Cheukting/mathqa huggingface dataset:
Question (physics): a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 198 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 13
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 198 - $ 120 = $ 78 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 78 / $ 6 = 13 ans is e"
Answer: e
Question (physics): a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 10 : 30 am in the same direction at the rate of 84 km / h . at what time will the second train catch the first train ?
Options: a ) 4 : 30 , b ) 5 : 00 , c ) 5 : 30 , d ) 6 : 00 , e ) 6 : 30
Rationale: "in one hour and thirty minutes the first train travels 105 km . the second train catches the first train at a rate of 84 km / h - 70 km / h = 14 km / h . the second train will catch the first train in 105 / 14 = 7.5 hours , so at 6 : 00 pm . the answer is d ."
Answer: d
Question (other): a grocery store bought some apples at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples ?
Options: a ) 1 : 7 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 2 , e ) 2 : 5
Rationale: to avoid fractions , assume there were 45 apples . so the store bought them for 45 / 5 = 9 dollars . to break even , the selling price should be $ 9 too . 45 mangoes can be split into 1 : 4 , 2 : 3 or 1 : 2 . so let ' s try these . 45 split in the ratio 1 : 4 gives 9 and 36 . 9 apples split into 3 apples each will give $ 3 . 36 apples split into 6 apples each will give $ 6 . they add up to $ 9 so we have hit the right answer . answer ( c )
Answer: c
Question (physics): if 11 lions can kill 11 deers in 11 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 11 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 11 ( lions ) * 11 ( min ) / 11 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 11 answer : b"
Answer: b
Question (other): two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 6 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 19 : 2 , b ) 18 : 3 , c ) 29 : 11 , d ) 29 : 5 , e ) 29 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 6 = 15 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 4 + 7 / 2 = 29 / 4 = 7.25 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 7.25 : 2.75 = 29 : 11 . answer : c"
Answer: c
Question (gain): what is 1 percent of 12,356 ?
Options: a ) 123.56 , b ) 1.2356 , c ) 12.356 , d ) 0.012356 , e ) 0.0012356
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 1 ( 1 / 100 ) 12,356 . the answer is 123.56 . hence , the correct answer is a .
Answer: a
Question (probability): if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 3 . answer : b .
Answer: b
Question (gain): sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 35 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 48.3 % , b ) 52.8 % , c ) 55.5 % , d ) 58.3 % , e ) 61.4 %
Rationale: "35 % is 5 % - points above 30 % and 25 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 5 : 1 . 5 / 6 * 70 % = 58.3 % the answer is d ."
Answer: d
Question (other): a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 70 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 7 / 48,000 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 70 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 70 / 800 * 1 / 600 = 7 / 48,000 . answer : c ."
Answer: c
Question (physics): the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 9 , b ) 5 , c ) 7 , d ) 6 , e ) 10
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 24 / 60 ) ) km = 10 km . answer : e"
Answer: e
Question (general): the instructions state that cheryl needs 4 / 9 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: "total bought = 4 / 9 + 2 / 3 left part 8 / 18 - - - > 4 / 9 so used part 4 / 9 + 2 / 3 - 4 / 9 = 2 / 3 answer : c"
Answer: c
Question (gain): a sells a bicycle to b at a profit of 30 % and b sells it to c at a loss of 20 % . find the resultant profit or loss .
Options: a ) 5 % , b ) 4 % , c ) - 4 % , d ) - 12 % , e ) 2 %
Rationale: the resultant profit or loss = 30 - 20 - ( 30 * 20 ) / 100 = 4 % profit = 4 % answer is b
Answer: b
Question (physics): a man can row at 6 kmph in still water . if the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back , how far is the place ?
Options: a ) 5.33 km , b ) 6.33 km , c ) 5.63 km , d ) 7.33 km , e ) 5.93 km
Rationale: "speed in still water = 6 kmph speed of the current = 2 kmph speed downstream = ( 6 + 2 ) = 8 kmph speed upstream = ( 6 - 2 ) = 4 kmph let the required distance be x km total time taken = 2 hour x / 8 + x / 4 = 2 x + 2 x / 8 = 2 3 x / 8 = 2 3 x = 16 x = 5.33 km answer : a"
Answer: a
Question (physics): in a survey of 335 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 38 / 67 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 91
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 281 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 335 we have to find not part time and not uninsured . in other words not part time and insured = x / 335 = ( 281 - 104 + 13 ) / 335 = 38 / 67 answer is a ."
