Cheukting/mathqa huggingface dataset:
Question (other): the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is
Options: a ) 32 , b ) 37 , c ) 84 , d ) 29 , e ) 21
Rationale: explanation : let the numbers be x and 4 x . then , \ inline \ fn _ jvn x \ times 4 x = 84 \ times 21 \ : \ : \ leftrightarrow \ : \ : x ^ { 2 } = \ frac { 84 \ times 21 } { 4 } \ : \ : \ leftrightarrow \ : \ : x = 21 hence larger number = 4 x = 84 answer : c ) 84
Answer: c
Question (general): if it takes a tub 2 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 50 seconds , d ) 2 minutes , 14 seconds , e ) 4 minutes , 12 seconds
Rationale: "if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 2 minutes to drain 5 / 7 th of tub it takes 2 * ( 7 / 5 ) minutes to drain the entire tub and 2 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 4 / 5 minutes or 48 minutes so answer is a"
Answer: a
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 210 . the amount of the bill is
Options: a ) 1200 , b ) 1960 , c ) 1600 , d ) 1354 , e ) none of these
Rationale: "explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 210 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 210 or x = 1750 p . w . = rs . 1750 sum due = p . w . + t . d . = rs . ( 1750 210 ) = rs . 1960 . answer : b"
Answer: b
Question (general): how many numbers between 100 and 630 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 13 , e ) 99
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 600 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 630 : 630 / 42 = 13 hence , 42 * 15 = 630 is the last number divisible by 42 within 630 hence , total numbers divisible by 2 , 3 , 7 together are ( 15 â € “ 2 ) = 13 answer : d"
Answer: d
Question (physics): a and b together can complete a work in 12 days . a alone can complete it in 20 days . if b does the work only for half a day daily , then in how many days a and b together will complete the work ?
Options: a ) 10 days , b ) 11 days , c ) 15 days , d ) 20 days , e ) none of these
Rationale: b ' s 1 day ' s work = ( 1 / 12 - 1 / 20 ) = 2 / 60 = 1 / 30 now , ( a + b ) ' s 1 day ' s work = ( 1 / 20 + 1 / 60 ) = 4 / 60 = 1 / 15 so , a and b together will complete the work in 15 days . correct option : c
Answer: c
Question (general): marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 120 . actual / projected * 100 = 75 / 120 * 100 = 62.5 % . answer : c"
Answer: c
Question (general): what is the tens digit of 7 ^ 1033 ?
Options: a ) 0 , b ) 1 , c ) 0 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1033 = 4 * 258 + 1 the ten ' s digit will be 0 . answer c"
Answer: c
Question (general): country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 360 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 24 million , b ) $ 120 million , c ) $ 644 million , d ) $ 540 million , e ) $ 720 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 360 mill / 2 month i . e . $ 180 mill / month difference / month = 180 - 120 = 60 difference / year = $ 60 mill * 12 = $ 720 mill answer : e"
Answer: e
Question (gain): a man is walking at the rate of 6 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1500 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 6 â ˆ — 5 / 18 = 5 / 3 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 5 / 3 â ˆ — 900 = 1500 meter option d"
Answer: d
Question (geometry): 2 minute is taken to travel the diagonal of square field at 3 km / hour . calculate the area of field ?
Options: a ) 25 are
b ) 30 are
c ) 50 are
d ) 60 are
e ) 45 are
Rationale: speed of man = [ 3 * 5 / 18 ] m / sec . = 5 / 6 m / sec . , distance travel in 2 minute = { 5 / 6 * 2 * 60 } m . = 100 m . diagonal of square field = 100 m area of field = 1 / 2 * diagonal ^ 2 = [ 1 / 2 * 100 * 100 ] sq . m = 5000 sq . m = 5000 / 100 = 50 are ( 1 are = 100 sq . m ) answer c
Answer: c
Question (physics): a 400 meter long train crosses a platform in 45 seconds while it crosses a signal pole in 30 seconds . what is the length of the platform ?
