Cheukting/mathqa huggingface dataset:
Question (other): in a certain kindergarten , half of the children are allergic to peanuts , 10 children are not allergic to cashew nuts , 10 children are allergic to both peanuts and cashew nuts , and 18 children are allergic to cashew nuts . how many of the kindergarten ' s children are not allergic to peanuts and are not allergic to cashew nuts ?
Options: a ) 14 , b ) 10 , c ) 8 , d ) 6 , e ) 4
Rationale: we are given children allergic to cashew nuts as 18 and not allergic to cashew nuts as 10 , so total = 10 + 18 = 28 . . . children allergic to both are 10 . . . 18 are allergic to cashew nuts , so and half or 28 / 2 = 14 are allergic to peanuts . . so children allergic to at least one of the two are 18 + 14 - 10 = 22 . . therefore children not allergic to any of the two are 28 - 22 = 6 answer : d
Answer: d
Question (physics): a train 1100 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 m , b ) 256 m , c ) 200 m , d ) 278 m , e ) 287 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1100 + x ) / 60 = 65 / 3 x = 200 m . answer : c"
Answer: c
Question (general): the sum of number of boys and girls in a school is 300 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 75
Rationale: "we have x + x % of 300 = 300 x + x / 100 * 300 = 300 4 * x = 300 x = 75 answer is e"
Answer: e
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.82 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.55
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.82 = 3 * x - - > x = $ 0.55 . answer : e ."
Answer: e
Question (physics): the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 162 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 45 % , e ) 72 %
Rationale: answer : d 162 ° divided by 360 ° equals 0.45 , therefore the sector is equal to 45 % of the total
Answer: d
Question (general): 1100 boys and 700 girls are examined in a test ; 42 % of the boys and 30 % of the girls pass . the percentage of the total who failed is ?
Options: a ) 63.3 % , b ) 52.4 % , c ) 81.2 % , d ) 75.4 % , e ) 69.1 %
Rationale: total number of students = 1100 + 700 = 1800 number of students passed = ( 42 % of 1100 + 30 % of 700 ) = 462 + 210 = 672 number of failures = 1128 * 100 / 1800 = 190 / 3 % = 63.3 % answer is a
Answer: a
Question (gain): john makes $ 60 a week from his job . he earns a raise and nowmakes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17 % , d ) 17.2 % , e ) 18 %
Rationale: "increase = ( 10 / 60 ) * 100 = ( 1 / 6 ) * 100 = 16.66 % . b"
Answer: b
Question (general): two heavily loaded sixteen - wheeler transport trucks are 690 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 120 , b ) 130 , c ) 150 , d ) 320 , e ) 450
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 690 - 90 = 600 k ratio of speeds 9 : 8 - > 510 / 17 = 30 truck a = 90 + 30 * 9 = 360 truck b = 30 * 8 = 240 delta = 120 km answer a"
Answer: a
Question (physics): on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 42 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 14.81 , c ) 14.8 , d ) 14.82 , e ) 18.3
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 42 inch = ( 136 ã — 42 ) / 312 = 18.3 km answer : e"
Answer: e
Question (gain): on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 800 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 15 , c ) $ 23 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 800 ( 1.05 ) ^ 2 = 800 ( 1.1025 ) = 882 thus , tim earned 105 dollars , while lana earned 82 dollars the difference is $ 23 and the answer is c ."
