Cheukting/mathqa huggingface dataset:
Question (general): there were 35 students in a hostel . due to the admission of 7 new students , ; he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . what was the original expenditure of the mess ?
Options: a ) 320 , b ) 120 , c ) 400 , d ) 420 , e ) 514
Rationale: "sol . let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42  7 x = 84  x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . . answer d"
Answer: d
Question (general): 1 , 0.5 , 0.5 , 0.75 , 1.5 , ____
Options: a ) 1.25 , b ) 5.75 , c ) 3.25 , d ) 3.75 , e ) none
Rationale: "1 , 0.5 , 0.5 , 0.75 , 1.5 , . . . . . 1 * 0.5 = 0.5 0.5 * 1 = 0.5 0.5 * 1.5 = 0.75 0.75 * 2 = 1.5 so , 1.5 * 2.5 = 3.75 answer : d"
Answer: d
Question (gain): what percent of 15 kg is 30 gms ?
Options: a ) 25 , b ) 66 , c ) 20 , d ) 19 , e ) 17
Rationale: "explanation : required percentage = ( 30 / 15000 * 100 ) % = 1 / 5 % = 0.2 % answer : c ) . 20 %"
Answer: c
Question (gain): if $ 100 invested at a certain rate of simple interest amounts to $ 140 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 270
Rationale: 100 amounts to 140 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 140 100 + 100 * ( r / 100 ) * ( 3 ) = 140 = > r = 40 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 270 answer is e .
Answer: e
Question (gain): the owner of a furniture shop charges his customer 100 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 800 , b ) 650 , c ) 500 , d ) 600 , e ) 250
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 200 ) = rs . 500 . answer : c"
Answer: c
Question (general): if a father said to his elder son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 25 years now , what was the son ' s age 4 years back ?
Options: a ) 7.5 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: let son ' s present age be a years . then , ( 25 − a ) = a ⇒ 2 a = 25 ⇒ a = 25 / 2 = 12.5 son ' s age 4 years back = 12.5 - 4 = 8.5 answer : b
Answer: b
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 13 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 40 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 13 + 24 + 15 + 29 + 8 = 89 % . so remaining 11 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 11 % will be 40 degrees . . imo option b ."
Answer: b
Question (general): 7 , 10.5 , 15.75 , 23.63 , 35.43 , ( . . . )
Options: a ) 52.112 , b ) 53.156 , c ) 54 , d ) 89 , e ) 88
Rationale: "7 ( 7 ã — 3 ) ã · 2 = 10.5 ( 10.5 ã — 3 ) ã · 2 = 15.75 ( 15.75 ã — 3 ) ã · 2 = 23.63 ( 23.63 ã — 3 ) ã · 2 = 35.43 ( 35.43 ã — 3 ) ã · 2 = 53.156 answer is b"
Answer: b
Question (general): jim ’ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.25 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.5 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 25 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 25 = 2.25 + 9 * . 25 = 4.5 $ answer b"
Answer: b
Question (general): payal finished 2 / 3 of a book . she calculated that she finished 20 more pages than she has yet to read . how long is her book ?
Options: a ) a ) 60 , b ) b ) 150 , c ) c ) 130 , d ) d ) 90 , e ) e ) 210
Rationale: let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x − 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x − 1 / 3 * x = 20 1 / 3 * x = 20 x = 60 so the book is 270 pages long . answer is a .
Answer: a
Question (geometry): the surface of a cube is 384 sq cm . find its volume ?
Options: a ) 8 cc , b ) 9 cc , c ) 512 cc , d ) 4 cc , e ) 6 cc
Rationale: "6 a 2 = 384 = 6 * 64 a = 8 = > a 3 = 512 cc answer : c"
Answer: c
Question (general): the tax on a commodity is diminished by 10 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % decrease , b ) 3.5 % increase , c ) 9 % decrease , d ) 3 % decrease , e ) 2 % increase
Rationale: "100 * 100 = 10000 90 * 115 = 10350 - - - - - - - - - - - 10000 - - - - - - - - - - - 350 100 - - - - - - - - - - - ? = > 3.5 % decrease answer : b"
Answer: b
Question (physics): a monkey ascends a greased pole 19 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 23 rd , d ) 35 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 17 metres , he ascends in 34 minutes . â ˆ ´ he reaches the top in 35 th minute . answer d"
Answer: d
Question (geometry): the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 4 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle .
