Cheukting/mathqa huggingface dataset:
Question (physics): two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 44 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 140 sec , b ) 132 sec , c ) 192 sec , d ) 252 sec , e ) none
Rationale: "solution relative speed = ( 44 - 40 ) kmph = 4 kmph = ( 4 x 5 / 18 ) m / sec = ( 20 / 18 ) m / sec time taken = ( 350 x 18 / 20 ) sec = 140 sec . answer a"
Answer: a
Question (general): tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 37 pages per hour . if tom starts reading a novel at 4 : 00 , and jan begins reading an identical copy of the same book at 4 : 56 , at what time will they be reading the same page ?
Options: a ) 7 : 26 , b ) 7 : 56 , c ) 8 : 26 , d ) 8 : 56 , e ) 9 : 26
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 28 pages in the first 56 minutes . jan can catch tom at a rate of 7 pages per hour , so it will take 4 hours to catch tom . the answer is d ."
Answer: d
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 42 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 27
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 42 = > x = 9 so deepak age is = 3 ( 9 ) = 27 option e"
Answer: e
Question (physics): an outlet pipe can empty 2 / 3 of a cistern in 20 minutes . in 8 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 9 , d ) 4 / 15 , e ) 9 / 20
Rationale: "8 / 20 * 2 / 3 = 4 / 15 the answer is d ."
Answer: d
Question (general): the number of diagonals of a polygon of n sides is given by the formula f = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "f = n ( n - 3 ) f = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 16 sec . what is the length of the platform ?
Options: a ) 287 m , b ) 431.25 m , c ) 267 m , d ) 287.25 m , e ) 656 m
Rationale: "speed = 300 / 16 = 75 / 4 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 75 / 4 = > x = 731.25 m answer : b ( 431.25 )"
Answer: b
Question (physics): two poles of height 6 meters and 11 meters stand on a plane ground . if the distance between their feet is 12 meters then find the difference in the distance between their tops :
Options: a ) 12 m , b ) 5 m , c ) 13 m , d ) 11 m , e ) 12 m
Rationale: distance between their tops = sqrt ( 12 ^ 2 + ( 11 - 6 ) ^ 2 ) = sqrt 169 = 13 m answer : c
Answer: c
Question (physics): if teena is driving at 55 miles per hour and is currently 7.5 miles behind loe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of loe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . loe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d"
Answer: d
Question (other): a bag contains 4 red , 5 blue and 3 green balls . if 3 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 33 , b ) 1 / 22 , c ) 1 / 12 , d ) 1 / 44 , e ) 1 / 55
Rationale: "p ( both are red ) , = 4 c 3 / 12 c 3 = 1 / 55 e"
Answer: e
Question (geometry): the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 507 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "area = l * w = 3 w ^ 2 = 507 w ^ 2 = 169 w = 13 the answer is c ."
Answer: c
Question (physics): the amount of time that three people worked on a special project was in the ratio of 3 to 5 to 6 . if the project took 140 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 32 hours , b ) 40 hours , c ) 35 hours , d ) 30 hours , e ) 36 hours
Rationale: "let the persons be a , b , c . hours worked : a = 3 * 140 / 14 = 30 hours b = 5 * 140 / 14 = 50 hours c = 6 * 140 / 14 = 60 hours c is the hardest worker and a worked for the least number of hours . so the difference is 60 - 30 = 30 hours . answer : d"
Answer: d
Question (gain): a student gets 60 % in one subject , 80 % in the other . to get an overall of 75 % how much should get in third subject .
Options: a ) 75 % , b ) 25 % , c ) 85 % , d ) 55 % , e ) 65 %
Rationale: let the 3 rd subject % = x 60 + 80 + x = 3 * 75 140 + x = 225 x = 225 - 140 = 85 answer : c
Answer: c
Question (general): according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 20 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 15 , b ) 34 , c ) 50 , d ) 67 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 20 oz can = 300 oz / 20 oz = 15 answer a , 15 cans"
Answer: a
Question (gain): john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.36 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.36 - - > 15 p - 13.5 p = 36 - - > p = 24 . answer : a ."
Answer: a
Question (gain): a , b and c invested rs . 8000 , rs . 4000 and rs . 8000 respectively in a business . a left after six months . if after eight months , there was a gain of rs . 4005 , then what will be the share of b ?
Options: a ) rs 690 , b ) rs 790 , c ) rs 890 , d ) rs 990 , e ) none of these
Rationale: "explanation : a : b : c = ( 8000 * 6 ) : ( 4000 * 8 ) : ( 8000 * 8 ) = 48 : 32 : 64 = 3 : 2 : 4 so b share = ( 2 / 9 ) * 4005 = rs 890 option c"
Answer: c
Question (physics): two pumps are connected to an empty tank . pump x fills the tank with water at a constant rate , while pump y drains water out of the tank at a constant rate . the two pumps finish filling the tank in 6 times the duration it would take pump x alone to fill the tank . if pump y alone can empty a whole tank in 48 minutes , then how many minutes does it take pump x alone to fill the tank ?
