Cheukting/mathqa huggingface dataset:
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of w is less than the square root of w . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "w 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Question (general): 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is
Options: a ) 24 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "solution let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = 12 x = 240 ‹ = › x = 20 . therefore bigger part = ( 54 - x ) = 34 . answer d"
Answer: d
Question (physics): a work which could be finished in 9 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "explanation : x - - - - - - - 9 ( x + 10 ) - - - - 6 x * 9 = ( x + 10 ) 6 x = 20 answer : b"
Answer: b
Question (gain): if the compound interest on a certain sum of money for 6 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 1800 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 6 yrs = ( 3000 x 10 x 6 ) / 100 = 1800 / - answer : c ."
Answer: c
Question (physics): a bicycle wheel has a diameter of 0.66 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 448 , c ) 1408 , d ) 482 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.66 m ) = 482.5 . hence 482 complete revolutions . answer d"
Answer: d
Question (gain): a sum of money amounts to rs . 9800 after 5 years and rs . 12015 after 8 years at the same rate of simple interest . the rate of interest per annum is ?
Options: a ) 12.05 % , b ) 5 % , c ) 13.05 % , d ) 22.05 % , e ) 18.05 %
Rationale: s . i . for 3 years = ( 12015 - 9800 ) = rs . 2215 s . i . for 5 years = rs . 2215 / 3 * 5 = rs . 3691 . principal = ( 9800 - 3675 ) = rs . 6108 hence , rate = ( 100 * 3691 ) / ( 6125 * 5 ) = 12.05 % answer : a
Answer: a
Question (general): how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 51 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: a + b / ab = 2 / 3 3 = 1 * 3 or 3 * 1 a + b in both case = 4 correct 0 answer : e
Answer: e
Question (general): a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 8 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 27 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : d ."
Answer: d
Question (general): the average age of one class strength 32 students is 16 yrs . if the staff ' s age is also included , the average increases by one year . find the age of the staff
Options: a ) 50 , b ) 52 , c ) 49 , d ) 32 , e ) 35
Rationale: total age of students = > 32 × 16 = 512 yrs total age inclusive staff = 33 × ( 16 + 1 ) = 561 = > staff ' s age 561 - 512 = 49 yrs answer c
Answer: c
Question (geometry): the area of a rectangular plot is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the plot ?
Options: a ) 14 m , b ) 20 m , c ) 18 m , d ) 12 m , e ) 15 m
Rationale: "lb = 460 m 2 let breath = b l = b * ( 100 + 15 ) / 100 = 115 b / 100 from these 115 b / 100 * b = 460 b 2 = 46000 / 115 = 400 b = root of 400 = 20 m answer b"
Answer: b
Question (general): a man purchased 5 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 250 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 5 * 100 + 5 * 150 = 1250 1500 – 1250 = 250 a"
Answer: a
Question (general): working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 8 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 4 days ?
Options: a ) 30 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: 5 machines do x units in 8 days we have x / 8 = > rate of the 5 machines we know that we need to have 3 x units in 4 days therefore , we need to get to 3 x / 4 rate of the machines . rate of one machine is x / 8 * 1 / 5 = x / 40 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 4 days . 3 x / 4 work needs to be done by machines that work at x / 40 rate . let ' s assign a constant y for the number of machines : ( x / 40 ) * y = 3 x / 4 y = 3 x / 4 * 40 / x cancel 4 with 40 , and x with x and get - > 30 . answer choice a
Answer: a
Question (geometry): in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 2,2 ) , ( 8,2 ) , ( 3,5 ) , ( 9,5 ) ?
Options: a ) 18 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 8 - 2 = 6 unit delta y will give us the dimension of the other side of parallelogram = 5 - 2 = 3 unit area of parallelogram = 6 * 3 = 18 answer is a"
Answer: a
Question (gain): on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 10 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 600 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,000
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 10 % . 10 x = 200 = > x = 2000 answer e"
Answer: e
Question (gain): there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 50 %
Options: a ) 40.8 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 50 / 100 = 50.40 so x = 40.8 answer : a"
Answer: a
Question (gain): jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much q does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) q = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Question (gain): machine p and machine q are each used to manufacture 440 sprockets . it takes machine p 10 hours longer to produce 440 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 440 / x = 440 / 1.1 x + 10 1.1 ( 440 ) = 440 + 11 x 11 x = 44 x = 4 the answer is b ."
Answer: b
Question (gain): a retailer buys 100 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 110 , b ) 175 , c ) 212 , d ) 218 , e ) 220
Rationale: "let the market price of each pen be $ 1 then , cost price of 100 pens = $ 36 selling price of 100 pens = 99 % of $ 100 = $ 99 profit % = ( ( 63 * 100 ) / 36 ) % = 175 % answer b"
Answer: b
Question (general): 3 litre of water is added to 11 litre of a solution containing 42 % of alcohol in the water . the percentage of alcohol in the new mixture is ?