Options: a ) 20 cm , b ) 25 cm , c ) 26 cm , d ) 100 / 3 cm , e ) 23 cm
Rationale: explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 4 ) - 2 x * x = 75 = > 3 x - 25 = 75 = > x = 100 / 3 . length of the rectangle = 100 / 3 cm . answer : option d
Answer: d
Question (general): there is a 1 km long wire placed on some number of poles which are in equal distance . if the number of poles is reduced by 1 then the distance of wire between each poles increases 1 ( 2 / 3 ) . how many poles are there initially .
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 26 answer : c
Answer: c
Question (gain): by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at :
Options: a ) rs . 80 , b ) rs . 96 , c ) rs . 106 , d ) rs . 108 , e ) rs . 118
Rationale: michel earns rs 135 by investing rs 1620 to earn rs 8 how much he have to invest ? = ( 8 * 1620 ) / 135 = rs 96 answer : b
Answer: b
Question (general): the initial price of an article is rs . 2000 which increases 30 % increse in its price in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . what is the final price of the article ?
Options: a ) rs . 1748 , b ) rs . 1948 , c ) rs . 1848 , d ) rs . 2048 , e ) rs . 2148
Rationale: the initial price of the article , four years age is rs . 2000 in the 1 st year , price of the article = 2000 + 600 = rs . 2600 . in the 2 nd year , price = 2600 - 20 % of 2600 = 2200 - 520 = rs . 1680 . in the 3 rd year , price = 1680 + 10 % of 1680 = 1680 + 168 = rs . 1848 . required price = rs . 1848 answer : c
Answer: c
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 900 in 16 years ?
Options: a ) 6.25 % , b ) 1.25 % , c ) 4 % , d ) 5 % , e ) 3.25 %
Rationale: "150 = ( 750 * 16 * r ) / 100 r = 1.25 % answer : b"
Answer: b
Question (general): if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 58 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "four wheeler = 14 * 4 = 56 ( max ) 2 wheel = 1 so no of 4 wheeler = 14 answer : d"
Answer: d
Question (probability): if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly once in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.375 , c ) 0.325 , d ) 0.5 , e ) 0.666
Rationale: total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 th thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : b
Answer: b
Question (physics): a pipe takes a hours to fill the tank . but because of a leakage it took 2 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 120 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 120 x = 120 min answer : e"
Answer: e
Question (other): if the ratio of two number is 5 : 7 and lcm of the number is 320 then what is the number .
Options: a ) 15 , b ) 9 , c ) 10 , d ) 11 , e ) 35
Rationale: "product of two no = lcm * hcf 5 x * 7 x = 320 * x x = 9 answer : b"
Answer: b
Question (general): find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 2030 ?
Options: a ) rs . 2000 , b ) rs . 1750 , c ) rs . 2010 , d ) rs . 2005 , e ) none of these
Rationale: "explanation : 2030 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1750 answer : option b"
Answer: b
Question (physics): machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 7000 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 7000 envelopes b will take 7000 / 1400 hrs = 5 hrs so the answer is choice d"
Answer: d
Question (geometry): abcd is a square aegf is a rectangle . . such that the rectangle shares 25 % of the area of the suare also ae lies on the line ab and ag lies on segment of ad . if the square shares half the area of the rectangle what is the ratio ae : ag ?
Options: a ) 1 : 4
b ) 8 : 1
c ) 4 : 1
d ) 3 : 1
e ) 1 : 3
Rationale: a - - - - - - - - - - - - b - - - - - - - - e | | 50 % | g - - - - - - - - - - - - | - - - - - - - - f | | | 75 % | d - - - - - - - - - - - c remaining square 75 % and remaining rectangle 50 % rectangle share 25 % area of square so , ab x ag = ( ad x ab ) / 4 ad = 4 ag - - - - - - - - - - - - - - - - - - ( 1 ) square share half the area of rectangle so , ag x ab = ( ae x ag ) / 2 ab = ae / 2 - - - - - - - - - - - - - - - - - - ( 2 ) in square all sides are equal i . e . ab = bc = cd = ad so , equation ( 1 ) and ( 2 ) both are equal ae / 2 = 4 ag ae / ag = 8 ae : ag = 8 : 1 answer : b
Answer: b
Question (general): 2 cow ’ s and 10 goats are brought for rs . 1500 . if the average price of a goat be rs . 70 . what is the average price of a cow .