Answer: c
Question (physics): the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is :
Options: a ) 279 , b ) 283 , c ) 308 , d ) 318 , e ) 328
Rationale: "other number = ( 11 * 7700 ) / 275 = 308 . answer : c"
Answer: c
Question (geometry): in measuring the sides of a rectangle , one side is taken 8 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 5 % , e ) 2.6 %
Rationale: "let the sides of the rectangle be a and b . actual area of the rectangle without error = ab new side a ( 8 % in excess ) = a + 0.08 a = 1.08 a new side b ( 5 % in deficit ) = b - 0.05 b = 0.95 b area of the new rectangle = ( 1.08 a ) ( 0.95 b ) = ( 1.0260 ) ab say a = 1 and b = 1 area of the original rectangle = 1 area of the new rectangle = 1.026 change in the area calculation = . 026 error percentage in the area calculated = 2.6 % answer : e"
Answer: e
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 3200 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 4050 , e ) 2288
Rationale: "3200 * 9 / 8 * 9 / 8 = 4050 answer : d"
Answer: d
Question (general): on a certain test , bill scored 20 more points than john , but half as many points as sue . if the sum of the scores of the 3 students was 160 points , how many points did bill receive ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 80 , e ) 100
Rationale: consider john ' s points as x so bill ' s points are x + 20 so sue ' s points are 2 x + 40 total of all three students is 4 x + 60 , but this total is given as 160 x = 25 so bill ' s points = 25 + 20 = 45 correct answer option b
Answer: b
Question (other): two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 2 : 3 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 99 : 61 , b ) 99 : 160 , c ) 61 : 160 , d ) 61 : 99 , e ) 99 : 160
Rationale: "vessel a = 300 gallons - - > milk = 120 , water = 180 ; vessel b = 500 gallons - - > milk = 375 , water = 125 ; vessel a + b = 800 gallons - - > milk = 495 , water 305 . the ratio = 495 / 305 - - > reduce by 5 = 99 / 61 . answer : a ."
Answer: a
Question (physics): a man swims downstream 45 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 10 , e ) 10.5
Rationale: "45 - - - 3 ds = 15 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 15 + 6 ) / 2 = 10.5 answer : e"
Answer: e
Question (general): the product of two successive numbers is 1122 . which is the smaller of the two numbers ?
Options: a ) 34 , b ) 36 , c ) 33 , d ) 38 , e ) 31
Rationale: "c 33 from the given alternatives , 33 × 34 = 1122 ∴ smaller number = 33"
Answer: c
Question (general): a library has an average of 630 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 305 , c ) 280 , d ) 285 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 630 x 5 + 240 x 25 / 30 ) = 305 answer : option b"
Answer: b
Question (gain): the sale price of a trolley bag including the sale tax is rs . 1232 . the rate of sale tax is 10 % . if the shopkeeper has made a profit of 12 % , the cost price of the trolley bag is :
Options: a ) rs 1000 , b ) rs 1515 , c ) rs 1525 , d ) rs 1250 , e ) none of these
Rationale: "explanation : 110 % of s . p . = 1232 s . p . = rs . ( 1232 x 100 / 110 ) = rs . 1120 . c . p . = rs ( 100 / 112 x 1120 ) = rs 1000 answer : a"
Answer: a
Question (gain): rs 4000 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) rs 4000 , b ) rs 2800 , c ) rs 3800 , d ) rs 3500 , e ) rs 3100
Rationale: "explanation : average rate = ( 144 / 4000 ) * 100 = 3.6 ratio = 14 : 6 = 7 : 3 so , first part = ( 7 / 10 ) * 4000 = rs 2800 . answer : b"
Answer: b
Question (physics): a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 4.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "d = 25 * 60 + 4500 = 6000 m t = 6000 / 60 * 18 / 5 = 360 sec = 6 mins answer : d"
Answer: d
Question (probability): the only items of clothing at michelle ’ s boutique are 4 shirts , 8 pairs of pants and 18 ties . what is the probability of randomly selecting 2 ties out of all the items in michelle ’ s boutique ?
Options: a ) 51 / 145 , b ) 9 / 25 , c ) 3 / 5 , d ) 94 / 145 , e ) 5 / 6
Rationale: we have 4 shirts , 8 pairs of pants and 18 ties . i . e 30 items total ways of picking two items out of all = 30 c 2 = 435 total ways of picking two items out of all ties = 18 c 2 = 153 required probability = 153 / 435 = 51 / 145 answer : option a
Answer: a
Question (gain): in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 26 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 32 , b ) 40 , c ) 48 , d ) 54 , e ) 60
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.26 ( 800 ) = 232 the answer is a ."
