Cheukting/mathqa huggingface dataset:
Question (general): at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 80 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?
Options: a ) 2 , b ) 3 , c ) 9 , d ) 15 , e ) 30
Rationale: "withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the “ deficit ” below the average of 90 created on the x days the restaurant served only 80 customers per day . 30 / 10 = 3 days . choice ( a ) . withthe formula , we can set up the following : 90 = ( 80 x + 120 ) / ( x + 1 ) 90 x + 90 = 80 x + 120 10 x = 30 x = 3 answer choice ( b )"
Answer: b
Question (gain): bhanu spends 30 % of his income on petrol on scooter 10 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 70 , c ) 128 , d ) 797 , e ) 120
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 10 % ( 700 ) = rs . 70 answer : b"
Answer: b
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is odd , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 1 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 384 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 1 , 3 , 5 , 7 , 9 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 5 * 5 * 4 * 4 = 400 numbers with one 1 - s , 1 x 1 x 1 * 1 * 4 * 4 = 16 . thus there are 400 - 16 = 384 such numbers . answer : c ."
Answer: c
Question (geometry): if the length of the sides of two cubes are in the ratio 5 : 1 , what is the ratio of their total surface area ?
Options: a ) 5 : 1 , b ) 10 : 1 , c ) 25 : 1 , d ) 50 : 1 , e ) 150 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 5 x ) ^ 2 = 150 x ^ 2 . the ratio of surface areas is 25 : 1 . the answer is c ."
Answer: c
Question (general): the average monthly salary of 24 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 400 . what is the manager ' s monthly salary ?
Options: a ) rs . 11,300 , b ) rs . 11,500 , c ) rs . 11,302 , d ) rs . 11,301 , e ) rs . 11,303
Rationale: explanation : manager ' s monthly salary = rs . ( 1900 x 25 - 1500 x 24 ) = rs . 11,500 answer : b
Answer: b
Question (other): the triplicate ratio of 1 : 4 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 64 , e ) 1 : 2
Rationale: "1 ^ 3 : 4 ^ 3 = 1 : 64 answer : d"
Answer: d
Question (gain): in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 347000 , d ) 333200 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 × 476000 = 33320000 / 100 = 333200 d )"
Answer: d
Question (physics): in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 400 m ?
Options: a ) 122.9 m , b ) 127.5 m . , c ) 122.2 m , d ) 85 m , e ) 12289 m
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 400 m , the number of meters by which a beats c = ( 400 * 212.5 ) / 1000 = 85 m . answer : d"
Answer: d
Question (physics): a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 3 days . b can do the work alone in ?
Options: a ) 18 , b ) 12 , c ) 11 , d ) 19 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 3 6 / x = 1 / 3 = > x = 18 so , b takes 9 hours to finish the work . answer : a"
Answer: a
Question (general): paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to paul and 40 % of his income to quentin , quentin ' s new income would be what fraction of paul ' s new income ?
Options: a ) 11 / 12 , b ) 13 / 17 , c ) 22 / 30 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get p = 12 and q 8.8 so 8.8 / 12 = = 2.2 / 3 ans : c"
Answer: c
Question (geometry): if the length of the side of a square is doubled , what is the ratio of the areas of the original square to the area of the new square ?
Options: a ) 1 : 4
b ) 2 : 4
c ) 3 : 4
d ) 4 : 4
e ) 5 : 4
Rationale: solution if x be the side of the original square , then its area is equal to x 2 if x is doubled to 2 x , then the new area is equal to ( 2 x ) 2 = 4 x 2 the ratio of the areas of the original square to the area of the new square x 2 / ( 4 x 2 ) = 1 / 4 or 1 : 4 answer is a
Answer: a
Question (general): in country x a returning tourist may import goods with a total value of $ 500 or less tax free , but must pay an 8 percent tax on the portion of the total value in excess of $ 500 . what tax must be paid by a returning tourist who imports goods with a total value of $ 730 ?