Options: a ) 420 , b ) 400 , c ) 430 , d ) 410 , e ) 450
Rationale: "explanation : average price of a goat = rs . 70 total price of 8 goats = 10 * 70 = rs . 700 but total price of 2 cows and 8 goats = rs . 1500 total price of 2 cows is = 1500 - 700 = 800 average price of a cow = 800 / 2 = rs . 400 answer : b"
Answer: b
Question (general): if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value f of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] f = z - x = x + 9 - x = 9 ans : d"
Answer: d
Question (geometry): the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by two - thirds of the males and one - third of the females in the class ?
Options: a ) 160 , b ) 168 , c ) 191 , d ) 192 , e ) 204
Rationale: "2 / 3 * 2 / 5 + 1 / 3 * 3 / 5 = 4 / 15 + 3 / 15 = 7 / 15 the number of degrees is 7 / 15 * 360 = 168 degrees the answer is b ."
Answer: b
Question (general): last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 60 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 796 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: "= ( 750 * 6 + 810 * 20 ) / 26 = 796 answer is b . posted from my mobile device"
Answer: b
Question (general): in the set of positive integers from 1 to 60 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 185 , c ) 190 , d ) 160 , e ) 165
Rationale: 1 - 60 5 - 15 - 25 - 35 - 45 are valid multiples of 5 . add them 5 + 15 + 25 + 35 + 45 + 55 = 180 a
Answer: a
Question (physics): a train is 360 meter long is running at a speed of 54 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 65 seconds , b ) 33.33 seconds , c ) 40 seconds , d ) 97 seconds , e ) 26 seconds
Rationale: "speed = 54 km / hr = 54 * ( 5 / 18 ) m / sec = 15 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 15 ) = 33.33 seconds answer : b"
Answer: b
Question (general): if a certain number is divided by 12 , the quotient , dividend , and divisor , added together , will amount to 64 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 12 + x + 12 = 64 . and x - 624 / 13 = 48 ."
Answer: a
Question (general): the ages of two persons differ by 24 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,10 , c ) 25,15 , d ) 35,11 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 24 ) years . 5 ( x - 5 ) = ( x + 24 - 5 ) or 4 x = 44 or x = 11 . their present ages are 35 years and 11 years option d"
Answer: d
Question (general): what is the remainder when the number t = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus t = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Question (other): the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 15000 , then find the annual income of a ?
Options: a ) 187888 , b ) 276889 , c ) 267777 , d ) 504000 , e ) 297112
Rationale: "b ' s monthly income = 15000 * 112 / 100 = rs . 16800 b ' s monthly income = 2 parts - - - - > rs . 16800 a ' s monthly income = 5 parts = 5 / 2 * 16800 = rs . 42000 a ' s annual income = rs . 42000 * 12 = rs . 504000 answer : d"
Answer: d
Question (gain): if an article is sold at 18 % profit instead of 9 % profit , then the profit would be $ 72 more . what is the cost price ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: "9 % * cost price = $ 72 1 % * cost price = $ 72 / 9 = $ 8 the cost price is $ 800 . the answer is d ."
Answer: d
Question (general): by approximately what percent is x greater than 1 / 3 if ( 2 / 3 ) ( x ) = 1 ?
Options: a ) 173 % , b ) 516 % , c ) 461 % , d ) 350 % , e ) 290 %
Rationale: "what percent is x greater than 1 / 3 if ( 2 / 3 ) ( x ) = 1 ? = > x = 3 / 2 % change = [ ( 3 / 2 - 1 / 3 ) / ( 1 / 3 ) ] * 100 = 350 ans d , 350 %"
Answer: d
Question (physics): a train 1500 m long can cross an electric pole in 50 sec and then find the speed of the train ?