Options: a ) 32 , b ) 34 , c ) 36 , d ) 38 , e ) 40
Rationale: let v be the volume of the tank . let r be the rate per minute that pump x fills the tank . let t be the time it takes pump x to fill the tank . the rate at which pump y empties the tank is v / 48 per minute . ( r - v / 48 ) * 6 t = v = rt . ( r - v / 48 ) * 6 = r 5 r = v / 8 . r = v / 40 . it takes pump x 40 minutes to fill the tank . the answer is e .
Answer: e
Question (gain): a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 16.80 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 80
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 16.80 when c . p = ( 100 * 16.80 ) / 21 = 50 answer : e"
Answer: e
Question (general): given a two - digit number , the unit ' s digit exceeds its 10 ' s digit by 5 and the product of the given number and the sum of its digits is equal to 90 , which of the options is the number ?
Options: a ) 27 , b ) 16 , c ) 38 , d ) 61 , e ) 83
Rationale: using the elimination method the option that fits this description is 27 7 - 2 = 5 ( unit ' s digit that exceeds its ten ' s digit by 3 ) 27 * 9 = 243 ( the product of the given number and the sum of its digits is equal to 175 ) answer : a
Answer: a
Question (general): if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 240 - 80 / 60 - 40 * 10 = ?
Options: a ) 14.5 , b ) 13.5 , c ) 12.5 , d ) 17.5 , e ) 11.5
Rationale: explanation : given : 240 - 80 / 60 - 40 * 10 = ? substituting the coded symbols for mathematical operations , we get , 240 / 80 * 60 / 40 + 10 = ? 3 * 1.5 + 10 = 14.5 answer : a
Answer: a
Question (physics): a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5.5 hours , then the distance covered at 40 kmph is
Options: a ) 130 km , b ) 160 km , c ) 100 km , d ) 140 km , e ) none of these
Rationale: "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5.5 or , x / 40 + ( 250 - x ) / 60 = 5.5 or , ( 3 x + 500 - 2 x ) / / 120 = 5.5 or 500 + x = 660 x = 160 answer : b"
Answer: b
Question (general): the least number which when increased by 3 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 427 , b ) 859 , c ) 869 , d ) 861 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 3 = 864 - 3 = 861 . answer d"
Answer: d
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.15 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 30 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.15 = 1.25 km = 1250 m . required time = 1250 * 3 / 125 = 30 sec . answer : b"
Answer: b
Question (gain): what is the compound interest on rs : 80,000 for 4 months at the rate of 5 % per annum
Options: a ) 1341.69 , b ) 1342.69 , c ) 1343.69 , d ) 1344.69 , e ) 1345.69
Rationale: "it is monthly compound rate = 5 / 12 % per month 80000 * ( 1 + 5 / 1200 ) ^ 4 - 80000 = 1341.69 answer : a"
Answer: a
Question (general): tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?
Options: a ) 1 / 2 , b ) 1 / 2 , c ) 8 / 15 , d ) 9 / 20 , e ) 9 / 24
Rationale: "explanation : here , s = { 1 , 2 , 3 , 4 , . . . . , 19 , 20 } . let e = event of getting a multiple of 3 or 5 = { 3 , 6 , 9 , 12 , 15 , 18 , 5 , 10 , 20 } . p ( e ) = n ( e ) / n ( s ) = 9 / 20 answer : d"
Answer: d
Question (physics): the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 770 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 14 + 8 ) = 770 d = 70 the answer is c ."
Answer: c
Question (geometry): what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 5 , 12 and 13 ?
Options: a ) 2.5 , b ) 6.5 , c ) 5 , d ) 6.0 , e ) 7
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 13 / 2 = 6.5 ans . b"
Answer: b
Question (gain): the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % then determine the value of x .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "explanation : let the cost price 1 article = re 1 cost price of x articles = x s . p of x articles = 20 gain = 20 - x = > 25 = ( 20 − x / x ∗ 100 ) = > 2000 − 100 x = 25 x = > x = 16 option c"
Answer: c
Question (general): how many positive integers less than 260 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 45 , d ) 53 , e ) 64
Rationale: "260 / 4 = 65 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 65 - 20 = 45 answer : c"
Answer: c
Question (geometry): the area of sector of a circle whose radius is 10 metro and whose angle at the center is 42 â ° is ?
