Cheukting/mathqa huggingface dataset:
Question (general): if the average ( arithmetic mean ) of x + 1 , x + 5 , and x + 9 is 0 , then x =
Options: a ) – 5 , b ) – 4 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 1 + x + 5 + x + 9 ) / 3 = 0 = > 3 x + 15 = 0 = > x = - 5 answer a"
Answer: a
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 14 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 5333 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.14 t + 0.08 ( p - t ) = 1440 - - - - > t = 5333 . b is the correct answer ."
Answer: b
Question (geometry): what should be added to 4750 so that it may become a perfect square ?
Options: a ) 11 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "69 x 69 = 4761 4761 - 4750 = 11 if added to 11 get perfect square answer = a"
Answer: a
Question (gain): john makes $ 60 a week from his job . he earns a raise andnow makes $ 72 a week . what is the % increase ?
Options: a ) 20 % , b ) 16.66 % , c ) 16.56 % , d ) 17.66 % , e ) 18.1 %
Rationale: "increase = ( 12 / 60 ) * 100 = ( 1 / 5 ) * 100 = 20 % . a"
Answer: a
Question (general): 50 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 51 , e ) 81
Rationale: "explanation : 50 + 5 * 12 / ( 180 / 3 ) = 50 + 5 * 12 / ( 60 ) = 50 + ( 5 * 12 ) / 60 = 50 + 1 = 51 . answer : d"
Answer: d
Question (gain): find number which is 50 % less than 60 .
Options: a ) 18 , b ) 30 , c ) 32 , d ) 26 , e ) 98
Rationale: explanation : 50 % less is 50 % of the given number therefore , 50 % of 60 is 30 . answer : b
Answer: b
Question (general): mark bought a set of 6 flower pots of different sizes at a total cost of $ 7.80 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.93 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 7.80 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.75 the other 5 pots are . . . . 1.75 1.50 1.25 1.00 0.75 total = $ 7.80 so this must be the answer . b
Answer: b
Question (general): a certain basketball team that has played 2 / 3 of its games has a record of 18 wins and 2 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "18 wins , 2 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 2 games so it can lose another 5 at most . answer ( c )"
Answer: c
Question (geometry): a circular well with a diameter of 2 metres , is dug to a depth of 10 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 31.4 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 1 × 1 × 10 ) m 3 ‹ = › 31.4 m 3 . answer b"
Answer: b
Question (gain): a sum fetched a total simple interest of $ 4241.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8930
Rationale: "e 8930 principal = $ 100 x 4241.25 / 9 x 5 = $ 424125 / 45 = $ 8930 ."
Answer: e
Question (general): the unit digit in the product ( 635 * 767 * 984 * 489 ) is :
Options: a ) 0 , b ) 8 , c ) 3 , d ) 2 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 7 * 4 * 9 ) = 0 answer : a"
Answer: a
Question (general): in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals .
Options: a ) 10 , b ) 12 , c ) 17 , d ) 22 , e ) 30
Rationale: bunuel , my answer for exactly 2 people was 17 and this was my approach : 100 % = ( a + b + c ) - ( anb + anc + bnc ) - 5 % + 22 % which leads me to x = 100 % = ( 50 + 30 + 20 ) - ( at least 2 people ) - 5 % + 22 % . c
Answer: c
Question (other): a certain bag contains 60 balls — 22 white , 18 green , 2 yellow , 15 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.7 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.91
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 2 ) / 60 = 42 / 60 = 0.7 . answer : a ."
Answer: a
Question (gain): if the personal income tax rate is lowered from 38 % to 30 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36500 ?
Options: a ) $ 1825 , b ) $ 5000 , c ) $ 3150 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 38 - 33 ) % of 36500 = 1825 . answer : a"
Answer: a
Question (general): elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 48 and elvin ' s total telephone bill for february was 90 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 6 , e ) $ 28
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d"
Answer: d
Question (gain): in the recent , climate conference in new york , out of 500 men , 300 women , 500 children present inside the building premises , 10 % of the men , 60 % of the women and 70 % of the children were indians . find the percentage of people who were not indian ?
Options: a ) 59.54 % , b ) 66.25 % , c ) 55.39 % , d ) 63.21 % , e ) 64.22 %
Rationale: "solution : number of indians men present there = 500 * 10 / 100 = 50 indian women = 300 * 60 / 100 = 180 indian children = 500 * 70 / 100 = 350 . total member present in climate conference = 500 + 300 + 500 = 1300 total indian = 50 + 180 + 350 = 580 hence , % of indian present there = 580 * 100 / 1300 = 44.61 % % of people who were not indian = 100 - 44.61 = 55.39 % . answer c"
Answer: c
Question (other): two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ?