Options: a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 110
Rationale: "length = speed * time speed = l / t s = 1500 / 50 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : c"
Answer: c
Question (gain): in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 35 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 33 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: total men in company 35 % means total women in company 65 % ( assume total people in company 100 % ) no of men emplyess attended picnic = 35 x ( 20 / 100 ) = 7 no of women empolyees attened picnin = 65 x ( 40 / 100 ) = 26 total percentage of empolyess attened the picnic = 7 + 26 = 33 % answer : a
Answer: a
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 60 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 26
Rationale: "we have : l = 20 ft and lb = 60 sq . ft . so , b = 3 ft . length of fencing = ( l + 2 b ) = ( 20 + 6 ) ft = 26 ft . answer : e"
Answer: e
Question (general): if an integer w is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that w ( w + 1 ) ( w + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: for w total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d
Answer: d
Question (general): tickets numbered from 1 to 24 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 ] p ( e ) = n ( e ) / n ( s ) = 8 / 24 = 1 / 3 the answer is a .
Answer: a
Question (gain): the difference of two numbers is 20 % of the larger number . if the smaller number is 12 , the larger one is :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) none of these
Rationale: "let the larger number be x . then , x - 12 = 20 % of x < > x - ( x / 5 ) = 12 4 x / 5 = 12 < = > x = ( 12 ∗ 5 ) / 5 = 15 . answer : a"
Answer: a
Question (other): sandy is younger than molly by 14 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 36 , b ) 45 , c ) 54 , d ) 63 , e ) 72
Rationale: "s = m - 14 s / m = 7 / 9 9 s = 7 m 9 ( m - 14 ) = 7 m m = 63 the answer is d ."
Answer: d
Question (general): carrie likes to buy t - shirts at the local clothing store . they cost $ 8.75 each . one day , she bought 18 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 70 , c ) $ 200 , d ) $ 171.6 , e ) $ 190
Rationale: $ 8.75 * 18 = $ 70 . answer is b .
Answer: b
Question (general): a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 8 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 ) 46 % , d ) 52 % , e ) 56 %
Rationale: "( 8 / 108 ) / ( 3 / 20 ) = 30 / 54 = 49,3 % it means that 8 / 108 represents only 49,3 % . therefore a decrease of 46 % . answer c"
Answer: c
Question (general): a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 72
Rationale: "explanation : as there is meal for 70 adults and 14 have their meal , the meal left can be catered to 56 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 56 adults = 72 children hence , the meal can be catered to 72 children . answer : e"
Answer: e
Question (general): a batch of cookies was divided amomg 2 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 11 , d ) 7 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 2 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 2 ) = 5 / 12 x = 5 / 11 answer : c . 5 / 11"
Answer: c
Question (general): robert ' s salary was decreased by 60 % and subsequently increased by 60 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 36 % , e ) 50 %
Rationale: let original salary be $ 100 salary after decreasing 60 % = 100 - 100 x 60 / 100 = $ 40 salary after increasing 60 % on $ 40 = 40 + 40 x 60 / 100 = $ 64 percentage of loss = 100 - 64 = 36 % answer : d
Answer: d
Question (gain): a candidate got 34 % of the votes polled and he lost to his rival by 640 votes . how many votes were cast ?
Options: a ) 2000 , b ) 2400 , c ) 2800 , d ) 3200 , e ) 3600
Rationale: "let x be the total number of votes . 0.34 x + 640 = 0.66 x 0.32 x = 640 x = 640 / 0.32 = 2000 the answer is a ."
Answer: a
Question (general): if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 11 ¤ √ 11 =
Options: a ) 44 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: x = √ 11 and y also = √ 11 applying the function ( √ 11 + √ 11 ) ^ 2 - ( √ 11 - √ 11 ) ^ 2 = ( 2 √ 11 ) ^ 2 - 0 = 4 x 11 = 44 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 11 and y = √ 11 you get the answer 44 . answer a
Answer: a
Question (other): of the people who responded to a market survey , 200 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 4 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 160 , c ) 250 , d ) 350 , e ) 480
Rationale: "ratio = 4 : 1 = > 4 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 200 = > 4 x = 200 = > x = 50 hence total no . of respondents = 200 + 50 = 250 hence c is the answer ."
Answer: c
Question (general): 5358 x 55 = ?
Options: a ) 272258 , b ) 272358 , c ) 294690 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 5 ) = 5358 x 50 + 5358 x 5 = 267900 + 26790 = 294690 . c )"
Answer: c