Cheukting/mathqa huggingface dataset:
Question (other): in a class , 10 students like to play basketball and 8 like to play cricket . 4 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 14
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 10 + 8 - 4 = 14 e )"
Answer: e
Question (general): a box contains 9 apples , 8 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 5 times in a row ) = 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 * 4 / 5 = 4 / 9 < 0.5 the answer is c ."
Answer: c
Question (general): what is the units digit of ( 5 ! * 4 ! - 3 ! * 5 ! ) / 120
Options: a ) 7 , b ) 8 , c ) 9 , d ) 4 , e ) 1
Rationale: "( 5 ! * 4 ! - 3 ! * 5 ! ) / 9 = 5 ! ( 4 ! - 3 ! ) / 120 = 120 ( 24 - 6 ) / 120 = 18 units digit of the above product will be equal to 8 answer b"
Answer: b
Question (geometry): the area of circle o is added to its diameter . if the circumference of circle o is then subtracted from this total , the result is 4 . what is the area of circle o ?
Options: a ) 2 / π
b ) 2
c ) 8
d ) 4
e ) 4 π
Rationale: area + diameter - circumference = 4 pi * r ^ 2 + 2 r = 4 + 2 pi * r isolate r and get r ( pi * r + 2 ) = 4 + 2 pi * r r = ( 4 + 2 pi * r ) / ( pi * r + 2 ) = > 2 ( 2 + pi * r ) / ( pi * r + 2 ) r = 2 area = pi * r ^ 2 = > pi * 4 e
Answer: e
Question (general): ( 3080 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 330 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9240 ) / 28 = 330 option c"
Answer: c
Question (physics): the length of the bridge , which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds , is
Options: a ) 200 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) none
Rationale: "sol . speed = [ 45 x 5 / 18 ] m / sec = ( 25 / 2 ) m / sec ; time = 30 sec . let the length of bridge be x metres . then , 130 + x / 30 = 25 / 2 ⇔ 2 ( 130 + x ) = 750 ⇔ x = 245 m . answer c"
Answer: c
Question (general): the sum of the even numbers between 1 and n is 89 * 90 , where n is an odd number , then n = ?
Options: a ) 167 , b ) 173 , c ) 179 , d ) 185 , e ) 193
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 89 * 90 then a = 89 and n = 179 . the answer is c ."
Answer: c
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will be pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) none
Rationale: "sol . speed = [ 45 x 5 / 18 ] m / sec = 25 / 2 m / sec . total distance covered = ( 360 + 140 ) m = 500 m . ∴ required time = ( 500 x 2 / 25 ) sec = 40 sec . answer a"
Answer: a
Question (gain): a person distributed 10 % of his income to his 2 children each . he deposited 20 % of his income to his wife ' s account . he donated 10 % of remaining amount to an orphan house . finally he has $ 500 . find his total income ?
Options: a ) $ 900 , b ) $ 1000 , c ) $ 1200 , d ) $ 1150 , e ) $ 1500
Rationale: "2 children got = 2 * 10 % = 20 % wife got = 20 % orphan house = 10 % total = 20 + 20 + 10 = 50 % remaining = 100 - 50 = 50 % 50 % = 500 100 % = 500 * 100 / 50 = $ 1000 answer is b"
Answer: b
Question (general): if q is a positive integer and q ^ 2 is divisible by 12 , then the largest positive integer that must divide q ^ 3 is
Options: a ) 2 ^ 3 , b ) 2 ^ 6 , c ) 3 ^ 3 , d ) 6 ^ 3 , e ) 12 ^ 2
Rationale: since q is an integer so q can not have a 2 and sqrt 3 ( because squaring this will give us a 2 ^ 2 and 3 ( making the product as 12 , and making q ^ 2 as a multiple of 12 ) ) q ^ 2 is divisible by 12 ( 12 = 2 * 2 * 3 ) , so , q should have at least one 2 and one 3 so that q ^ 2 has a 2 ^ 2 and two 3 so , q will have a 2 and a 3 . or q will be a multiple of 6 so , largest possible integer than should divide q ^ 3 is 6 ^ 3 so , answer will be d
Answer: d
Question (general): the average weight of 8 persons increases by 5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 105 kg
Rationale: "total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 65 + 40 ) kg = 105 kg . answer : e"
Answer: e
Question (geometry): two cubes of their volumes in the ratio 64 : 343 . the ratio of their surface area is :
Options: a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 7
Rationale: "the ratio of their surface area is 64 : 343 4 : 7 answer is e ."
