Cheukting/mathqa huggingface dataset:
Question (physics): there are two inlets and one outlet to a cistern . one of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern . both of the inlets are turned on at 8 : 30 am with the cistern completely empty , and at 10 : 30 am , the outlet is turned on and it takes 1 more hour to fill the cistern completely . how much time does the outlet working alone takes to empty the cistern when the cistern is full ?
Options: a ) 2 hours , b ) 2.5 hours , c ) 3 hours , d ) 3.5 hours , e ) 8 hours
Rationale: "the combined inflow rate of the two inlets is 1 / 4 + 1 / 8 = 3 / 8 cistern / hour . thus , working together , it takes 8 / 3 hours ( time is reciprocal of rate ) to fill the cistern . from 8 : 30 am to 10 : 30 am , so in 2 hours , the inlet pipes will fill ( time ) * ( rate ) = 2 * 3 / 8 = 3 / 4 th of the cistern . then the outlet is turned on and the remaining 1 / 4 th of the cistern is filled in 1 hour . letting x to be the rate of the outlet , we would have : 3 / 8 - x = 1 / 4 - - > x = 1 / 8 cistern / hour , which means that it takes 8 hours the outlet working alone to empty the cistern . answer : e ."
Answer: e
Question (general): if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 80 , how much more remains to be paid ?
Options: a ) $ 640 , b ) $ 680 , c ) $ 720 , d ) $ 760 , e ) $ 800
Rationale: "90 % remains to be paid so the remaining amount is 9 * 80 = $ 720 . the answer is c ."
Answer: c
Question (gain): mike needs 30 % to pass . if he scored 212 marks and falls short by 22 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 777 , c ) 780 , d ) 867 , e ) 232
Rationale: "if mike had scored 22 marks more , he could have scored 30 % therefore , mike required 212 + 22 = 234 marks let the maximum marks be m . then 30 % of m = 234 ( 30 / 100 ) × m = 234 m = ( 234 × 100 ) / 30 m = 23400 / 30 m = 780 answer : c"
Answer: c
Question (other): if shares of two persons in profits are rs . 400 and rs . 500 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 4 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 400 : 500 = 4 : 5 answer : b"
Answer: b
Question (general): in the xy - plane , the point ( 2 , 1 ) is the center of a circle . the point ( - 2 , 1 ) lies inside the circle and the point ( 2 , - 5 ) lies outside the circle . if the radius r of the circle is an integer , then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 2 , 1 ) and the point inside the circle ( - 2 , 1 ) is 4 units ( both points are on y = 1 line so the distance will simply be 2 - ( - 2 ) = 4 ) so the radius must be more than 4 units . the distance between the center ( 2,1 ) and the point outside the circle ( 2 , - 5 ) is 6 units ( both points are on x = 2 line so the distance will simply be 1 - ( - 5 ) = 6 ) so the radius must be less than 6 units , which implies 4 < r < 6 , thus as r is an integer then r = 5 . answer : b .
Answer: b
Question (physics): the sum of three consecutive integers is 102 . find the lowest of the three ?
Options: a ) 15 , b ) 33 , c ) 56 , d ) 96 , e ) 88
Rationale: "explanation : three consecutive numbers can be taken as ( p - 1 ) , p , ( p + 1 ) . so , ( p - 1 ) + p + ( p + 1 ) = 102 3 p = 102 = > p = 34 . the lowest of the three = ( p - 1 ) = 34 - 1 = 33 . answer b"
Answer: b
Question (general): in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 21,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 147 % , d ) 150 % , e ) 225 %
Rationale: "the percent increase is ( 21947 - 8902 ) / 8902 = 13045 / 8902 = 1.47 so the approximate answer is c"
Answer: c
Question (general): if k is the greatest positive integer such that 4 ^ k is a divisor of 16 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "16 / 4 = 4 16 / 16 = 1 4 + 1 = 5 k = 5 answer : c"
Answer: c
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 20 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 767 , e ) 432
Rationale: "1 h - - - - - 4 ? - - - - - - 60 12 h rs = 16 + 20 = 36 t = 12 d = 36 * 12 = 432 answer : e"
Answer: e
Question (physics): johnny makes $ 8.25 per hour at his work . if he works 2 hours , how much money will he earn ?
Options: a ) $ 30.50 , b ) $ 16.50 , c ) $ 28.50 , d ) $ 12 , e ) $ 9.60
Rationale: 8.25 * 2 = 16.50 . answer is b .