Options: a ) $ 58.40 , b ) $ 40 . 00 , c ) $ 24.60 , d ) $ 18.40 , e ) $ 16.00
Rationale: the tourist must pay tax on $ 730 - $ 500 = $ 230 . thus the amount to be paid is 0.08 * $ 230 = $ 18.40 . answer : d .
Answer: d
Question (general): total 45 cows 15 cow gives each 2 liter milk 15 cow gives each 3 / 4 liter milk 15 cow gives each 1 / 4 liter milk this is split into 3 son per each 15 cows & 15 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "15 cow 2 liter each = 30 liter 15 cow 3 / 4 liter each = 3 / 4 = 0.75 * 15 = 11.25 15 cow 1 / 4 liter each = 1 / 4 = 0.25 * 15 = 3.75 add 30 + 11.25 + 3.75 = 45 milk split into 3 son each 15 liter then 45 / 3 = 15 answer : c"
Answer: c
Question (other): if both 2 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "the number a must include at least 3 ^ 2 = 9 the answer is b ."
Answer: b
Question (physics): an outlet pipe can empty 3 / 4 of a cistern in 12 minutes . in 4 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "4 / 12 * 3 / 4 = 1 / 4 the answer is c ."
Answer: c
Question (general): a couple decides to have 6 children . if they succeed in having 6 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 3 girls and 3 boys ?
Options: a ) 1 , b ) 9 / 64 , c ) 1 / 8 , d ) 3 / 16 , e ) 9 / 32
Rationale: "sample space = 2 ^ 6 = 64 . favourable events = { bbbggg } , { bgbgbg } , { bgbggb } , { bggbbg } { gggbbb } , { gbgbgb } , { gbbggb } . { gbgbbg } { gbbgbg } probability = 9 / 64 = 9 / 64 ans ( b ) ."
Answer: b
Question (physics): how long does a train 110 meters long running at the speed of 72 km / hour take to cross a bridge 132 meters in length ?
Options: a ) 15 seconds , b ) 12.1 seconds , c ) 10 seconds , d ) 8.1 seconds , e ) none of these
Rationale: "explanation : speed = 72 km / hour = 72 * ( 5 / 18 ) m / sec = 20 m / sec total distance to be covered = 110 + 132 = 142 meters time = distance / speed = 242 / 20 = 12.1 seconds option b"
Answer: b
Question (general): the averageincome of m and n is rs . 5050 . the average monthly income of n and o is rs . 6250 and the average monthly income of m and ois rs . 5200 . the income of m is ?
Options: a ) rs . 2000 , b ) rs . 3000 , c ) rs . 4000 , d ) rs . 4500 , e ) rs . 5000
Rationale: let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) m + o = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( m + n + o ) = 33000 or m + n + o = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get m = 4000 . m ' s monthly income = rs . 4000 c
Answer: c
Question (gain): a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 1 a rupee . find his net profit or loss percent ?
Options: a ) 330 % , b ) 390 % , c ) 200 % , d ) 250 % , e ) 300 %
Rationale: "the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 1 he selling at 3 a rupee , his sp = 4 profit = sp - cp = 4 - 1 = 3 profit percent = 3 / 1 * 100 = 300 % answer : e"
Answer: e
Question (physics): a can do a job in 5 days and b can do it in 15 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 12 ½ days , e ) 7 ½ days
Rationale: "explanation : 1 / 5 + 1 / 15 = 4 / 15 = 4 / 15 15 / 4 = 15 / 4 * 2 = 7 ½ days answer : e"
Answer: e
Question (gain): a tank contains 10,000 gallons of a solution that is 3 percent sodium chloride by volume . if 4,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 5 % , c ) 6.25 % , d ) 6.67 % , e ) 11.7 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 4,000 = 6,000 gallons and sodium chloride is 300 gallons ( 3 % of initial solution of 10,000 gallons ) then sodium chloride is 300 / 6,000 * 100 = 5 % of the remaining solution of 6,000 gallons . answer : b ."