Answer: e
Question (general): if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 , then n =
Options: a ) 3 , b ) 6 , c ) 12 , d ) 27 , e ) 24
Rationale: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 = > 4 x 2 ^ 2 n = 4 ^ 28 = 2 ^ 56 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 56 = > 2 ^ ( 2 n + 2 ) = 2 ^ 56 = > 2 n + 2 = 56 = > n = 27 so . answer will be d ."
Answer: d
Question (general): a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order y ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75
Rationale: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . y = 12.5 * 6 = 75 . e
Answer: e
Question (general): if a / b = 4 / 3 , then ( 3 a + 2 b ) / ( 3 a - 2 b ) = ?
Options: a ) 6 , b ) 3 , c ) 5 , d ) - 1 , e ) none
Rationale: answer dividing numerator as well as denominator by b , we get given exp . = ( 3 a + 2 b ) / ( 3 a - 2 b ) = ( 3 a / b + 2 ) / ( 3 a / b - 2 ) = [ ( 3 x 4 ) / 3 + 2 ] / [ ( 3 x 4 ) / 3 - 2 ] = ( 4 + 2 ) / ( 4 - 2 ) = 3 option : b
Answer: b
Question (other): two numbers are in the ratio 3 : 4 . if their l . c . m . is 60 . what is sum of the numbers ?
Options: a ) 35 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 60 = > 12 x = 60 = > x = 60 / 12 = 5 sum of the numbers = 3 x + 4 x = 7 x = 7 x 5 = 35 answer : option a"
Answer: a
Question (physics): a train traveled the first d miles of its journey it an average speed of 40 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 96 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 100 , d ) 120 , e ) 135
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 40 + d / y + d / 160 = 96 solving for d and y , 15 y = 11 y + 480 4 y = 400 y = 100 answer c"
Answer: c
Question (general): a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 15000 left with him . find salary . .
Options: a ) $ 150000 , b ) $ 18000 , c ) $ 180000 , d ) $ 1800 , e ) none
Rationale: [ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 15000 , = [ 1 - 9 / 10 ] * total salary = $ 15000 , total salary = $ 15000 * 10 = $ 150000 , correct answer ( a )
Answer: a
Question (general): 17200 x 223 + 17200 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 2658560 , d ) 5160000 , e ) none of them
Rationale: "= 17200 x ( 223 + 77 ) ( by distributive law ) = 17200 x 300 = 5160000 answer is d"
Answer: d
Question (physics): how many cuboids of length 5 m , width 3 m and height 2 m can be farmed from a cuboid of 12 m length , 14 m width and 10 m height .
Options: a ) 82 , b ) 56 , c ) 80 , d ) 56 , e ) 100
Rationale: "( 12 ã — 14 ã — 10 ) / ( 5 ã — 3 ã — 2 ) = 56 answer is b ."
Answer: b
Question (general): what is the lowest positive integer that is divisible by each of the integers 1 through 12 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 27,720
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , 2 * 5 , 11 , and 2 ^ 2 * 3 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 * 11 = 27,720 the answer is e ."
Answer: e
Question (physics): the length of the bridge , which a train 160 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 377 , b ) 367 , c ) 237 , d ) 215 , e ) 267
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 x = 215 m . answer : d"
Answer: d
Question (general): car dealership x , the total profit from sales increased by 30 percent over the previous years , while the number of cars sold decreased by 30 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 30 % , c ) 52 % , d ) 63 % , e ) 85.71 %
Rationale: let profit be x and cars sold be y originally profit / car = x / y now it is 1.3 x / 0.7 y = 13 / 7 ( x / y ) increase in profit per car = ( ( 6 / 7 ) ( x / y ) ) / ( x / y ) * 100 = 85.71 % answer = e
Answer: e
Question (physics): arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 30 days .
Options: a ) 16 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 20 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 30 * 6 / 10 = 18 days . answer : c"
Answer: c
Question (physics): 10 men and 15 women together can complete a work in 8 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 127 days , b ) 667 days , c ) 177 days , d ) 187 days , e ) 600 days
Rationale: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 8 15 women ' s 1 day work = ( 1 / 8 - 10 / 100 ) = 1 / 40 1 woman ' s 1 day work = 1 / 600 1 woman alone can complete the work in 600 days . answer : e"
Answer: e
Question (other): if m = 3 ^ n , what is the greatest value of n for which m is a factor of 28 !