Answer: b
Question (general): the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number t ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = t answer : b"
Answer: b
Question (general): how many positive integers less than 5,000 are evenly divisible by neither 18 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 18 5000 / 18 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 18 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 18 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4428 answer d ."
Answer: d
Question (general): evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70"
Answer: d
Question (general): if xy denotes x is raised to the power y , find the last two digits of 19413844 + 19714181
Options: a ) 154 , b ) 677 , c ) 784 , d ) 148 , e ) 132
Rationale: "1941 ^ 3844 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 4 = 16 = 2 means last two digit = 61 and 1971 ^ 4181 unit digit = 1 10 th digit = 7 * 1 = 7 mean last two digit = 71 hence , 71 + 61 = 132"
Answer: e
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 172 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 172 = > 4 x / 10 = 172 = > 4 x = 1720 = > x = 430 . answer : a"
Answer: a
Question (physics): 12 buckets of water fill a tank when the capacity of each bucket is 55 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 5 litres ?
Options: a ) 142 , b ) 130 , c ) 132 , d ) 123 , e ) 120
Rationale: "capacity of the tank = ( 12 ã — 55 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 55 / 5 = 12 ã — 11 = 132 answer is c"
Answer: c
Question (physics): yesterday i noticed that in my clock , there is time when the hour needle and the minute needle are exactly between 1 and 2 . also both the needles lie on top of each other . what time i and talking about ?
Options: a ) 10 : 00 , b ) 11 : 00 , c ) 09 : 00 , d ) 12 : 00 , e ) 07 : 00
Rationale: d 12 : 00 both minute and hour clock lie exactly between the number one and two in the number .
Answer: d
Question (gain): a watch was sold at a loss of 46 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 280 , b ) 288 , c ) 279 , d ) 277 , e ) 290
Rationale: "54 % 104 % - - - - - - - - 50 % - - - - 140 100 % - - - - ? = > rs . 280 answer : a"
Answer: a
Question (general): ( 168 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 354 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 168 x 1265 / 100 ) ÷ 6 = 212520 / 600 = 354 answer : option a"
Answer: a
Question (general): there are 15 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 650 , b ) 750 , c ) 850 , d ) 950 , e ) 1050
Rationale: "the number of ways to choose two teams is 15 c 2 = 15 * 14 / 2 = 105 the total number of games in the season is 10 * 105 = 1050 . the answer is e ."
Answer: e
Question (general): if 3 : 12 : : x : 16 , then find the value of x
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : treat 3 : 12 as 3 / 12 and x : 16 as x / 16 , treat : : as = so we get 3 / 12 = x / 16 = > 12 x = 48 = > x = 4 option b
Answer: b
Question (general): bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 8 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 10 left in his pocket . what was the value of n ?
Options: a ) $ 32 , b ) $ 36 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer b if he had 36 , then he spent 9 at hardware store now he was left with 27 $ he spent 8 dollars on cleaning , thus he remained with 19 $ he then spent 1 / 2 of 19 , or 9.50 , hence , the only option that can be right is a . ans a"
Answer: a
Question (physics): john can complete a given task in 20 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 4 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 6 , b ) 10 , c ) 8 , d ) 7.5 , e ) 3.5
Rationale: "john 6 * 20 = 120 jane 10 * 12 = 120 in 4 days working alone john did : 4 days * rate = 4 * 6 = 24 , so working together they did 120 - 24 = 96 - - > rate ( a + b ) * t = 96 - > 16 * t = 96 , t = 6 . hence the answer is b ( john worked 4 days + 6 days they worked together = 10 days )"
Answer: b
Question (general): in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 1 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 45 , c ) 270 , d ) 90 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 1 / 3 ) of total igneous rocks . ( 1 / 3 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 3 ) = 90 total sedimentary rocks = 2 * total igneous rocks = 2 * 90 = 180 total number of rocks = 90 + 180 = 270 answer ( c )"
Answer: c
Question (physics): at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 5 / 6 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 4 / 7 , b ) 5 / 9 , c ) 6 / 11 , d ) 7 / 12 , e ) 8 / 13
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 5 x / 6 ) ( 3 y / 4 ) = 5 xy / 8 the total number of boxes is xy + 5 xy / 8 = 13 xy / 8 the fraction loaded by the day crew is xy / ( 13 xy / 8 ) = 8 / 13 the answer is e ."