Answer: b
Question (general): in a simultaneous throw of a pair of dice , find the probability of getting a total more than 8
Options: a ) 1 / 2 , b ) 7 / 12 , c ) 3 / 7 , d ) 5 / 12 , e ) 6 / 17
Rationale: "total number of cases = 7 * 7 = 49 favourable cases = [ ( 2,7 ) , ( 3,6 ) , ( 3,7 ) , ( 4,5 ) , ( 4,6 ) , ( 4,7 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 5,7 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) , ( 6,7 ) , ( 7,2 ) , ( 7,3 ) , ( 7,4 ) , ( 7,5 ) , ( 7,6 ) , ( 7,7 ) ] = 21 so probability = 21 / 49 = 3 / 7 answer is c"
Answer: c
Question (gain): what is the value of â ˆ š 81 % ?
Options: a ) 25 % , b ) 36 % , c ) 42 % , d ) 60 % , e ) 90 %
Rationale: "explanation : br > â ˆ š 81 % = â ˆ š 81 / â ˆ š 100 = 9 / 10 = 90 / 100 = 90 % correct answer is e ) 90 %"
Answer: e
Question (general): if x is 20 percent more than y and y is 50 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %
Rationale: "let ' s take values of x , y , z which can satisfy given equations . let z = 200 , so y becomes 100 ( since y is 50 % less than z ) , x becomes 120 ( since 20 % more than y ) now req is ( x / z ) * 100 = ( 120 / 200 ) * 100 = 60 % answer : e"
Answer: e
Question (gain): a sum of money at simple interest amounts to rs . 1072 in 2 years and to rs . 1144 in 4 years . the sum is :
Options: a ) rs . 1000 , b ) rs . 850 , c ) rs . 500 , d ) rs . 1200 , e ) rs . 900
Rationale: "s . i . for 2 years = rs . ( 1144 - 1072 ) = rs . 72 . s . i . for 1 year = rs . 72 / 2 = rs . 36 . principal = rs . ( 1072 - 72 ) = rs . 1000 . answer : option a"
Answer: a
Question (gain): an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 12 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 80.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 20 % , thus he must pay slightly more than $ 80 . only answer choice d fits . answer : d ."
Answer: d
Question (physics): a , b and c can do a work in 15 , 20,45 days respectively . in how many days they can complete the work together .
Options: a ) 5.2 days , b ) 9.2 days , c ) 8.2 days , d ) 6.2 days , e ) 7.2 days
Rationale: lcm = 180 no of days = [ 180 / ( 180 / 15 + 180 / 20 + 180 / 45 ) = [ 180 / ( 12 + 9 + 4 ) ] = [ 180 / 25 ] = 7.2 days answer : e
Answer: e
Question (general): the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is :
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) none
Rationale: "solution let the numbers be x and ( x + 1365 ) . then , x + 1365 = 6 x + 15 ⇔ 5 x = 1350 ⇔ x = 270 . answer b"
Answer: b
Question (physics): how long does a train 100 m long running at the speed of 65 km / hr takes to cross a bridge 145 m length ?
Options: a ) 13.6 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec
Rationale: "speed = 65 * 5 / 18 = 18 m / sec total distance covered = 100 + 145 = 245 m . required time = 245 / 18 = 13.6 sec . answer : a"
Answer: a
Question (general): lilly has 10 fish and rosy has 11 fish . in total , how many fish do they have in all ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "10 + 11 = 21 the answer is c ."
Answer: c
Question (gain): what percent is 4 gm of 1 kg ?
Options: a ) 1.5 % , b ) 0.4 % , c ) 2.5 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 4 / 1000 × 100 = 400 / 1000 = 2 / 5 = 0.4 % b )"
Answer: b
Question (geometry): the curved surface of a right circular cone of height 15 cm and base diameter 16 cm is
Options: a ) 40 ∏ cm ³
b ) 60 ∏ cm ³
c ) 136 ∏ cm ³
d ) 138 ∏ cm ³
e ) none
Rationale: sol . h = 14 cm , r = 7 cm . so , l = √ r ² + h ² = √ 8 ² + ( 15 ) ² = 17 cm . ∴ curved surface area = ∏ rl = ( ∏ * 8 * 17 ) cm ² = 136 ∏ cm ² answer c
Answer: c
Question (general): we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: "let x be the number of canoes . then 3 x / 4 is the number of kayaks . 11 x + ( 3 x / 4 ) * 16 = 460 11 x + 12 x = 460 23 x = 460 x = 20 ( canoes ) 3 x / 4 = 15 ( kayaks ) there were 20 - 15 = 5 more canoes rented out . the answer is d ."