Options: a ) 13 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 , 24,27 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 24 = 3 x 8 - > 1 27 = 3 x 3 x 3 - > 3 - - - - count 3 ' s = 13 so answer is 13 answer : a"
Answer: a
Question (physics): a train which has 390 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 26 sec , b ) 39 sec , c ) 36 sec , d ) 29 sec , e ) 30 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 390 / ( ( 45 - 9 ) ( 5 / 18 ) = 390 / 36 * ( 5 / 18 ) = 390 / 10 = 39 sec answer : b"
Answer: b
Question (gain): if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 51.25 , b ) rs . 51.27 , c ) rs . 51.79 , d ) rs . 51.8 , e ) rs . 51.93
Rationale: "sum = ( 50 * 100 ) / ( 2 * 5 ) = rs . 500 amount = [ 500 * ( 1 + 5 / 100 ) 2 ] = rs . 551.25 c . i . = ( 551.25 - 500 ) = rs . 51.25 . answer : a"
Answer: a
Question (general): the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 6.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 6.50
Rationale: "i tried using time / rate approach : - initial price difference = 6.80 - 3.20 = 3.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 3.6 = t ( 5.4 x ) - > t = ( 3.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 3.6 / 5.4 = 6.5 answer e ."
Answer: e
Question (gain): a person borrows 9000 for 9 years at 3 % p . a . simple interest . he immediately lends it to another person at 7 % p . a . for 9 years . find his gain in the transaction per year .
Options: a ) 380 , b ) 360 , c ) 340 , d ) 300 , e ) 180
Rationale: "gain in 9 years = [ ( 9000 ã — 9 ã — 7 / 100 ) â ˆ ’ ( 9000 ã — 9 ã — 3 / 100 ) ] = ( 5670 â € “ 2430 ) = 3240 â ˆ ´ gain in 1 year = ( 3240 / 9 ) = 360 answer b"
Answer: b
Question (general): 2001 + 1015
Options: a ) 8390 , b ) 3016 , c ) 2808 , d ) 3890 , e ) 2080
Rationale: b
Answer: b
Question (gain): a shopkeeper has 280 kg of apples . he sells 40 % of these at 30 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 30 %
Rationale: "if the total quantity was 100 then 40 x 30 % + 60 x 30 % = 30 this profit will remain same for any total quantity unless the % of products remains the same . hence ' e ' is the answer"
Answer: e
Question (physics): the speed of a boat in still water in 42 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 33.7 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 4 ) = 46 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 46 = 33.7 km answer : c"
Answer: c
Question (general): the average expenditure of a labourer for 5 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 69.5 , b ) 71.2 , c ) 60.4 , d ) 62.1 , e ) 72.1
Rationale: "income of 6 months = ( 5 × 85 ) – debt = 425 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 695 average monthly income = 695 ÷ 10 = 69.5 answer a"
Answer: a
Question (geometry): a rectangular field has a length 10 meters more than it is width . if the area of the field is 119 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 ( too high ) 18 * 8 = 144 ( too high ) 17 * 7 = 119 the length is 17 meters . the answer is c ."
Answer: c
Question (gain): in country z , 12 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 35 % , b ) 43 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 12 % job of choice total = 40 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 25 % of 60 % = 15 % . we can also see that 28 % of the people have their job of choice and a diploma ( 40 % - 12 % = 28 % ) . 28 % + 15 % = 43 % . therefore 43 % of the people in country z have a diploma . ans b"
Answer: b
Question (gain): in a village of 2,500 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 221 / 250 , b ) 199 / 250 , c ) 33 / 50 , d ) 8 / 25 , e ) 51 / 250
Rationale: "to solve this we would need to know the number of people who are less than 70 years old , the number of males , and the number of males who are less than 70 years old . overlapping sets : quantity of a or b = a + b - ( a ∩ b ) = quantity of a + quantity of b - ( intersection of a and b ) number of males = 2500 - 850 = 1650 number of people below 70 years old = 2500 - 800 = 1700 number of males below 70 years old = 1700 - ( 850 * 0.4 ) = 1360 total number of people who are male or below 70 = 1650 + 1700 - 1360 = 1990 probability of male or below 70 = 1990 / 2500 = 199 / 250 answer : b"
Answer: b
Question (physics): two pipes a and b can separately fill a tank in 12 and 15 minutes respectively . a third pipe c can drain off 56 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 549 , b ) 540 , c ) 542 , d ) 672 , e ) 279
Rationale: "1 / 12 + 1 / 15 - 1 / x = 1 / 15 x = 12 12 * 56 = 672 answer : d"
Answer: d
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % 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 $ 1640 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 13000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.12 t + 0.08 ( p - t ) = 1640 - - - - > t = 13000 . e is the correct answer ."