Answer: e
Question (general): a man has some hens and cows . if the number of heads be 50 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 30 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 50 implies , 2 x + 4 y = 140 and x + y = 50 solving these two equations , we get x = 30 and y = 20 therefore , hens are 26 . answer : d"
Answer: d
Question (physics): the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 4.4 miles in the fifth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 45 , b ) 48 , c ) 51 , d ) 54 , e ) 57
Rationale: "( 4.4 miles / 8 minutes ) * 60 minutes / hour = 33 mph let x be the original speed . x - 4 ( 3 ) = 33 x = 45 mph the answer is a ."
Answer: a
Question (gain): a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 9 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 36.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.91 * 150 x = 136.5 x hence total profit = 36.5 % option d"
Answer: d
Question (general): if p / q = 6 / 7 , then 2 p + q = ?
Options: a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 19
Rationale: "let p = 6 , q = 7 then 2 * 6 + 7 = 19 so 2 p + q = 19 . answer : e"
Answer: e
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 9 minutes , then the area of the park ( in sq . m ) is
Options: a ) 153200 , b ) 153400 , c ) 153600 , d ) 194400 , e ) 154200
Rationale: "perimeter = distance covered in 9 min . = 12000 x 9 m = 1800 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1800 or x = 180 . length = 540 m and breadth = 360 m . area = ( 540 x 360 ) m 2 = 194400 m 2 . d"
Answer: d
Question (general): a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.08 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fourth day it is overdue ?
Options: a ) $ 0.62 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.08 2 nd day fine - 0.08 * 2 = 0.16 ( as doubling gives lower value ) 3 rd day fine - 0.16 * 2 = 0.32 ( as doubling gives lower value ) 4 th day fine - 0.32 + 0.3 = 0.62 ( as doubling gives higher value we add 0.3 this time ) answer : a ."
Answer: a
Question (physics): it is currently 7 : 05 pm . what time was it in the morning exactly 51132 minutes ago ?
Options: a ) 6 : 53 , b ) 6 : 55 , c ) 6 : 59 , d ) 7 : 03 , e ) 7 : 09
Rationale: convert 51,132 minutes to hours by dividing by 60 : 51,132 / 60 = 852 r 12 . that is 852 hours , 12 minutes . convert 852 hours to days by dividing by 24 : 852 / 24 = 35 r 12 . that is 35 days , 12 hours . thus 852 hours before 7 : 05 pm is 12 hours before 7 : 05 pm which is 7 : 05 am . 12 minutes before that is 6 : 53 am . a
Answer: a
Question (general): mary and mike enter into a partnership by investing $ 800 and $ 200 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1200 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3000 , b ) $ 3500 , c ) $ 4000 , d ) $ 4200 , e ) $ 4500
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 8 : 2 . i . e . , 80 % of 2 x would go to mary and 20 % of 2 x would go to mike . hence , mary would get ( 80 - 20 ) % of 2 x more than mike or 60 % of 2 x = $ 1200 i . e . , ( 60 / 100 ) * 2 x = 1200 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a"
Answer: a
Question (geometry): the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4332 sq cm . what is the ratio of the width and the area of the rectangle ?
Options: a ) 1 : 72 , b ) 1 : 76 , c ) 1 : 80 , d ) 1 : 84 , e ) 1 : 88
Rationale: "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4332 12 x ^ 2 = 4332 x ^ 2 = 361 x = 19 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 76 the answer is b ."
Answer: b
Question (general): if a and b are positive numbers , and a ^ 3 + b ^ 3 = 30 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a = 3.1 and b is very small , then a ^ 3 + b ^ 3 can equal 30 . if a > 4 , then a ^ 3 + b ^ 3 > 30 . the answer is b ."
Answer: b
Question (general): an owner of a pizza stand sold small slices of pizza for rs . 150 each and large slices for rs . 250 each . one night he sold 5000 slices , for a total of rs . 10.50 lakh . how many small slices were sold ?