Options: a ) 200 , b ) 400 , c ) 350 , d ) 1800 , e ) 45
Rationale: "speed = [ 400 / 30 ] m / sec = 40 / 3 m / sec . let the length of the platform be x meters . then , x + 400 / 45 = 40 / 3 3 ( x + 400 ) = 1800 è x = 200 m . answer : a"
Answer: a
Question (physics): a and b complete a work in 8 days . a alone can do it in 14 days . if both together can do the work in how many days ?
Options: a ) 5 days , b ) 8 days , c ) 6 days , d ) 3.15 days , e ) 2.75 days
Rationale: "1 / 8 + 1 / 14 = 11 / 56 56 / 11 = 5 days answer : a"
Answer: a
Question (general): if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 27 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 34 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 54 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 34 hence , the correct answer is c"
Answer: c
Question (physics): a person travels equal distances with speed of 3 km / hr , 4 km / hr and 5 km / hr and takes a total of 47 minutes . find the total distane
Options: a ) 3 km , b ) 4 km , c ) 6 km , d ) 9 km , e ) 5 km
Rationale: explanation : let the distance be 3 x km , then , x / 3 + x / 4 + x / 5 = 47 / 60 47 x / 60 = 47 / 60 x = 1 so total distance = 3 * 1 = 3 km option a
Answer: a
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 3 seconds . find the length of the train .
Options: a ) 60 , b ) 50 , c ) 75 , d ) 100 , e ) 120
Rationale: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 3 = 50 meter answer : b"
Answer: b
Question (gain): sam invested $ 15000 @ 10 % per annum for one year . if the interest is compounded half yearly , then the amount received by sam at the end of the year will be ?
Options: a ) $ 16537.50 , b ) $ 24512.56 , c ) $ 18475.89 , d ) $ 15478.56 , e ) $ 12456.35
Rationale: p = $ 15000 r = 10 % p . a . = 5 % t = 2 half years amount = 15000 * ( 1 + 5 / 100 ) ^ 2 = 15000 * 21 / 20 * 21 / 20 = $ 16537.50 answer is a
Answer: a
Question (physics): two cars start at the same time from opposite ends of a highway that is 45 miles long . one car is riding at 14 mph and the second car is riding at 16 mph . how long after they begin will they meet ?
Options: a ) 1 , b ) 1.2 , c ) 1.25 , d ) 1.35 , e ) 1.5
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 16 + 14 = 30 mph total distance to be covered = 45 miles . time taken would be : 45 miles / 30 mph = 1.5 hours e is the answer ."
Answer: e
Question (gain): a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 300 before any discount ?
Options: a ) $ 230.00 , b ) $ 145.60 , c ) $ 168.80 , d ) $ 182.00 , e ) $ 210.00
Rationale: "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 300 would be . . . . . ( $ 300 ) ( . 7 ) ( . 8 ) = ( $ 300 ) ( . 56 ) = 168 final answer : c"
Answer: c
Question (physics): tim and é lan are 180 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 130 miles . , b ) 135 miles . , c ) 145 miles . , d ) 120 miles . , e ) 165 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice d meet the 2 : 1 ( tim : elan = 120 : 60 ) ratio of maintaining total distance traveled 180 miles socorrect answer d"
Answer: d
Question (general): for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 960 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 10 , b ) 16 , c ) 12 , d ) 14 , e ) 19
Rationale: "we know that : x > 1 , y > 1 , and x + 3 y < 960 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest no all factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 960 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 960 so , 3 y < 448 = = > y < 448 / 3 so , y can take any value which is less than 448 / 3 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . b"
Answer: b
Question (physics): a man rows his boat 90 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 9 kmph , b ) 6 kmph , c ) 5 kmph , d ) 8 kmph , e ) 7 kmph
Rationale: "speed downstream = d / t = 90 / ( 2 1 / 2 ) = 36 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 36 - 18 ) / 2 = 9 kmph answer : a"
Answer: a
Question (general): what is the smallest positive integer k such that the product of 1575 x k is a perfect square ?