Answer: a
Question (general): mary and mike enter into a partnership by investing $ 900 and $ 100 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 $ 1600 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3500 , b ) $ 3400 , c ) $ 3300 , d ) $ 3200 , e ) $ 3000
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 9 : 1 . i . e . , 90 % of 2 x would go to mary and 10 % of 2 x would go to mike . hence , mary would get ( 90 - 10 ) % of 2 x more than mike or 80 % of 2 x = $ 1600 i . e . , ( 60 / 100 ) * 2 x = 1600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : e"
Answer: e
Question (other): if 63 percent of a class answered the first question on a certain test correctly , 49 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 22 % , b ) 24 % , c ) 26 % , d ) 28 % , e ) 32 %
Rationale: "63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 49 % - 17 % = 32 % . the answer is e ."
Answer: e
Question (physics): the speed of a boat in still water is 12 kmph . what is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 10 kmph
Rationale: "x = the speed of the stream ( 12 + x ) / ( 12 - x ) = 2 / 1 12 + x = 24 - 2 x 3 x = 12 x = 4 km / hour if the speed of the stream is 4 km / hour , then the ' downstream ' speed of the boat is 12 + 4 = 16 km / hour and the ' upstream ' speed of the boat is 12 - 4 = 8 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 8 = 16 km downstream and 2 x 16 = 32 km / hour upstream . answer : d"
Answer: d
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 2 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 9 , e ) 2 : 2
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : option b explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"
Answer: b
Question (physics): a birthday child reaches into a bag filled with toys ( 1 yo - yo , 1 ball , 1 whistle , and 1 box crayons ) . if the child randomly picks 3 toys , what is the probability the child will pick the yo - yo and a ball as two of the 3 toys ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 2 / 5
Rationale: combination formula : ncr = n ! / ( r ! ( n - r ) ! ) , where n is the population / set , and r is the sample / subset . total number possible = 4 c 3 - 4 ! / ( 3 ! ( 4 - 3 ) ! ) = 4 number yo - yo possible = 1 c 1 = 1 number ball possible = 1 c 1 = 1 number other possible = 2 c 1 = 2 probability formula : p ( a ) = ( number favorable outcomes ) / ( total number possible outcomes ) p ( yb ) = ( 1 c 1 ) ( 1 c 1 ) ( 2 c 1 ) / 4 c 3 = 2 / 4 = 1 / 2 answer : b
Answer: b
Question (general): 3 investors , a , b , and c , divide the profits from a business enterprise in the ratio of 5 : 7 : 8 , respectively . if investor a earned $ 2500 , how much money did investors b and c earn in total ?
Options: a ) $ 4,000 , b ) $ 4,900 , c ) $ 7,500 , d ) $ 9,500 , e ) $ 10,500
Rationale: let profit for a = 5 x profit for b = 7 x profit for c = 8 x investor a earned = 2500 5 x = 2500 = > x = 500 total profit for b and c = 7 x + 8 x = 15 x therefore , 15 x = 15 * 500 = 7,500 answer c
Answer: c
Question (physics): suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 580 ( before payroll deductions ) ?
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 580 x = 80 / 0.16 = 500 the answer is b ."
Answer: b
Question (general): find the least number of complete years in which a sum of money put out at 15 % compound interest will be more than double of itself ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "5 years answer : a"
Answer: a
Question (general): jim â € ™ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.3 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.95 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: let the fixed charge of jim â € ™ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 3 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 3 = 2.25 + 9 * . 3 = 4.95 $ answer b
Answer: b
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 15 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 10 % . if ron imported a $ 15,000 imported car and ended up paying $ 1800 in taxes , what is the first tier ' s price level ?
