 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 54
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 900 * 3 / 50 = 54 sec answer : e"
Answer: e
Question (general): what will be the vulgar fraction of 0.8
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.8 = 80 / 100 = 4 / 5 option b"
Answer: b
Question (general): jenny can divide her sweets equally to 5 people and also to 6 people equally but not to 12 people . what could be the number ?
Options: a ) 120 , b ) 134 , c ) 127 , d ) 30 , e ) 650
Rationale: option ( b ) and ( c ) are ruled out as they are not divisilble by 5 and 6 . 120 is both divisible by 5 and 6 but also by 12 , so it wrong . 650 is divisible by 5 but not by 6 . hence , ( d ) is the answer , as it is both divisible by 5 or 6 but not by 12
Answer: d
Question (physics): one pipe can fill a pool 1.5 times faster than a second pipe . when both pipes are opened , they fill the pool in five hours . how long would it take to fill the pool if only the slower pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 12.5 , d ) 9 , e ) 7.2
Rationale: "say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.5 r = 3 r / 2 . since when both pipes are opened , they fill the pool in five hours , then their combined rate is 1 / 5 pool / hour . thus we have that r + 3 r / 2 = 1 / 5 - - > r = 2 / 25 pool / hour - - > time is reciprocal of rate thus it ' s 25 / 2 = 12.5 hours . answer : c ."
Answer: c
Question (gain): a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 35 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 27.7
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 35 % of the final price - - > ( final price ) * 0.65 = $ 18 - - > ( final price ) = $ 27.7 . answer : e ."
Answer: e
Question (general): at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 11 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 21 so a + b = 7 total number of people = 7 answer : b"
Answer: b
Question (gain): a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 684 , what is the reduced price for kg ?
Options: a ) 72 , b ) 27 , c ) 34 , d ) 28 , e ) 20
Rationale: "684 * ( 20 / 100 ) = 136 - - - - 4 ? - - - - 1 = > rs . 34 answer : c"
Answer: c
Question (general): if 522 x is a 3 digit no . with as a digit x . if the no . is divisible by 6 , what is the value of the digit x is ?
Options: a ) 1 , b ) 6 , c ) 4 , d ) 7 , e ) 9
Rationale: if a number is divisible by 6 , it must be divisible by both 2 and 3 in 522 x , to this number be divisible by 2 , the value of x must be even . so it can be 2,4 or 6 from given options 552 x is divisible by 3 , if sum of its digits is a multiple of 3 . 5 + 5 + 2 + x = 12 + x , if put x = 2 , 12 + 2 = 14 not a multiple of 3 if put x = 4 , 12 + 6 = 18 is a multiple of 3 if put x = 6 , 12 + 2 = 14 not a multiple of 3 the value of x is 6 . b
Answer: b
Question (general): what is the value of ( p + q ) / ( p - q ) if p / q is 8 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 9 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 8 + 1 ) / ( 8 - 1 ) = 9 / 7 answer : e"
Answer: e
Question (general): cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 7 , d ) 2 : 6 , e ) 1 : 4
Rationale: "2 % is 3 % - points below 5 % and 10 % is 5 % - points above 5 % . the ratio of a : b should be 3 : 5 . the answer is b ."
Answer: b
Question (geometry): the side of a rhombus is 28 m and length of one of its diagonals is 12 m . the area of the rhombus is ?
Options: a ) 326.2 , b ) 324.2 , c ) 328.2 , d ) 338.2 , e ) 328.9
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 28 ; p = 12 a = 1 / 2 * 12 * √ 4 ( 28 ) 2 - ( 12 ) 2 = 1 / 2 * 12 * √ 3136 - 144 = 1 / 2 * 12 * √ 2992 a = 328.2 answer : c"
Answer: c
Question (general): what is the remainder when 14,456 × 15,657 × 16,788 is divided by 10 ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 3 , e ) 2
Rationale: "only the unit ' s digit of the product will decide the remainder when divided by 10 . hence , 6 * 7 * 8 = will give units digit as 6 so , whatever be the number , if it ends in 6 , the remainder after dividing with 10 will be 6 . optiona"
Answer: a
Question (general): the product of two numbers is 2028 and their hcf is 13 . what are the number of such pairs ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 23 , e ) 25
Rationale: "let the numbers be 13 x and 13 y ( hcf of the numbers = 13 ) 13 x × 13 y = 2028 xy = 12 co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) ( we need to take only co - primes with product 12 . if we take two numbers with product 12 , but not co - prime , the hcf will not remain as 13 ) hence the numbers with hcf 13 and product 2028 = ( 13 × 1 , 13 × 12 ) and ( 13 × 3 , 13 × 4 ) = ( 13 , 156 ) and ( 39 , 52 ) so , there are 2 pairs of numbers with hcf 13 and product 2028 answer is b"
Answer: b
Question (geometry): a hall is 24 meters long and 12 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 1896
b ) 1912
c ) 2108
d ) 2304
e ) 2524
Rationale: 2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 2304 the answer is d .
Answer: d