Options: a ) 122,195 , b ) 121,199 , c ) 120,192 , d ) 102,192 , e ) 126,109
Rationale: "( 5 x - 30 ) : ( 8 x - 30 ) = 5 : 9 x = 24 = > 120,192 answer : c"
Answer: c
Question (general): find k if 56 / k = 4 .
Options: a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13
Rationale: "since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d"
Answer: d
Question (physics): a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 30 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a"
Answer: a
Question (physics): a 400 meter long train crosses a man standing on the platform in 10 sec . what is the speed of the train ?
Options: a ) 144 , b ) 108 , c ) 278 , d ) 126 , e ) 112
Rationale: "s = 400 / 10 * 18 / 5 = 144 kmph answer : a"
Answer: a
Question (gain): a man took a loan from a bank at the rate of 9 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 15,000 , d ) rs . 20,000 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d"
Answer: d
Question (general): what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 / 44444444 ^ 2 )
Options: a ) 88888883 , b ) 88888884 , c ) 88888885 , d ) 88888886 , e ) 88888873
Rationale: "let x = 44444444 , then 44444445 = x + 1 88888885 = 2 x - 3 44444442 = x - 2 44444438 = x - 6 44444444 ^ 2 = x ^ 2 then substitute it in equation ( x + 1 ) ( 2 x - 3 ) ( x - 2 ) + ( x - 6 ) / x ^ 2 ans is 2 x - 5 i . e 88888883 answer : a"
Answer: a
Question (general): jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ?
Options: a ) 75 , b ) 90 , c ) 45 , d ) 80 , e ) 84
Rationale: e 84 explanation : let us assume that jack lived for p years . p / 6 + p / 12 + p / 7 + 5 + p / 2 + 4 = x = > p = 84 . therefore , jack lived for 84 years .
Answer: e
Question (general): if 7 a - 3 b = 10 b + 40 = - 12 b - 2 a , what is the value of 9 a + 9 b ?
Options: a ) - 5 , b ) - 3 , c ) 0 , d ) 3 , e ) 5
Rationale: ( i ) 7 a - 13 b = 40 ( ii ) 2 a + 22 b = - 40 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c .
Answer: c
Question (gain): the price of a book is increased from $ 300 to $ 420 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 420 â € “ rs 300 = rs 120 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 120 300 ) * 100 = 40 % c"
Answer: c
Question (physics): a train 210 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 49 sec , e ) 28 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 210 + 140 = 350 m required time = 350 * 2 / 25 = 28 sec answer : e"
Answer: e
Question (general): the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 8 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2125
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 8 of that new total price : p = 1 / 8 * $ 3,000 = $ 375 . plug this value in the first equation : c + 375 = $ 2,500 - - > c = $ 2,125 . answer : e ."
Answer: e
Question (other): 39 ! is divided by 41 then what is the remainder ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7
Rationale: "substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a"
Answer: a
Question (general): if x is equal to the sum of the integers from 10 to 30 , inclusive , and y is the number of even integers from 10 to 30 , inclusive , what is the value of x + y ?
Options: a ) 401 , b ) 411 , c ) 421 , d ) 431 , e ) 441
Rationale: "x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d ."
Answer: d
Question (general): the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is : explanation :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 117 , e ) 121
Rationale: let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c
Answer: c
Question (general): if 42.36 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.36 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.36 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.36 = km / 50 . . . . . . 36 / 100 = 3 m / 50 . . . . . . m = 6 k + m = 3 + 6 = 9 answer : d"
Answer: d
Question (other): if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 14 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 20 , d ) 30 , e ) 174
Rationale: the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c .
Answer: c
Question (physics): how many seconds will a 700 meter 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 ) 287 , b ) 288 , c ) 600 , d ) 277 , e ) 121
Rationale: "let length of tunnel is x meter distance = 700 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 700 + x = ( 65 / 3 ) * 60 700 + x = 20 * 65 = 1300 x = 1300 - 700 = 600 meters answer : c"
Answer: c
Question (general): a bakery has 6 employees . it pays annual salaries of $ 16,000 to each of 2 employees , $ 18,000 to 1 employee , and $ 19,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 17,200 , b ) $ 17,500 , c ) $ 17,800 , d ) $ 18,000 , e ) $ 18,400
Rationale: "average = 2 ( 16000 ) + ( 18000 ) + 3 ( 19000 ) / 6 = $ 17,833 the answer is c ."