Answer: a
Question (gain): a $ 500 investment and a $ 1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1 , 500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 10 5 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the ratio of investments is 500 : 1,500 = 1 : 3 . the deviation from the average return from $ 500 investment and $ 1,500 investment must be in the ration 3 : 1 . $ 500 investment return has the deviation from the mean of 8.5 - 7 = 1.5 % , thus $ 1,500 investment return must have the deviation from the mean equal to 0.5 % , which means that $ 1 , 500 investment has 8.5 + 0.5 = 9 % yearly return . answer : a ."
Answer: a
Question (physics): 8 : 4 seconds : : ? : 4 minutes
Options: a ) 10 , b ) 8 , c ) 20 , d ) 25 , e ) 30
Rationale: "8 * 4 = 4 * x x = 8 answer : b"
Answer: b
Question (physics): a river 2 m deep and 45 m wide is flowing at the rate of 7 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 m 3 , b ) 4580 m 3 , c ) 10500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 7000 * 2 * 45 ) / 60 = 10500 m 3 answer : option c"
Answer: c
Question (geometry): what is the area of square field whose side of length 10 m ?
Options: a ) 100 , b ) 662 , c ) 772 , d ) 882 , e ) 21
Rationale: "10 * 10 = 100 sq m answer : a"
Answer: a
Question (gain): at a local appliance manufacturing facility , the workers received a 25 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 125 = 1250 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 125 = 8 so he can reduce his work by 2 hours . which is 20 % . answer c"
Answer: c
Question (general): if 625 ^ ( - x ) + 5 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . a"
Answer: a
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4529 , b ) s . 4586 , c ) s . 4597 , d ) s . 4530 , e ) s . 5436
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 6 = rs . 5436 answer : e"
Answer: e
Question (gain): a car dealership has 40 cars on the lot , 10 % of which are silver . if the dealership receives a new shipment of 80 cars , 25 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 21 % , e ) 22 %
Rationale: the number of silver cars is 0.1 * 40 + 0.25 * 80 = 24 the percentage of cars which are silver is 24 / 120 = 20 % the answer is c .
Answer: c
Question (other): apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 333 and for 36 kgs of apples is 366 then the cost of first 15 kgs of apples is
Options: a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 150 , e ) 3.61
Rationale: "ans : by framing equations we get 30 l + 3 q = 333 30 l + 6 q = 366 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 60 l + 6 q = 666 30 l + 6 q = 366 30 l = 300 = > l = 10 then we get l = 10 cost of 15 kgs of apples = 15 x 10 = 150 answer : d"
Answer: d
Question (other): the sub - duplicate ratio of 16 : 36 is
Options: a ) 4 : 6 , b ) 1 : 2 , c ) 1 : 3 , d ) 1 : 4 , e ) 2 : 3
Rationale: "root ( 16 ) : root ( 36 ) = 4 : 6 answer : a"
Answer: a
Question (general): there are 2 red chips and 4 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 50 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ b _ b _ b _ b so . . 6 ! / number of repeated letters ( 2 ! ) ( 4 ! ) = 10 ans : e"
Answer: e
Question (physics): a can give b 70 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 139.78 , b ) 139.13 , c ) 139.22 , d ) 111.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 930 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 930 = 860.21 m . b can give c = 1000 - 860.21 = 139.78 m . answer : a"
Answer: a
Question (physics): find the area of trapezium whose parallel sides are 10 cm and 18 cm long , and the distance between them is 10.00001 cm .