Options: a ) 30 % , b ) 33 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 × 42 100 = 11 × 42100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 × 42 100 14 × 100 = 11 × 4210014 × 100 = 11 × 3 100 = 33 % b )
Answer: b
Question (probability): from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red card is drawn ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 26 , d ) 1 / 13 , e ) 5 / 13
Rationale: "the total number of cards is 52 . the number of red cards is 26 . p ( red card ) = 26 / 52 = 1 / 2 the answer is a ."
Answer: a
Question (physics): a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 26 , b ) 95 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 10 = rs . 95 answer : b"
Answer: b
Question (general): a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 375
Rationale: max no . of crates = 5 . max weight = 120 kg max . weight carried = 5 * 120 = 600 kg = c
Answer: c
Question (physics): a student completes a 3 part exam as follows . the student completes sections a in 24 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 7 : 8 , b ) 6 : 7 , c ) 5 : 6 , d ) 4 : 5 , e ) 3 : 4
Rationale: the time spent on section b and section c is 18 minutes each . the ratio of c to a is 18 : 24 = 3 : 4 the answer is e .
Answer: e
Question (general): the average of first 3 prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50
Rationale: 23 + 29 + 31 = 83 / 3 = 27.7 answer : d
Answer: d
Question (gain): a reduction of 44 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.3 , b ) 8.3 , c ) 7.3 , d ) 3.3 , e ) 1.3
Rationale: "explanation : 40 * ( 44 / 100 ) = 17.6 - - - 64 ? - - - 12 = > rs . 3.30 answer : d"
Answer: d
Question (general): if x and y are integers , what is the least positive number of 24 x + 16 y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "24 x + 16 y = 8 ( 3 x + 2 y ) which will be a minimum positive number when 3 x + 2 y = 1 . 3 ( 1 ) + 2 ( - 1 ) = 1 then 8 ( 3 x + 2 y ) can have a minimum positive value of 8 . the answer is e ."
Answer: e
Question (general): a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1987 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1987 + 19 = 2006 . answer : d ."
Answer: d
Question (physics): a cistern is filled by a tap in 3 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how long will it take the leak to empty it ?
Options: a ) 11 , b ) 12 , c ) 29 , d ) 28 , e ) 29
Rationale: 2 / 7 - 1 / x = 1 / 4 x = 28 answer : d
Answer: d
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 / 3 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 19 / 3 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 3 means that its equation is y = 1 / 3 * x . thus : ( x , 1 ) = ( 3 , 1 ) and ( 10 , y ) = ( 10,10 / 3 ) - - > x + y = 3 + 10 / 3 = 19 / 3 . answer : d ."
Answer: d
Question (general): a 40 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 810 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 4.0 assume x gallons of water are added . 4.0 / 40 + x = 8 / 100 400 = 8 x + 320 8 x = 80 x = 10 correct option : a"
Answer: a
Question (general): if 10 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: n ( n - 1 ) / 2 = 10 * 9 / 2 = 45 answer : e
Answer: e
Question (general): 6 x – 5 y + 3 z = 22 4 x + 8 y – 11 z = 7 5 x – 6 y + 2 z = 12 given the equations above , x + y + z = ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: ( 6 x – 5 y + 3 z ) - ( 5 x – 6 y + 2 z ) = 22 - 12 or , x + y + z = 10 option a is the ans
Answer: a
Question (general): the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 60 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 43 % , e ) 79 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 60 % then output equals 176 to restore new holidy demand output to original 100 . final - initial / final * 100 = 76 / 176 * 100 = 8 / 33 * 100 = 43 % approxiamately . option d is correct ."
Answer: d
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 405 , b ) 420 , c ) 440 , d ) 447 , e ) 490
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 38 t t = 14 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 14 = 490 miles answer : - e"
Answer: e
Question (gain): a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,200
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 2500 net price of the car in 02 = 18700 + 2500 = $ 21200 correct option : e"
Answer: e
Question (physics): jerry travels 8 miles at an average speed of 40 miles per hour , stops for 15 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 35 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: total time taken by jerry = ( 8 / 40 ) * 60 minutes + 15 minutes + ( 20 / 60 ) * 60 minutes = 47 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 47 / 60 ) hours = 28 * 60 / 47 = 35 miles per hour answer : option a
Answer: a
Question (gain): john makes $ 40 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 50 %
Rationale: "increase = ( 20 / 40 ) * 100 = 50 % . e"
Answer: e
Question (general): - 69 * 39 + 450 = ?