Answer: d
Question (general): set w consists of all the prime numbers between 10 and 25 . what is the range of set w ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: answer of set w is 12 .
Answer: a
Question (physics): at 15 : 15 pm railway time , what will be the angle between minute and hour hand ?
Options: a ) 238 , b ) 360 , c ) 377 , d ) 277 , e ) 291
Rationale: at 15 : 15 both minute and hour hands will be in same position . hence the angle between them will be zero degrees . however 360 degree also means both minute and hour hands are in same position . hence correct answers are both zero and 360 degrees answer : b
Answer: b
Question (gain): x and y start a business with rs . 2000 and rs . 12000 respectively . hoe should they share their profits at the end of one year ?
Options: a ) 1 : 6 , b ) 6 : 1 , c ) 1 : 5 , d ) 5 : 1 , e ) 1 : 4
Rationale: "they should share the profits in the ratio of their investments . the ratio of the investments made by x and y = 2000 : 12000 = > 1 : 6 . answer : a"
Answer: a
Question (physics): a train 130 m long crosses a platform with a speed of 70 kmph in 20 sec ; find the length of the platform ?
Options: a ) 150 , b ) 145 , c ) 165 , d ) 162 , e ) 152
Rationale: "d = 130 + x t = 20 s = 130 + x / 15 * 18 / 5 = 70 kmph . = > ( 130 + x ) * 18 = 5250 = > 130 + x = 292 = > x = 162 m answer : d"
Answer: d
Question (geometry): the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 288 meters , what is the width of the field ?
Options: a ) 50
b ) 60
c ) 70
d ) 80
e ) 90
Rationale: let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 288 , 2 ( 7 / 5 ) w + 2 w = 288 solve the above equation to find : w = 60 m and l = 84 m . correct answer b ) 60
Answer: b
Question (gain): ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 9 percent . overall he make a .
Options: a ) 228 , b ) 288 , c ) 27 , d ) 120 , e ) 881
Rationale: let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 9 / 100 ) = 8000 + 720 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 720 = rs . 120 as this is positive , an overall profit of rs . 200 was made . answer : d
Answer: d
Question (gain): sheela deposits rs . 3800 in bank savings account . if this is 32 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 20000 , c ) 11875 , d ) 12340 , e ) none of these
Rationale: "explanation : 32 % of income = rs . 3800 100 % of income = 3800 x 100 / 32 = rs . 11875 answer : c"
Answer: c
Question (general): there are 11 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 35 , b ) 45 , c ) 55 , d ) 65 , e ) 75
Rationale: 11 c 2 = 55 the answer is c .
Answer: c
Question (general): if greg buys 6 shirts , 4 trousers and 2 ties , the total cost is $ 80 . if greg buys 4 shirts , 2 trousers and 2 ties , the total cost is $ 140 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
Options: a ) $ 60 , b ) $ 64 , c ) $ 75 , d ) $ 110 , e ) can not be determined
Rationale: solution : 6 x + 4 y + 2 z = 80 4 x + 2 y + 2 z = 140 adding both the equations = 10 x + 6 y + 4 z = 220 5 x + 3 y + 2 z = 110 ans d
Answer: d
Question (geometry): three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 138 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters , b ) 19 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 138 = 200 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : b ."