Options: a ) 7 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 1575 = 3 ^ 2 * 5 ^ 2 * 7 , so if k = 7 then 1575 k = ( 3 * 5 * 7 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Question (gain): in a public show 75 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 150
Rationale: "75 % of 600 = 75 / 100 × 600 = 450 therefore , the number of vacant seats = 600 - 450 = 150 . answer : e"
Answer: e
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 180 . the amount of the bill is
Options: a ) 1200 , b ) 1764 , c ) 1680 , d ) 1354 , e ) none of these
Rationale: "explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 180 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 180 or x = 1500 . p . w . = rs . 1500 . sum due = p . w . + t . d . = rs . ( 1500 180 ) = rs . 1680 . answer : c"
Answer: c
Question (general): a project scheduled to be carried out over a single fiscal year has a budget of $ 12600 , divided into 12 equal monthly allocations . at the end of the sixth month of that fiscal year , the total amount actually spent on the project was $ 6580 . by how much was the project over its budget ?
Options: a ) $ 380 , b ) $ 540 , c ) $ 280 , d ) $ 1380 , e ) $ 1430
Rationale: difficulty level : 600 each month ' s budget = 12600 / 12 = 1050 budget for 6 months = 6 * 1050 = 6300 actual amount spent = 6580 amount spent over the budget = 6580 - 6300 = 280 answer ( c ) , regards ,
Answer: c
Question (physics): a man rows his boat 85 km downstream and 25 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 12 , c ) 5 , d ) 8 , e ) 9
Rationale: "speed downstream = d / t = 85 / ( 2 1 / 2 ) = 34 kmph speed upstream = d / t = 25 / ( 2 1 / 2 ) = 10 kmph the speed of the stream = ( 34 - 10 ) / 2 = 12 kmph answer : b"
Answer: b
Question (general): a cement mixture is composed of 3 elements . by weight , 1 / 4 of the mixture is sand , 2 / 5 of the mixture is water , and the remaining 14 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 9 , b ) 14 , c ) 28 , d ) 40 , e ) 60
Rationale: let the total weight be x . sand content = ( 1 / 4 ) x water content = ( 2 / 5 ) x gravel = x - ( 1 / 4 ) x - ( 2 / 5 ) x = ( 7 / 20 ) x = 14 x = 40 then answer will be d = 40
Answer: d
Question (geometry): the length of a rectangle is 2 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 50 square inches
b ) 75 square inches
c ) 68 square inches
d ) 89 square inches
e ) 92 square inches
Rationale: if the width is 5 in and the length is 2 times the width , then the length is 2 * 5 = 10 in the area is given by 5 * 10 = 50 square inches correct answer a
Answer: a
Question (geometry): if a is the smallest positive integer such that 5880 multiplied by a is the square of an integer , then ya must be
Options: a ) 30 , b ) 15 , c ) 12 , d ) 23 , e ) 17
Rationale: 5880 = 2 * 2 * 7 * 7 * 5 * 6 , so we need one 5 and one 6 to make it a square of a number . so 5 * 6 = 30 ans : a
Answer: a
Question (general): working simultaneously and independently at an identical constant rate , 6 machines of a certain type can produce a total of x units of product p in 10 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 5 x units of product p in 6 days ?
Options: a ) 50 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "6 machines do x units in 10 days we have x / 10 = > rate of the 6 machines we know that we need to have 5 x units in 6 days therefore , we need to get to 5 x / 6 rate of the machines . rate of one machine is x / 10 * 1 / 6 = x / 60 . now , we need to know how many machines need to work simultaneously , to get 5 x done in 6 days . 5 x / 6 work needs to be done by machines that work at x / 60 rate . let ' s assign a constant y for the number of machines : ( x / 60 ) * y = 5 x / 6 y = 5 x / 6 * 60 / x cancel 6 with 60 , and x with x and get - > 50 . answer choice a"
Answer: a
Question (gain): if the difference between the compound interest & simple interest of a certain sum of money is rs . 72 at 12 % p . a . per two year . find the sum ( in rs . ) ?