Answer: c
Question (general): find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 35 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1631
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 35 5 x = 1330 x = 266 large number = 266 + 1365 = 1631 e"
Answer: e
Question (geometry): how many odd numbers between 10 and 1400 are the squares of integers ?
Options: a ) 14 , b ) 17 , c ) 20 , d ) 23 , e ) 26
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is b ."
Answer: b
Question (general): n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 * n is divided by 4 ?
Options: a ) 8 , b ) 2 , c ) 6 , d ) 7 , e ) 1
Rationale: explanation : let n = 4 * q + 3 . then , 2 * n = 8 * q + 6 = 4 ( 2 * q + 1 ) + 2 . thus when 2 * n is divided by 4 , the reminder is 2 . answer : b ) 2
Answer: b
Question (other): a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 200 , b ) $ 900 , c ) $ 700 , d ) $ 600 , e ) $ 400
Rationale: "b ' s share = 2700 * 3 / 9 = $ 900 answer is b"
Answer: b
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 18 . the larger of the two numbers is :
Options: a ) 276 , b ) 414 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b"
Answer: b
Question (general): if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) =
Options: a ) 2925 , b ) 3456 , c ) 4581 , d ) 3683 , e ) 1308
Rationale: 6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b
Answer: b
Question (physics): a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together , what part of the same work they can finish in a day ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 1 , e ) 1 / 4
Rationale: given that b alone can complete the same work in days = half the time taken by a = 9 days a ’ s one day work = 1 / 18 b ’ s one day work = 1 / 9 ( a + b ) ’ s one day work = 1 / 18 + 1 / 9 = 1 / 6 answer : b .
Answer: b
Question (gain): an empty fuel tank with a capacity of 212 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 98 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 212 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 212 - a gallons of fuel b is 0.16 ( 212 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 212 - a ) = 30 - - > a = 98 . answer : b ."
Answer: b
Question (geometry): the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams r ?
Options: a ) 16 , b ) r = 32 , c ) r = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Question (physics): 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 2 women and 10 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 2 women + 10 children ) ' s 1 day work = ( 2 / 70 + 10 / 140 ) = 1 / 10 2 women and 10 children will complete the work in 10 days . e"
Answer: e
Question (physics): a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 11 , d ) 9.5 , e ) 10
Rationale: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 11 110 660 it takes a total of nine hours to cover the 660 mile distance . answer : c . 11
Answer: c
Question (general): how many integers are divisible by 2 between 10 ! and 10 ! + 20 inclusive ?
Options: a ) 6 , b ) 7 , c ) 21 , d ) 9 , e ) 10
Rationale: "c = 21 10 ! is divisible by 2 there are 20 numbers between 10 ! and 10 ! + 20 that are divisible by 1 . hence 21"
Answer: c
Question (gain): ramesh purchased a refrigerator for rs . 14500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 20350 , d ) 17600 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 14,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 18125 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 18125 + 375 = rs . 18500 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 18500 * 110 / 100 = rs . 20350 answer : c"
Answer: c
Question (general): if equation | x / 2 | + | y / 2 | = 4 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 50 , c ) 108 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 8 | + | y / 8 | = 1 , so these are lines in four quadrants with x and y intercept as 8 , so it is a rhombus with diagonals of 16 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 16 * 16 = 108 . answer c .
Answer: c
Question (general): let f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c =
Options: a ) 18 , b ) 15 , c ) - 15 , d ) - 11 , e ) - 24
Rationale: "f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c = f ( 6 ) = 0 = 36 + 6 b + c - - - taking 36 to the other side - > 6 b + c = - 36 f ( - 1 ) = 0 = 1 - b + c - - - taking - b + c to the other side - > b - c = 1 when we add these 2 equations , we get 7 b = - 35 - - - > b = - 5 and while substituting b = - 5 we get c = - 6 . b + c = - 11 - - - answer d"
Answer: d
Question (general): approximately how many revolutions will be made by a car tire with a 13 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 120 , b ) 180 , c ) 772 , d ) 720 , e ) 1,440
Rationale: "diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 103.68 = 771.60 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"
Answer: c
Question (general): if x / y = 2 / 5 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 7 / 3
Rationale: any x and y satisfying x / y = 2 / 5 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 5 , then ( x + y ) / ( x - y ) = ( 2 + 5 ) / ( 2 - 5 ) = - 7 / 3 . answer : e .
Answer: e
Question (geometry): if the radius of a circle is increased by 60 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 156 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c"
Answer: c