Options: a ) 36.7 , b ) 52.9 , c ) 52.8 , d ) 52.1 , e ) 52.2
Rationale: "42 / 360 * 22 / 7 * 10 * 10 = 36.7 m 2 answer : a"
Answer: a
Question (gain): 120 is what percent of 80 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 150 % , e ) 500 %
Rationale: "120 = x * 80 / 100 x = 150 % ans ; d"
Answer: d
Question (geometry): a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 140 square feet and its length is 4 feet longer than its width . if the uniform width between the rug and room is 4 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 46 , e ) 256
Rationale: "rug ' s area = 140 which is ( x ) x ( 4 + x ) = 140 so x = 10 rug maintains a uniform distance of 4 feet so room has dimension 10 + 8 and 14 + 8 i . e . 18 and 22 area of room 18 x 22 = 396 area covered is 140 so uncovered area is 396 - 140 = 256 ( answer e )"
Answer: e
Question (other): at a meeting , 25 attendants used a pencil and 15 attendants used a pen . if exactly 20 attendants used only one of the two types of writing tools , how many attendants wrote with both types of writing tools ?
Options: a ) 10 , b ) 6 , c ) 7 , d ) 4 , e ) 14
Rationale: say x attendants wrote with both writing tools . ( 25 - x ) + ( 15 - x ) = 20 - - > x = 10 . answer : a .
Answer: a
Question (general): in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 2 ) lies inside the circle and the point ( 5 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 5 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 5 , - 3 ) - - - > lesser than 7 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,2 ) - - - - > greater than 5 units . thus the radius is > 5 but < 7 and as it is an integer , the only possible value of radius = 6 units . a is the correct answer ."
Answer: a
Question (physics): working together , tim and tom can type 15 pages in one hour . if they would be able to type 18 pages in one hour if tom increases his typing speed by 60 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 15 tom increase speed by 60 % means he will type 1.6 y pages an hour . so we get x + 1.6 y = 18 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.6 y = 3 so y = 5 . . . so x = 10 ( y / x ) = 5 / 10 = 1 / 2 answer is ( a )"
Answer: a
Question (general): how many digits are in ( 12 × 10 ^ 14 ) ( 10 × 10 ^ 15 ) ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 32
Rationale: "the question simplfies to ( 12 × 10 ^ 14 ) ( 10 ^ 16 ) = > 12 * 10 ^ 30 = > will contain 30 zeros + 2 digit 12 = > 32 ans e"
Answer: e
Question (physics): 20 men can complete a piece of work in 30 days . in how many days can 25 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 24 , d ) 27 , e ) 11
Rationale: "20 * 30 = 25 * x = > x = 24 days answer : c"
Answer: c
Question (geometry): a lamp is put on one corner of a square plot of side 50 m . it ' s light reaches 21 m . find the area of that plot that is lit by that lamp ?
Options: a ) 248
b ) 312.5
c ) 346.5
d ) 392.5
e ) 424
Rationale: area covered by lamp = pi * r ^ 2 / 4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1 / 4 part lit is of the plot ) where r = 21 m = length of part lit so area = ( 22 / 7 ) * 21 * 21 / 4 = 346.5 sq m answer : c
Answer: c
Question (gain): what is 12.5 % of 4 / 12 of 600 ?
Options: a ) 25 , b ) 24 , c ) 30 , d ) 27 , e ) 28
Rationale: "12.5 % = 12.5 / 100 = 1 / 8 of 4 / 12 = 1 / 8 * 4 / 12 = 1 / 24 of 600 = 1 / 24 * 600 = 25 ans - a"
Answer: a
Question (general): what is 985 * 985 ?
Options: a ) 954,169 , b ) 964,219 , c ) 964,549 , d ) 965,019 , e ) 970,225
Rationale: "if you take a base of 1000 then 985 is 15 less than 1000 to get the product of 985 x 985 write like this 985 - 15 ( as 15 less than base 1000 ) 985 - 15 now 15 x 15 = 225 and 985 - 15 = 970 so 985 x 985 = 970225 . . . ( bingo the answer is e . you can even have a shortcut . . . . . . 15 x 15 = 225 . . . only answer choice has last three digits as 225 . . so no need to calculate 985 - 15 . after you get 15 x 15 you can straight way pick answer choice e ."
Answer: e
Question (general): find the slope of the line perpendicular to the line y = ( 1 / 6 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 6 , d ) 4 , e ) 5
Rationale: "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 6 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 6 ) = - 1 solve for m m = - 6 correct answer c ) - 6"
Answer: c
Question (general): find the mean proportional between 36 & 49 ?