Answer: b
Question (general): if jenee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 3 / 50 , e ) 1 / 20
Rationale: perhaps it is also easy to just translate the % into fractions : 6 % : 6 / 100 = 3 / 50 7 % : 7 / 100 8 % : 8 / 100 = 4 / 50 = 2 / 25 9 % : 9 / 100 only 3 / 50 exists in the answer choices , so ans d
Answer: d
Question (physics): length of a rectangular plot is 28 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 54 m , b ) 64 m , c ) 74 m , d ) 84 m , e ) 94 m
Rationale: "let breadth = x metres . then , length = ( x + 28 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 28 ) + x ] = 200 2 x + 28 = 100 2 x = 72 x = 36 . hence , length = x + 28 = 64 m b"
Answer: b
Question (general): if x = 3 y , where y is a prime number greater than 2 , how many different positive even divisors does x have , including x ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it can not be determined from the information given
Rationale: for x to have even divisors , xx has to be an even number . we know that x = 3 y , where yy is a prime number greater than 2 . as 2 is the only even prime number , y has to be an odd prime number . this means that x must also be an odd number , since odd x odd = odd . as x is odd , it can not have any even divisors . therefore , a is the correct answer .
Answer: a
Question (geometry): if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a sixth of a circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 360 , d ) 6000 , e ) 36000
Rationale: 1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 60 degrees = 6000 anglets answer - d
Answer: d
Question (other): ratio of girl and boys in class is 5 : 6 . if 20 girl leave the class and ratio become 2 : 3 . calculate the no . of boys ?
Options: a ) 100 , b ) 120 , c ) 80 , d ) 90 , e ) none of the above
Rationale: girl 5 x and boys 6 x 5 x - 20 / 6 x = 2 / 3,15 x - 60 = 12 x , 3 x = 60 , x = 20 boys = 6 x = 120 answer b
Answer: b
Question (gain): if 30 % of a number exceeds 20 % of it by 18 , then find the number ?
Options: a ) 120 , b ) 200 , c ) 180 , d ) 150 , e ) none of these
Rationale: "let the number be x . 30 % of x = 30 / 100 * x = 3 x / 10 20 % of x = 20 / 100 * x = x / 5 = 2 x / 10 . given that 3 x / 10 - 2 x / 10 = 18 = > x = 180 . required number is 180 . answer : c"
Answer: c
Question (general): what is the sum of the numbers between 1 and 20 , inclusive ?
Options: a ) 310 , b ) 200 , c ) 215 , d ) 285 , e ) 210
Rationale: "sol . 1 + 2 + 3 . . . 17 + 18 + 19 + 20 answer . e"
Answer: e
Question (gain): a company recently conducted a survey and found that 30,000 of its customers live in rural areas . if the number of customers who live in urban areas is 130 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 65,000 , b ) 67,000 , c ) 69,000 , d ) 71,000 , e ) 73,000
Rationale: "the number of customers in urban areas is 30,000 + 1.3 * 30,000 = 69,000 . the answer is c ."
Answer: c
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 3 / 4 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 6 / 22 , b ) 5 / 22 , c ) 7 / 22 , d ) 4 / 22 , e ) 3 / 22
Rationale: "# of basic stereos was 3 / 4 of total and # of deluxe stereos was 1 / 4 of total , let ' s assume total = 16 , then basic = 12 and deluxe = 4 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 12 * 1 = 12 and total time for deluxe would be 4 * 7 / 5 = 28 / 5 - - > total time for both of them would be 12 + 28 / 5 = 88 / 5 - - > deluxe / total = 28 / 5 / 88 / 5 = 28 / 88 = 7 / 22 c"
Answer: c
Question (general): what is ( 24 ^ 7 + 24 ) / 24 ?
Options: a ) 159202573 , b ) 160902641 , c ) 172502765 , d ) 182302834 , e ) 191102977
Rationale: "( 24 ^ 7 + 24 ) / 24 = 24 * ( 24 ^ 6 + 1 ) / 24 = 24 ^ 6 + 1 clearly this is a number which ends with a 7 in the units place . the answer is e ."
Answer: e
Question (general): 3 consecutive even numbers are such that thrice the first number exceeds double the third number by 7 . what is the third number ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: let the three numbers be x , x + 2 , and x + 4 . 3 x = 2 ( x + 4 ) + 7 x = 15 and then the third number is x + 4 = 19 . the answer is a .
Answer: a