Cheukting/mathqa huggingface dataset:
Question (physics): it would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order . how many hours would it take both machines , working simultaneously at their respective constant rates , to complete the order ?
Options: a ) 72 / 17 , b ) 17 / 72 , c ) 14 / 24 , d ) 24 / 56 , e ) 34 / 56
Rationale: the rate of the first machine is 1 / 9 job per hour ; the rate of the second machine is 1 / 8 job per hour ; thus , the combined rate of the machines is 1 / 9 + 1 / 8 = 17 / 72 job per hour , which means that it takes 1 / ( 17 / 72 ) = 72 / 17 hours both machines to do the job . answer : a .
Answer: a
Question (general): 3034 − ( 1002 ÷ 20.04 ) = ?
Options: a ) 1964 , b ) 1984 , c ) 2964 , d ) 2984 , e ) none of these
Rationale: "explanation : = 3034 − ( 1002 / 2004 × 100 ) = 3034 − 50 = 2984 option d"
Answer: d
Question (general): a number is doubled and 9 is added . if the resultant is trebled , it becomes 57 . what is that number ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 57 2 x = 10 = > x = 5 answer : a"
Answer: a
Question (general): a room is 5 meters 76 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 137 , e ) 147
Rationale: "let us calculate both the length and width of the room in centimeters . length = 5 meters and 76 centimeters = 576 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 576 and 432 = 144 thus , the number of square tiles required = ( 576 x 432 ) / ( 144 x 144 ) = 4 x 3 = 12 answer : b"
Answer: b
Question (physics): a train sets off at 2 : 00 pm at the speed of 70 km / h . another train starts at 3 : 00 pm in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ?
Options: a ) 10 : 00 , b ) 10 : 30 , c ) 11 : 00 , d ) 11 : 30 , e ) 12 : 00
Rationale: in one hour the first train travels 70 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 70 / 10 = 7 hours , so at 10 : 00 pm . the answer is a .
Answer: a
Question (physics): a boat can travel with a speed of 15 km / hr in still water . if the speed of the stream is 5 km / hr . find the time taken by the boat to go 68 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 3 hours 24 minutes , e ) none
Rationale: "solution speed downstream = ( 15 + 5 ) km / hr = 20 km / hr . time taken to travel 68 km downstream = ( 68 / 20 ) hrs = 3 hrs 24 minutes . answer d"
Answer: d
Question (general): mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 9 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "if n = 10 mark sold 1 box and ann sold 8 boxes total 9 < 10 answer : b"
Answer: b
Question (general): 135 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 54 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 135 = 81 liters water = 54 liters 81 : ( 54 + p ) = 3 : 4 162 + 3 p = 324 = > p = 54 54 liters of water are to be added for the ratio become 3 : 4 . answer : d"
Answer: d
Question (general): 17 times a positive integer is more than its square by 60 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 5 , e ) 14
Rationale: "explanation : let the number be x . then , 17 x = x 2 + 60 = > x 2 - 17 x + 60 = 0 = > ( x - 12 ) ( x - 5 ) = 0 = > x = 5 or 12 answer : option d"
Answer: d
Question (probability): a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 3 / 40000 , b ) 1 / 3600 , c ) 1 / 20000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 40 / 1000 first then we can only pick 1 other pair from the 800 so total will be 40 / 800 * 1000 simplify and you get 1 / 20000 answer is c"
Answer: c
Question (probability): a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is
Options: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 23
Rationale: "explanation : total number of cases = 52 favourable cases = 2 probability = 2 / 56 = 1 / 26 answer is c"
Answer: c
Question (geometry): frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 480 square feet . how many feet offence does frank use ?
Options: a ) 14
b ) 47
c ) 54
d ) 180
e ) 64
Rationale: area = length x breadth 480 = 40 x breadth so , breadth = 12 units fencing required is - breadth + breadth + length 12 + 12 + 40 = > 64 feet answer must be ( e ) 64
Answer: e
Question (physics): the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 6804 cu . m . its width is
Options: a ) 3 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 6804 x = 3 answer : a"
Answer: a
Question (general): 90 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 35 , c ) 42 , d ) 27 , e ) 11
Rationale: x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 90 = 35 answer : b
Answer: b
Question (physics): a train running at 1 / 3 of its own speed reached a place in 9 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "time taken if run its own speed = 1 / 3 * 9 = 3 hrs time saved = 9 - 3 = 6 hrs answer : e"
Answer: e
Question (physics): the radius of a semi circle is 7 cm then its perimeter is ?