Options: a ) a ) 42 , b ) b ) 61 , c ) c ) 63 , d ) d ) 65 , e ) e ) 67
Rationale: "formula = √ a × b a = 36 and b = 49 √ 36 × 49 = 6 × 7 = 42 a"
Answer: a
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 1 : 3 and b : c = 1 : 5 . if the total runs scored by all of them are 95 , the runs scored by c are ?
Options: a ) 20.23 , b ) 20.13 , c ) 75 , d ) 20.93 , e ) 10.93
Rationale: a : b = 1 : 3 b : c = 1 : 5 a : b : c = 1 : 3 : 15 15 / 19 * 95 = 75 answer : c
Answer: c
Question (general): dacid obtained 61 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 72 , c ) 39 , d ) 37 , e ) 75
Rationale: "average = ( 61 + 65 + 82 + 67 + 85 ) / 5 = 72 answer : b"
Answer: b
Question (general): 7500 + ( 1250 / 50 )
Options: a ) 7500 , b ) 7525 , c ) 7550 , d ) 8000 , e ) none of these
Rationale: explanation : as per bodmas rule first we will solve the terms in the bracket then other . = 7500 + ( 25 ) = 7525 option b
Answer: b
Question (general): the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 50 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 50 = > x = 50 thus proved . . . option a ."
Answer: a
Question (other): in a certain town , the ratio of ny yankees fans to ny mets fans is 2 : 1 , and the ratio of ny mets fans to boston red sox fans is 3 : 7 . if there are 320 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 48 , b ) 52 , c ) 56 , d ) 60 , e ) 64
Rationale: "the ratio of yankees : mets : red sox = 6 : 3 : 7 the mets fans are 3 / 16 of the population . ( 3 / 16 ) * 320 = 60 the answer is d ."
Answer: d
Question (general): solve below question 2 x + 1 = - 11
Options: a ) - 8 , b ) - 6 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 11 x = - 6 b"
Answer: b
Question (general): if 7 / w + 7 / x = 7 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: given : 7 / w + 7 / x = 7 / ywx = y find : ( w + x ) / 2 = ? 7 ( 1 / w + 1 / x ) = 7 ( 1 / y ) - divide both sides by 7 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a
Answer: a
Question (physics): a man can row 10 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 5.02 , b ) 4.92 , c ) 4.82 , d ) 4.72 , e ) 4.61
Rationale: "m = 10 s = 1.2 ds = 10 + 1.2 = 11.2 us = 10 - 1.2 = 8.8 x / 11.2 + x / 8.8 = 1 x = 4.92 . answer : b"
Answer: b
Question (general): a large field of 700 hectares is divided into two parts . the difference of the areas of the two parts is one – fifth of the average o fthe two areas . what is the area of the smaller part in hectares ?
Options: a ) 225 , b ) 280 , c ) 300 , d ) 385 , e ) none
Rationale: "solution let the areas of the two parts be x and ( 700 - x ) hectares = [ x - ( 700 - x ) ] = 1 / 5 x [ x + ( 700 - x ) / 2 ] = 2 x - 700 = 70 x = 385 . answer d"
Answer: d
Question (physics): what is the least number of square tiles required to pave the floor of a room 13 m 44 cm long and 4 m 44 cm broad ?
Options: a ) 7724 , b ) 7804 , c ) 4144 , d ) 7844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1344 cm & 444 cm = 12 cm . area of each tile = ( 12 x 12 ) cm 2 ∴ required number of tiles = [ 1344 x 444 / 12 x 12 ] = 4144 . answer c"
Answer: c
Question (physics): micheal and adam can do together a piece of work in 20 days . after they have worked together for 16 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 80 days , b ) 100 / 3 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 16 = 4 / 5 left work = 1 - 4 / 5 = 1 / 5 adam completes 1 / 5 work in 10 day so he took 10 * 5 = 50 days to complete the left work alone . thus the rate of adam is 1 / 50 rate of micheal = 1 / 20 - 1 / 50 = 1 / ( 100 / 3 ) thus micheal takes 100 / 3 days to complete the whole work . ans . b ."
Answer: b
Question (general): a palindrome is a number that reads the same forward and backward , such as 171 . how many even , 6 - digit numbers are palindromes ?
Options: a ) 405 , b ) 450 , c ) 400 , d ) 900 , e ) 2500
Rationale: "first recognize you only need to consider the first three digits ( because the second three are just the first three flipped ) there are 900 possibilities for the first three digits of a 6 digit number , 100 - 999 inclusive . everything starting with a 2,4 , 6,8 will be even , which is 4 / 9 ths of the combinations . 4 / 9 * 900 = 400 answer : c"
Answer: c
Question (other): of the 200 stamps in a collection , 90 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 30 , b ) 80 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 30 ) = 80 the answer is b ."
Answer: b