Options: a ) 200 / 15 , b ) 200 / 17 , c ) 220 / 17 , d ) 240 / 17 , e ) 260 / 17
Rationale: 200 / 17 c . i = a - p a = p ( 1 + 12 / 100 ) ^ 2 s . i = p * 2 * 12 / 100 c . i - s . i = 72 given substitute and solve p = 200 / 17 answer : b
Answer: b
Question (general): each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 3125 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
Options: a ) 1287 , b ) 1285 , c ) 1283 , d ) 1280 , e ) 1281
Rationale: "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , c , e the answer to be d again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 1280 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 1280 = 3125 hence , correct answer = d"
Answer: d
Question (general): if n is a natural number , then 6 n ^ 2 + 6 n is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) 18 only , e ) 20 only
Rationale: "6 n ^ 2 + 6 n = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer is b"
Answer: b
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 120 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 27 sec , c ) 25 sec , d ) 24 sec , e ) 11 sec
Rationale: "explanation : d = 100 + 120 = 220 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 22 sec answer : option a"
Answer: a
Question (other): a certain fruit stand sold apples for $ 0.70 each and bananas for $ 0.60 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let ' s start with 1 apple for $ 0.70 . let ' s subtract $ 0.70 from $ 6.30 until we get a multiple of $ 0.60 . $ 6.30 , $ 5.60 , $ 4.90 , $ 4.20 = 7 * $ 0.60 the customer purchased 7 bananas and 3 apples . the answer is c ."
Answer: c
Question (gain): a man ' s speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is :
Options: a ) 8.5 km / hr , b ) 10 km / hr , c ) 12.5 km / hr , d ) 9 km / hr , e ) none of these
Rationale: "explanation : man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 15 - 2.5 = 12.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km / hr answer is b"
Answer: b
Question (gain): a shopkeeper sold an article at $ 1200 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 1000 , b ) $ 1020 , c ) $ 1040 , d ) $ 1060 , e ) $ 1080
Rationale: "let x be the cost price . 1.2 x = 1200 x = 1200 / 1.2 = 1000 the answer is a ."
Answer: a
Question (general): at company x , senior sales representatives visit the home office once every 20 days , and junior sales representatives visit the home office once every 15 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 60 - day period , senior representatives visit the home office 3 times while junior representatives visit 4 times , thus 33 % more . the answer is c ."
Answer: c
Question (gain): daniel went to a shop and bought things worth rs . 25 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 5 % , then what was the cost of the tax free items ?
Options: a ) a ) 18.7 , b ) b ) 20 , c ) c ) 21.3 , d ) d ) 21.5 , e ) e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 5 % ∴ ( 25 − 30 / 100 − x ) 5 / 100 = 30 / 100 ⇒ 5 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 6 ⇒ x = 25 − 0.3 − 6 = 18.7 a"
Answer: a
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 190 kilometers ?
Options: a ) 3.5 gallons , b ) 2.7 gallons , c ) 5.7 gallons , d ) 4.75 gallons , e ) 7.5 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 190 kilometers ? 190 ã · 40 = 4.75 ã — 1 gallon = 4.75 gallons correct answer is d ) 4.75 gallons"
Answer: d
Question (general): in the faculty of reverse - engineering , 300 second year students study numeric methods , 600 second year students study automatic control of airborne vehicles and 200 second year students study them both . how many students are there in the faculty if the second year students are approximately 70 % of the total ?
Options: a ) 750 , b ) 800 , c ) 900 , d ) 950 , e ) 1000
Rationale: "total number of students studying both are 300 + 600 - 200 = 700 ( subtracting the 200 since they were included in the both the other numbers already ) . so 70 % of total is 700 , so 100 % is 1000 answer is e"
Answer: e
Question (physics): a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.8 hr , b ) 2.4 hr , c ) 3.6 hr , d ) 1.8 hr , e ) 2.0 hr
Rationale: explanation : part filled by one tap in 1 hour = 1 / 4 part emptied by second tap 1 hour = 1 / 8 net part filled by both these taps in 1 hour = 1 / 3 - 1 / 8 = 5 / 24 i . e , the cistern gets filled in 24 / 5 hours = 4.8 hrs answer : option a
Answer: a
Question (other): in a graduating class of 233 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 114 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 233 = 30 greatest - smallest is 144 - 30 = 114 so answer must be a . 114"
Answer: a
Question (physics): on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 48 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 296 , e ) 302
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 48 cm . : 48 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 47 / ( 3.81 ) = 302 answer will be e ."
Answer: e