Options: a ) 2736 , b ) 2309 , c ) - 2801 , d ) - 2241 , e ) none of these
Rationale: "= > - 69 * ( 40 - 1 ) + 450 ; = > - ( 69 * 40 ) + 69 + 450 ; = > - 2760 + 519 = - 2241 . correct option : d"
Answer: d
Question (general): when n is divided by 24 , the remainder is 4 . what is the remainder when 3 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let n = 4 ( leaves a remainder of 4 when divided by 24 ) 3 n = 3 ( 4 ) = 12 , which leaves a remainder of 4 when divided by 8 . answer b"
Answer: b
Question (physics): two pipes a and b can separately fill a cistern in 45 minutes and 60 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 72 min , d ) 75 min , e ) 130 min
Rationale: "1 / 40 - ( 1 / 45 + 1 / 60 ) = - 1 / 72 third pipe can empty in 72 minutes answer : c"
Answer: c
Question (physics): a car takes 6 hours to cover a distance of 450 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 65
Rationale: "time = 6 distance = 450 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 450 / 9 = 50 kmph answer b ."
Answer: b
Question (probability): a letter lock consists of 3 rings each marked with 6 different letters . the number of distinct unsuccessful attempts to open the lock is at the most - .
Options: a ) 216 , b ) 243 , c ) 215 , d ) 729 , e ) 728
Rationale: since each ring consists of six different letters , the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216 . of these attempts , one of them is a successful attempt . maximum number of unsuccessful attempts = 216 - 1 = 215 . answer : c
Answer: c
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 10 minutes , then the area of the park ( in sq . m ) is
Options: a ) 153200 , b ) 240000 , c ) 153600 , d ) 154000 , e ) 154200
Rationale: "perimeter = distance covered in 10 min . = 12000 x 10 m = 2000 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 2000 or x = 200 . length = 600 m and breadth = 400 m . area = ( 600 x 400 ) m 2 = 240000 m 2 . b"
Answer: b
Question (general): average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 16 % the new mean is $ 850 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1250
Rationale: "0.16 x = 4 ( 850 - 800 ) 0.16 x = 200 x = 1250 answer e"
Answer: e
Question (physics): a person started from point a to point b and returned back to a with a speed of 60 kmh . if the distance between a and b is 120 km , calculate the time he travelled
Options: a ) 4 hours , b ) 2 hours , c ) 3 hours , d ) 6 hours , e ) 5 hours
Rationale: time = distance / speed total distance = ( from a - > b and from b - > a ) = 120 + 120 = 240 km speed = 60 kmh 240 / 60 = 4 answer : a
Answer: a
Question (probability): a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 15
Rationale: "the total number of ways to choose 5 managers is 7 c 5 = 21 we need to subtract the number of groups which include the two managers , which is 5 c 3 = 10 . 21 - 10 = 11 the answer is d ."
Answer: d
Question (gain): ravi and sunil are partners in a business . ravi invests rs . 15,000 for 8 months and sunil invested rs . 8000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 120000 : 80000 = 3 : 2 answer : c"
Answer: c
Question (gain): on a saturday night , each of the rooms at a certain motel was rented for either $ 50 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 50 , then the total rent the motel charged for that night would have been reduced by 25 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 400 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 50 $ , then total difference in prices = 10 $ * 10 = 100 $ total rent the motel charged would have been reduced by 25 % . 25 x = 100 = > x = 400 answer a
Answer: a
Question (gain): if price of t . v set is reduced by 10 % , then its sale increases by 85 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 67 , e ) 48
Rationale: - a + b + ( ( - a ) ( b ) / 100 ) = - 10 + 85 + ( - 10 * 85 ) / 100 = - 10 + 85 - 8.5 = 67 answer : d
Answer: d
Question (gain): a retailer buys a radio for rs 225 . his overhead expenses are rs 20 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 22.4 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 20 ) = 245 sell price = 300 gain = ( 55 / 245 ) * 100 = 22.4 % . answer : a"
Answer: a
Question (general): which number should replace both the asterisks in ( * / 18 ) x ( * / 162 ) = 1 ?
Options: a ) 27 , b ) 36 , c ) 54 , d ) 72 , e ) 90
Rationale: let ( y / 18 ) x ( y / 162 ) = 1 y ^ 2 = 18 x 162 = 18 x 18 x 9 y = ( 18 x 3 ) = 54 the answer is c .
Answer: c
Question (general): anne bought doughnuts for a class breakfast party . she bought 5 chocolate doughnuts , 6 coconut doughnuts , and 11 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 5 + 6 + 11 = 22 . answer is a ."
Answer: a
Question (other): a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 120 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 / 8,000 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 120 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 120 / 800 * 1 / 600 = 1 / 8,000 . answer : b ."
Answer: b
Question (gain): a man is walking at the rate of 10 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 ) 1250 meters , e ) 2500 meters
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 = 10 â ˆ — 5 / 18 = 25 / 9 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 25 / 9 â ˆ — 900 = 2500 meter option e"
Answer: e