Options: a ) 140 cm 2 , b ) 185 cm 2 , c ) 185 cm 2 , d ) 185 cm 2 , e ) 195 cm 2
Rationale: "explanation : area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 10 + 18 ) * ( 10 ) = 140 cm 2 answer : option a"
Answer: a
Question (physics): a car drives 40 miles on local roads at 20 mph , and 180 miles on the highway at 60 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 52 mph , e ) 58 mph
Rationale: "explanations 1 ) in phase # 1 of the trip , the car traveled 40 mi at 20 mph . that time of this phase was : time = distance / rate = ( 40 mi ) / ( 20 mph ) = 2 hr in phase # 2 of the trip , the car traveled 180 mi at 60 mph . that time of this phase was : time = distance / rate = ( 180 mi ) / ( 60 mph ) = 3 hr the total distance of the trip = 40 mi + 180 mi = 220 mi the total time of the trip = 2 hr + 3 hr = 5 hr the average speed of trip is given by speed = distance / time = ( 220 mi ) / ( 5 hr ) = 44 mph answer : c ."
Answer: c
Question (gain): a man sold 18 toys for rs . 16800 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) rs . 600 , b ) rs . 800 , c ) rs . 500 , d ) rs . 900 , e ) rs . 970
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 16800 . gain = sp – cp 3 x = 16800 – 18 x 21 x = 16800 x = rs . 800 . answer : b"
Answer: b
Question (general): in the coordinate plane , points ( x , 1 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x + y =
Options: a ) 6.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 1 ) = ( 4 , 1 ) and ( 10 , y ) = ( 10 , 2.5 ) - - > x + y = 4 + 2.5 = 6.5 answer : a ."
Answer: a
Question (gain): a doctor prescribed 20 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 25 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 20 c . c % prescribed dosage greater than the typical dosage = ( 20 - 16 / 16 ) * 100 % = ( 2 / 16 ) * 100 % = 25 % answer a"
Answer: a
Question (other): the ratio between the present age of p and q is 6 : 7 . if q is 4 years old then p , what will be the ratio of the ages of p and q after 4 year ?
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 7 : 8 , d ) 4 : 3 , e ) none of these
Rationale: "solution let p ' s age and q ' s age be 6 x years and 7 x years respectively . then , 7 x - 6 x = 4 ⇔ x = 4 . ∴ required ratio = ( 6 x + 4 ) : ( 7 x + 4 ) = 28 : 32 = 7 : 8 . answer c"
Answer: c
Question (general): 3 people have $ 28 , $ 72 , and $ 98 , respectively . if they pool their money then redistribute it among them , what is the maximum value for the median amount of money ?
Options: a ) $ 72 , b ) $ 85 , c ) $ 99 , d ) $ 101 , e ) $ 202
Rationale: solution - total money distributed is $ 198 . in order to maximize median , one person has to accept $ 0 and remaining two people share $ 99 each . hence median is $ 99 . ans c
Answer: c
Question (general): if a is an integer greater than 2 but less than 11 and b is an integer greater than 11 but less than 21 , what is the range of a / b ?
Options: a ) 52 / 45 , b ) 23 / 47 , c ) 60 / 41 , d ) 51 / 42 , e ) 41 / 60
Rationale: "the way to approach this problem is 2 < a < 11 and 11 < b < 21 minimum possible value of a is 3 and maximum is 10 minimum possible value of b is 12 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 10 / 12 - 3 / 20 = 41 / 60 hence e"
Answer: e
Question (gain): at what price must an article costing rs . 100 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 131.58 , b ) 62.0 , c ) 62.6 , d ) 62.1 , e ) 62.2
Rationale: "cp = 100 sp = 100 * ( 125 / 100 ) = 125 mp * ( 95 / 100 ) = 125 mp = 131.58 answer : a"
Answer: a
Question (physics): how long does a train 110 m long running at a speed of 72 kmph take to cross a bridge 132 m in length ?
Options: a ) 9.8 sec , b ) 12.1 sec , c ) 12.42 sec , d ) 14.3 sec , e ) 24.3 sec
Rationale: "72 km / hr = 72 * 5 / 18 m / sec = 20 m / sec time = d / s = 110 + 132 / 20 = 242 / 20 = 12.1 sec answer : b"
Answer: b
Question (physics): a train 110 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4 sec , e ) 2 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 110 * 3 / 55 ] sec = 6 sec answer : b"
Answer: b
Question (physics): a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 6 km ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 67 , e ) 7
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 6 t = 6 / 2 = 3 answer : a"
Answer: a
Question (general): in an election , candidate x got 75 % 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 favour of candidate ?