Answer: e
Question (general): in 10 years , a will be twice as old as b was 10 years ago . if a is now 5 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 35 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 5 = > 2 b - b - 5 = 30 b = 35 so the present age of b is 35 years answer : d"
Answer: d
Question (probability): a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: "5 choices for each of the 4 questions , thus total of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways . answer : c ."
Answer: c
Question (general): 1257 1275 1527 . . . . . . . . . . . . . . . . + 7521 the addition problem above shows 4 of the 24 different integers that can be formed by using each of the digits 1 , 25 and 7 exactly once in each integer . what is the sum t of the 24 integers ?
Options: a ) 26996 , b ) 44406 , c ) 60444 , d ) 66660 , e ) 99990
Rationale: this is the way i solved it : total no . of different combos = 24 , total digits 4 therefore each digit must repeat 24 / 4 = 6 times in each row . . so the right most row would add up to 1 x 6 + 2 x 6 + 5 x 6 + 7 x 6 = 6 + 12 + 30 + 42 = 90 . . each row would add up to 90 , so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90 + 9 and 9 stays and one 9 goes to the row to the left , so the last two digits of the sum t should be 90 ( e ) . . we could go on and solve the exact number but since only one answer choice has the last digits as 90 we need n ' t go any further . .
Answer: e
Question (gain): john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 20,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 40,402 , b ) 40404 , c ) 40000 , d ) 50000 , e ) 50005
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 20,000 ( 1 + 0.04 / 4 ) ^ 4 - 20,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 20,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 20,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 20,000 ( 1.0201 + 1 ) = 40,402 . hence answer is a ."
Answer: a
Question (physics): convert the 1 / 3 m / s into kilometers per hour ?
Options: a ) 2.9 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph
Rationale: "1 / 3 m / s = 1 / 3 * 18 / 5 = 12 / 10 = 1.2 kmph . answer : d"
Answer: d
Question (general): if x , y , and z are positive integers , and 3 x = 5 y = 6 z , then the least possible value of x + y + z is
Options: a ) 21 , b ) 28 , c ) 37 , d ) 42 , e ) 60
Rationale: "take lcm of 3,5 and 6 = 30 now 3 x = 30 = > x = 10 5 y = 30 = > y = 6 6 z = 30 = > z = 5 10 + 6 + 5 = 21 . option a ."
Answer: a
Question (general): evaluate : 19 + sqrt ( - 2 + 12 ã — 6 ã · 9 ) = ?
Options: a ) 51 , b ) 53 , c ) 55 , d ) 57 , e ) 59
Rationale: "according to order of operations , inner brackets first where 12 x 6 ã · 9 is first calculated since it has a multiplication and a division . 12 x 6 ã · 9 = 72 ã · 9 = 8 hence 19 + sqrt ( - 2 + 12 ã — 6 ã · 9 ) = 19 + sqrt ( - 2 + 8 ) = 19 + sqrt ( 6 ) = 19 + 36 = 55 correct answer c ) 55"
Answer: c
Question (general): the total number of digits used in numbering the pages of a book having 369 pages is
Options: a ) 732 , b ) 990 , c ) 999 , d ) 1305 , e ) 1405
Rationale: total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 270 ) = ( 9 + 180 + 810 ) = 999 . answer : c
Answer: c
Question (geometry): when 732 is subtracted form the square of a number , the answer that is obtained is 5280 . what is the number ?
Options: a ) 228
b ) 103
c ) 286
d ) 122
e ) 102
Rationale: explanation : let the number be x x 2 - 732 = 5280 x 2 = 5280 + ( 70 + 3 ) 2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2 ( 100 ) ( 3 ) + 32 = ( 100 + 3 ) 2 x = 100 + 3 = 103 . answer : b
Answer: b
Question (general): the average height of 35 boys in a class was calculated as 182 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 180.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 182 cm . wrong total height of 35 boys = 182 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - 60 / 35 cm = 182 cm - 1.71 cm = 180.29 cm . answer : b"
Answer: b
Question (physics): the length of a train and that of a platform are equal . if with a speed of 108 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 299 , b ) 266 , c ) 299 , d ) 900 , e ) 261
Rationale: "speed = [ 108 * 5 / 18 ] m / sec = 30 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 30 = > x = 30 * 60 / 2 = 900 answer : d"
Answer: d
Question (other): the simple form of the ratio 7 / 6 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 35 : 12
Rationale: "7 / 6 : 2 / 5 = 35 : 12 answer : e"
Answer: e