Options: a ) 32.8 , b ) 36 , c ) 32.1 , d ) 32.2 , e ) 32.9
Rationale: "radius = 7 cm then diameter = 14 cm 1 / 2 * 22 / 7 * 14 + 14 = 36 answer : b"
Answer: b
Question (general): two persons raj and ramu started working for a company in similar jobs on january 1 , 1991 . raj ' s initial monthly salary was rs 400 , which increases by rs 40 after every year . ramu ' s initial monthly salary was rs 500 which increases by rs 20 after every 6 months . if these arrangements continue till december 31 , 200 . find the total salary they received during that period .
Options: a ) rs 108000 , b ) rs 144000 , c ) rs 132000 , d ) rs 152400 , e ) none of these
Rationale: explanation : raj ' s salary as on 1 jan 1991 is rs 400 per month . his increment in his month salary is rs 40 per annum his total salary from 1 jan 1991 to 31 st dec 2000 i . e . in ten years = > 12 [ 2 ( 400 ) + ( 10 − 1 ) 40 ] × 10 / 2 . = > rs 69600 . ramu ' s salary as on jan 1 st 1991 is rs 550 and his half yearly increment in his month salary is rs 20 . his total salary from 1 jan 1991 to dec 31 , 2000 = > 6 [ 2 ( 500 ) + ( 20 − 1 ) 20 ] × 20 / 2 . = > rs 82000 . total salary of raj and ramu in the ten year period : = > rs . 69600 + rs . 82800 . = > rs 1 , 52400 . answer : d
Answer: d
Question (general): at a certain college , 80 percent of the total number of students are freshmen . if 60 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 25 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 24 %
Rationale: let ' s say there is a total of 100 students at this college . 80 percent of the total number of students are freshmen . # of freshmen = 80 % of 100 = 80 60 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 60 % of 80 = 48 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 48 = 24 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 24 / 100 = 24 % answer : e
Answer: e
Question (gain): difference of two numbers is 1670 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2490 , 4150 , e ) 2505 , 4175
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1670 5 * y / 3 – y = 1670 2 * y / 3 = 1670 y = [ ( 1670 * 3 ) / 2 ] = 2505 . one number = 2505 , second number = 5 * y / 3 = 4175 . answer e ."
Answer: e
Question (other): the ratio of flour to water to sugar in a recipe is 11 : 8 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 4 cups of water , how much sugar is required ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "the ratio of flour to water is 22 : 8 = 11 : 4 . the ratio of flour to sugar is 5.5 : 1 = 11 : 2 . the new ratio of flour to water to sugar is 11 : 4 : 2 if we need 4 cups of water , then we need 2 cups of sugar . the answer is d ."
Answer: d
Question (general): craig sells major appliances . for each appliance he sells , craig receives a commission of $ 50 plus 10 percent of the selling price . during one particular week craig sold 6 appliances for selling prices totaling $ 3620 . what was the total of craig ' s commissions for that week ?
Options: a ) $ 412 , b ) $ 526 , c ) $ 585 , d ) $ 605 , e ) $ 662
Rationale: craig receives a commission of $ 50 on each appliance plus a 10 % commission on total sales , thus his commission was 6 * 50 + 0.1 * 3620 = 662 . answer : e .
Answer: e
Question (general): if 8 ^ x = 2 ^ 9 , what is x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 2 ^ 3 x = 2 ^ 9 3 x = 9 , therefore x = 3 answer b
Answer: b
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 3 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 3 / 23
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 3 * x hence , a 1 + a 2 + . . + a 20 + n = 23 x so , the fraction asked = 3 x / 23 x = 3 / 23 answer e"
Answer: e
Question (general): i chose a number and divide it by 8 . then i subtracted 100 from the result and got 6 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 848
Rationale: "solution : let x be the number i chose , then x / 8 â ˆ ’ 100 = 6 x / 8 = 106 x = 848 answer e"
Answer: e
Question (physics): the population of a bacteria colony doubles every day . if it was started 7 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 128 , b ) 256 , c ) 512 , d ) 1024 , e ) 2048
Rationale: 2 ^ 7 ( 2 ) = 2 ^ 8 = 256 the answer is b .