Options: a ) $ 7000 , b ) $ 6500 , c ) $ 6050 , d ) $ 6000 , e ) $ 6100
Rationale: "let t be the tier price , p be total price = 15000 per the given conditions : 0.15 t + 0.10 ( p - t ) = 1800 0.15 t + 0.10 * 15000 - 0.10 t = 1800 0.05 t + 1500 = 1800 0.05 t = 1800 - 1500 = 300 t = 300 / 0.05 = 6000 answer d"
Answer: d
Question (physics): in what time will a train 90 meters long cross an electric pole , if its speed is 124 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2.6 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 124 * ( 5 / 18 ) = 34 m / sec time = distance / speed = 90 / 34 = 2.6 seconds option d"
Answer: d
Question (gain): what is the rate percent when the simple interest on rs . 600 amount to rs . 160 in 4 years ?
Options: a ) 6.66 % , b ) 7.66 % , c ) 6.06 % , d ) 6.16 % , e ) 8.66 %
Rationale: "160 = ( 600 * 4 * r ) / 100 r = 6.66 % answer : a"
Answer: a
Question (general): find two integers , neither of which ends in a zero , and whose product is exactly 10 , 000,000
Options: a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 128 and 78,125
Rationale: "10 , 000,000 = 10 ^ 7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 7 ) x ( 5 ^ 7 ) = 128 x 78125 so the numbers are 128 and 78,125 answer : e"
Answer: e
Question (general): a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 3000 as profit , what is their total profit ?
Options: a ) 21000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 3000 = > total profit = 3000 * 7 = 21000 . answer : option a"
Answer: a
Question (physics): a person crosses a 1080 m long street in 10 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 6.4 , c ) 4.8 , d ) 5.4 , e ) 5.5
Rationale: "speed = 1080 / ( 10 x 60 ) m / sec = 1.8 m / sec . converting m / sec to km / hr = 1.8 x ( 18 / 5 ) km / hr = 6.4 km / hr . answer : b"
Answer: b
Question (gain): exactly 12 % of the reporters for a certain wire service cover local politics in country x . if 40 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 80 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 12 reporters cover local politics . now , as 40 % of the reporters who cover all politics do not cover local politics then the rest 60 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 60 % of them equal to 12 ( # of reporters who cover local politics ) : 0.6 x = 12 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."
Answer: d
Question (gain): a man can row his boat with the stream at 6 km / h and against the stream in 3 km / h . the man ' s rate is ?
Options: a ) 1.5 kmph , b ) 3 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 6 us = 3 s = ? s = ( 6 - 3 ) / 2 = 1.5 kmph answer : a"
Answer: a
Question (physics): ronald and elan are working on an assignment . ronald takes 6 hours to type 32 pages on a computer , while elan takes 5 hours to type 40 pages . how much time will they take , working together on two different computers to type an assignment of 110 pages ?
Options: a ) 3 hours , b ) 6 hours , c ) 4 hours , d ) 8 hours , e ) 10 hours
Rationale: number of pages typed by ronald in one hour = 32 / 6 = 16 / 3 number of pages typed by elan in one hour = 40 / 5 = 8 number of pages typed by both in one hour = ( ( 16 / 3 ) + 8 ) = 40 / 3 therefore , time taken by both to type 110 pages = 110 x 3 / 40 = 8 hours . answer : d
Answer: d
Question (gain): an error 2 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is ?
Options: a ) 4.04 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 a )"
Answer: a
Question (general): the difference between a number and its two - fifth is 510 . what is 50 % of that number ?
Options: a ) 426 , b ) 425 , c ) 427 , d ) 428 , e ) 429
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 50 % of 850 = 425 . answer : b"
Answer: b
Question (gain): a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 46 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 54 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 45 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.46 m = = > revenue = price x quantity = 0.54 ( m + w ) = = > profit = 0.54 ( m + w ) - 0.46 m = 0.2 * ( 0.46 m ) [ 20 % of cost ] = = > 0.54 m + 0.54 w - 0.46 m = 0.092 m = = > 0.012 m = 0.54 w = = > m / w = 0.54 / 0.012 = 45 - - or - - w / m = 1 / 45 d is correct ."
Answer: d
Question (physics): a train 441 m long can cross an electric pole in 21 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 76 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: length = speed * time speed = l / t s = 441 / 21 s = 21 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 76 kmph answer : c
Answer: c