Options: a ) 280000 , b ) 300000 , c ) 355000 , d ) 356000 , 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 x = 75 % therefore , the number of valid votes polled in favour of candidate x = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 e )
Answer: e
Question (general): the average of first 15 natural numbers is ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "sum of 15 natural no . = 240 / 2 = 120 average = 120 / 15 = 8 answer : b"
Answer: b
Question (physics): at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 35 seconds . how long does it tick at 12 ′ o clock
Options: a ) 77 , b ) 76 , c ) 28 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 35 / 5 = 7 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 7 = 77 secs . answer : a"
Answer: a
Question (general): a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 20 as remainder . find the no . is ?
Options: a ) 122456 , b ) 220020 , c ) 220022 , d ) 235467 , e ) 220026
Rationale: "( 555 + 445 ) * 2 * 110 + 20 = 220000 + 20 = 220020 b"
Answer: b
Question (general): a case contains c cartons . each carton contains b boxes , and each box contains 300 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 300 bc , b ) 300 b / c , c ) 600 bc , d ) 600 b / c , e ) 600 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 300 clips / box = 600 bc paper clips the answer is c ."
Answer: c
Question (general): solve the equation for x : 2 x - 21 + 3 x = 4 + 9 - x
Options: a ) 4 , b ) 5 , c ) 5.6 , d ) 9.2 , e ) 3.1
Rationale: "c 5.6 5 x + x = 13 + 21 6 x = 34 = > x = 5.6"
Answer: c
Question (general): how many positive integers less than 5,000 are evenly divisible by neither 15 nor 20 ?
Options: a ) 4,514 , b ) 4,477 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 20 5000 / 20 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 20 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 20 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4477 answer b ."
Answer: b
Question (gain): the cost price of an article is 70 % of the marked price . calculate the gain percent after allowing a discount of 10 % .
Options: a ) 13.6 % , b ) 28.6 % , c ) 35.6 % , d ) 42.3 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 70 . s . p = rs . 90 . â ˆ ´ gain % = [ 20 / 70 * 100 ] % = 28.6 % . answer b"
Answer: b
Question (probability): lola rolls a die 3 times . what is the probability that she gets a 4 on the last one of the 3 rolls ?
Options: a ) 215 / 216 , b ) 216 , c ) 1 / 216 , d ) none , e ) 2
Rationale: the die has 6 sides and it was rolle 3 times , then 6 * 6 * 6 = 216 the number of ways to get 4 is 1 then 1 / 216 the probability would be 1 - 1 / 216 = 215 / 216 answer a
Answer: a
Question (general): the contents of a certain box consist of 48 apples and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 90 , b ) 72 , c ) 82 , d ) 54 , e ) 65
Rationale: "apple = ( apple + kiwi + x ) * 0.3 48 = ( 30 + 48 + x ) * 0.3 x = 82 answer : c"
Answer: c
Question (geometry): a rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn . if the area of the lawn is 2109 sq . m , then what is the width of the road ?
Options: a ) 2
b ) 3.5
c ) 3
d ) 4
e ) 5
Rationale: area of the park = ( 60 x 40 ) m 2 = 2400 m 2 . area of the lawn = 2109 m 2 . area of the crossroads = ( 2400 - 2109 ) m 2 = 291 m 2 . let the width of the road be x metres . then , 60 x + 40 x - x 2 = 291 x 2 - 100 x + 291 = 0 ( x - 97 ) ( x - 3 ) = 0 x = 3 . c )
Answer: c
Question (other): a group of people participate in some curriculum , 35 of them practice yoga , 20 study cooking , 15 study weaving , 7 of them study cooking only , 5 of them study both the cooking and yoga , 3 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "both cooking and weaving = 20 - ( 7 + 5 + 3 ) = 5 so , the correct answer is e ."
Answer: e