Answer: b
Question (general): light glows for every 32 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 180 times , b ) 381 times , c ) 155 times , d ) 392 times , e ) 150 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 32 ) = 15582 times . answer : c"
Answer: c
Question (geometry): if the height of a right cone c is 3 and the diameter of the base of c is 8 , what is the distance from the apex of c to any point on the circumference of the base of c ?
Options: a ) 3 √ 2
b ) 5
c ) 5 √ 2
d ) √ ( 67 )
e ) √ ( 73 )
Rationale: height of cone = 3 radius of base = 4 so the distance from the apex of c to any point on the circumference of the base of c will be a right angled triangle hence the distance is sqrt ( 3 ^ 2 + 4 ^ 2 ) = 5 answer : b
Answer: b
Question (physics): a can copy 50 papers in 10 hrs , while a & b can copy 70 papers in 10 hrs . how many hours are required for b to copy 26 papers ?
Options: a ) 11 hours , b ) 12 hours , c ) 13 hours , d ) 14 hours , e ) 18 hours
Rationale: a can copy 50 papers in 10 hrs , while a & b can copy 70 papers in 10 hrs . it means b can copy 20 papers in 10 hrs . then time taken by b to copy 26 papers = 26 * 10 / 20 = 13 hours answer : c
Answer: c
Question (general): 45 % of 816 - 23 % of ? = 240.7
Options: a ) 330 , b ) 440 , c ) 240 , d ) 550 , e ) 230
Rationale: "d 550 ( 816 * 45 ) / 100 - ( ? * 23 ) / 100 = 240.7 = > 367.2 - ( ? * 23 ) / 100 = 240.7 = > ( ? * 23 ) / 100 = 367.2 - 240.7 = > ? = ( 126.5 * 100 ) / 23 = 550"
Answer: d
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 121 hours and 100 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 100 : â ˆ š 121 = 10 : 11 . answer e"
Answer: e
Question (gain): shanmukham buys good worth rs . 6650 . he gets a rebate of 6 % on it . after getting the rebate , he pays sales tax @ 10 % . find the amount he will have to pay for the goods
Options: a ) 6999.2 , b ) 6876.1 , c ) 6654 , d ) 7000 , e ) none of these
Rationale: explanation : rebate = 6 % of rs . 6650 = rs . 6 / 100 x 6650 = rs . 399 . sales tax = 10 % of rs . ( 6650 399 ) = rs . 10 / 100 x 6251 = rs . 625.10 final amount = rs . ( 6251 + 625.10 ) = rs . 6876.10 answer : b
Answer: b
Question (general): the maximum numbers of students among them 781 pens and 710 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 71 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 781 and 710 . â € ¹ = â € º 71 . answer a"
Answer: a
Question (geometry): what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 27 units ?
Options: a ) 8.5 units , b ) 6 units , c ) 3 units , d ) 5 units , e ) 2 units
Rationale: "sides are 8 , 15 and 27 . . . thus it is right angle triangle since 27 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 27 + 15 + 8 / 2 = 30 thus , 60 = 30 * r and hence r = in - radius = 2 option e"
Answer: e
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 3 years hence ?
Options: a ) 58 , b ) 59 , c ) 62 , d ) 66 , e ) 74
Rationale: explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 3 years , their ages will be 43 and 23 . sum of their ages = 43 + 23 = 66 . d )
Answer: d
Question (physics): two trains 120 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 11.6 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 190 = 310 m . required time = 310 * 9 / 250 = 11.6 = 11.6 sec . answer : b"
Answer: b
Question (gain): krishan and nandan jointly started a business . krishan invested 4 times as nandan did and invested his money for trible time as compared to nandan . if the gain is proportional to the money invested and the time for which the money is invested and the total gain was rs . 26000 , find the nandan ' s earning .