Options: a ) 3000 , b ) 2000 , c ) 4000 , d ) 2500 , e ) 3500
Rationale: explanatory answer this question is a word problem in linear equations . the problem is solved by framing two linear equations from the information given in the question and solving them . let ' s ' be the number of small slices and ' b ' the number of large slices sold on that night . therefore , s + b = 5000 . . . eqn ( 1 ) each small slice was sold for rs . 150 . therefore , ' s ' small slices would have fetched rs . 150 s . each large slice was sold for rs . 250 . therefore , ' b ' large slices would have fetched rs . 250 b . total value of sale = 150 s + 250 b = 10 , 50000 ( note the left hand side is in rupees and hence we have to convert right hand also to rupees from lakhs of rupees ) or 150 s + 250 b = 10 , 50000 . . . eqn ( 2 ) multiplying equation ( 1 ) by 150 , we get 150 s + 150 b = 7 , 50000 . . . eqn ( 3 ) subtracting eqn ( 3 ) from eqn ( 2 ) , we get 100 b = 300000 or b = 3000 we know that s + b = 5000 so , s = 5000 - b = 5000 - 3000 = 2000 . 2000 small slices were sold . answer b
Answer: b
Question (physics): a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 189 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 189 km time taken = distance / speed = 189 / 27 = 7 hours . answer : option e"
Answer: e
Question (general): light glows for every 21 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 236 times , c ) 382 times , d ) 392 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 21 ) = 236 times . answer : b"
Answer: b
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 240 = 600 m required time = 600 * 2 / 25 = 48 sec answer : d"
Answer: d
Question (gain): a man buys a cycle for rs . 1400 and sells it at a loss of 12 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1232 , d ) s . 1202 , e ) s . 1204
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 12 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1232 . answer : c"
Answer: c
Question (geometry): all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes have only one face coloured ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 24 , e ) 2
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having only one face coloured = ( x - 2 ) 2 x no . of faces = ( 4 - 2 ) ^ 2 x 6 = 24 answer : d"
Answer: d
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 20 percent on clothing , 50 percent on food , and 30 percent on other items . if jill paid a 10 percent tax on the clothing , 15 percent tax on the food , and no tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 12.45 , b ) 12.5 , c ) 12.65 , d ) 12.35 , e ) 12.25
Rationale: "assume she has $ 200 to spend . tax clothing = 20 % = $ 40 = $ 10.00 food = 50 % = $ 100 = $ 15.00 items = 30 % = $ 60 = $ 0.00 total tax = $ 25.00 % of total amount = 25 / 200 * 100 = 12.25 % answer e"
Answer: e
Question (physics): if there are 26 laborers in a crew , and on a certain day , 10 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 39.5 % , b ) 38.5 % , c ) 36.5 % , d ) 37.5 % , e ) 30.5 %
Rationale: "10 / 26 * 100 = 38.46 38.5 % correct answer b"
Answer: b
Question (general): how many 3 - digit numbers can be formed from the digits 2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and if the repetition is allowed ?
Options: a ) 20 , b ) 5 , c ) 10 , d ) 36 , e ) 25
Rationale: "since , each desired number is divisible by 5 , so we must have 5 at the unit place . so , the tens place can now be filled by any of the remaining 6 digits ( 2 , 3 , 6 , 7 , 9 , 5 ) therefore the 3 - digit no can be formed by ( 6 * 6 * 1 ) = 36 ways - - - - - - ( since repetition is allowed ) ans - d"
Answer: d
Question (gain): the profit obtained by selling an article for rs . 66 is the same as the loss obtained by selling it for rs . 52 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) none of these
Rationale: "s . p 1 - c . p = c . p – s . p 2 66 - c . p = c . p - 52 2 c . p = 66 + 52 ; c . p = 118 / 2 = 59 answer : d"
Answer: d
Question (other): if 7 and 9 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 14 , e ) 21
Rationale: "60 n / 7 * 9 should be integer = > 2 * 2 * 3 * 5 * n / 7 * 3 * 3 = 2 * 2 * 5 * n / 21 must be an integer for this to be true n must multiple of 21 , thus min of n = 21 hence e"
Answer: e
Question (other): a bag contains 5 red , 4 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 33 , d ) 4 / 27 , e ) 3 / 23
Rationale: "p ( both are red ) , = 5 c 212 c 2 = 5 c 212 c 2 = 10 / 66 = 5 / 33 c"
Answer: c
Question (gain): in an election between two candidates , the first candidate got 70 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "let v be the total number of votes . 0.3 v = 240 v = 800 the answer is a ."
Answer: a
Question (gain): seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 38 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 86.66 % , e ) 66.66 %
Rationale: - - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 38 % 0.4 x + ( m - x ) 0.25 = 0.38 m 0.15 x = 0.13 m x = 0.8666 m x = 86.66 % of m d
Answer: d