Options: a ) 4000 , b ) 1000 , c ) 5000 , d ) 3000 , e ) 2000
Rationale: 4 : 1 3 : 1 - - - - - - 12 : 1 13 - - - - - rs . 26000 1 - - - - - ? = > rs . 26000 / 13 = rs . 2000 answer : e
Answer: e
Question (general): what is the 21 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 3 rd , 6 th , 9 th , . . . ) to the right of the decimal point is 7 , thus 21 st digit to the right of the decimal point is also 7 . answer : d ."
Answer: d
Question (general): two brothers ram and ravi appeared for an exam . the probability of selection of ram is 2 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 2 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 2 / 7 x 1 / 5 = 2 / 35 answer : a"
Answer: a
Question (geometry): if a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the longer sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 104 and a perimeter of 42 . we ' re asked for the length of one of the longer sides of the rectangle . since the answers are all integers , and the area is 104 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 104 , so the correct answer is probably a or c . let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 104 . . . . 104 / 8 = 13 = the longer side perimeter = 8 + 8 + 13 + 13 = 42 d"
Answer: d
Question (gain): a cricket bat is sold for $ 900 , making a profit of $ 75 . the profit percentage would be
Options: a ) 9 % , b ) 12 % , c ) 10 % , d ) 36 % , e ) 40 %
Rationale: "75 / ( 900 - 75 ) = 75 / 825 = 0.9 bit more than 9 % . answer : a"
Answer: a
Question (general): if 4 ^ ( 2 x + 2 ) = 16 ^ ( 3 x − 1 ) , what is the value of x ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: 2 ^ ( 4 x + 4 ) = 2 ^ ( 12 x - 4 ) 4 x + 4 = 12 x − 4 x = 1 answer b
Answer: b
Question (general): the product of three consecutive numbers is 720 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 17 , d ) 38 , e ) 56
Rationale: "product of three numbers = 720 720 = 8 * 9 * 10 so , the three numbers are 8 , 9 and 10 . and sum of smallest of these two = 8 + 9 = 17 . answer : option c"
Answer: c
Question (general): you collect pens . suppose you start out with 25 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 75 , e ) 43
Rationale: "solution start with 25 pens . mike gives you 22 pens : 25 + 22 = 47 pens . cindy doubles the number of pens you have : 47 ã — 2 = 94 pens . sharon takes 19 pens from you : 94 - 19 = 75 pens . so you have 75 at the end . correct answer : d"
Answer: d
Question (general): the population of a town increased from 1 , 45,000 to 2 , 30,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5.8 % , c ) 6.8 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 230500 - 145000 ) = 85500 . increase % = ( 85500 / 145000 x 100 ) % = 58 % . required average = ( 58 / 10 ) % = 5.8 % . answer : option b"
Answer: b
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 1 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 1 . so , x = 65 / 4 ounces . water = ( 60 / 65 ) * ( 65 / 4 ) = 15 ounces . ans a"
Answer: a
Question (other): in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 8 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 8 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 18 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 8 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 8 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 8 ) ( 1 ) 11 x = 7 x + 8 4 x = 8 x = 2 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 2 ) = 30 final answer : c"
Answer: c
Question (general): the number 523 fbc is divisible by 7 , 89 . then what is the value of f * b * c
Options: a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280
Rationale: lcm of 7 , 8 and 9 is 504 , thus 523 fbc must be divisible by 504 . 523 fbc = 523000 + fbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + fbc = k * 504 . k = 1 fbc = 152 - - > f * b * c = 10 k = 2 fbc = 656 - - > f * b * c = 180 as fbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d .
Answer: d
Question (general): the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 2 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 2 = 8 total number of axles = 9 t = 1.50 + 0.50 ( 9 − 2 ) = 1.50 + . 5 * 7 = 1.5 + 1.5 = 5 $ answer e"
Answer: e
Question (gain): indu gave bindu rs . 5000 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 5 , e ) 1
Rationale: "5000 = d ( 100 / 4 ) 2 d = 8 answer : a"
Answer: a