Cheukting/mathqa huggingface dataset:
Question (physics): if 4 men working 10 hours a day earn rs . 1200 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 1680 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1200 : x hence 4 * 10 * x = 9 * 6 * 1200 or x = 9 * 6 * 1200 / 4 * 10 = 1620 answer : c"
Answer: c
Question (general): a test has 180 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 29 , b ) 33 , c ) 35 , d ) 40 , e ) 42
Rationale: "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 180 . thus 5 c < = 340 and so c < = 68 . then 40 < = c < = 68 and c can have 29 possible values . the answer is a ."
Answer: a
Question (general): jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 49 what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 49 = ( 4 / 7 ) * ( 4 / 7 ) therefore probability that the next one she draws is pink = 3 / 7 option ( c )"
Answer: c
Question (general): if x is 25 percent greater than 88 , then x =
Options: a ) 110 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x = 88 * 1.25 = 110 so the answer is a ."
Answer: a
Question (physics): a cistern 8 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 40 , b ) 48 , c ) 54 , d ) 62 , e ) 76
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 8 x 1.25 ) + 8 x 4 ] = 62 the answer is d ."
Answer: d
Question (general): at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 48 ¢ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 48 , the ratio should be 2 : 3 . mary must put back 5 oranges . the answer is e ."
Answer: e
Question (general): david has $ 1800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b
Answer: b
Question (geometry): two cylinders of the radius in the ratio 3 : 5 and heights in the ratio 10 : 9 . then find the volumes ratio ?
Options: a ) 4 : 5
b ) 1 : 5
c ) 3 : 5
d ) 1.5 : 5
e ) 2 : 5
Rationale: π r ( power 2 ) h : π r ( power 2 ) h 9 × 10 : 25 × 9 90 : 225 2 : 5 answer is e .
Answer: e
Question (physics): the length of the bridge , which a train 125 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 235 , b ) 240 , c ) 245 , d ) 250 , e ) 255
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 125 + x ) / 30 = 25 / 2 x = 250 m . answer : option d"
Answer: d
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 540 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,000 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 540 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 23000 answer : a"
Answer: a
Question (gain): a computer store offers employees a 30 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1500 dollars and marked up the price 30 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 30 % off retail price ) as opposed to the final retail price .
Options: a ) 525 , b ) 545 , c ) 565 , d ) 575 , e ) 585
Rationale: "cost price = 1500 profit = 30 % = 30 % of 1500 = 450 selling price = cp + profit sp = 1950 a discount of 30 % to employees means 30 % off on 1950 so 30 % of 1950 = 585 ans e"
Answer: e
Question (physics): car a runs at the speed of 65 km / hr & reaches its destination in 5 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 12 : 7 , c ) 13 : 7 , d ) 15 : 6 , e ) 65 : 56
Rationale: sol . distance travelled by car a = 65 ã — 5 = 325 km distance travelled by car b = 70 ã — 4 = 280 km ratio = 325 / 280 = 65 : 56 e
Answer: e
Question (general): if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: "( i ) 9 a - 11 b = 70 ( ii ) 2 a + 22 b = - 70 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Question (general): how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 17 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "so i can write this as in - 3 i + 4 < = 17 or in - 3 i < = 13 so n can have - 10 to 16 = 15 true values . . . . a"
Answer: a
Question (physics): there are 250 men and 150 women in a committee , if all will work they will complete 12 units per day , if all men work they will complete 15 units per day , how many units will women complete per day ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: i think there is a mistake in this question . if all men and women together complete 12 units , how only men can do 15 units of work a day ? forgetting about the reality , women can do - 3 units a day . answer : b
Answer: b
Question (gain): the cash difference between the selling prices of an article at a profit of 10 % and 6 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 55 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 110 % of x / 106 % of x = 110 / 106 = 55 / 53 = 55 : 53 answer : b"
Answer: b
Question (gain): in order to obtain an income of rs . 650 from 10 % stock at rs . 96 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 2368 , d ) 1987 , e ) 2732
Rationale: to obtain rs . 10 , investment = rs . 96 . to obtain rs . 650 , investment = = rs . 6240 . answer : b
Answer: b
Question (other): there are 380 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 57 , d ) 171 , e ) 220
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 380 = 220 answer : e"
Answer: e
Question (gain): we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 5 % . the total investment with interest at the end of the year was $ 1,046 . how much money did we invest at 3 % ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 280 , d ) $ 320 , e ) $ 360
Rationale: "let x be the money invested at 3 % . 1.03 x + 1.05 ( 1000 - x ) = 1046 . 0.02 x = 1050 - 1046 . 0.02 x = 4 . 2 x = 400 . x = 200 . the answer is a ."
Answer: a
Question (general): a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number e of ways this can be done is :
Options: a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225
Rationale: we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = { 1 , 2 , 3 , 4 , 5 } and 15 - 3 = { 0 , 1 , 2 , 4 , 5 } . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2 , 3 , 4 , 5 and 0 , 1 , 2 , 4 , 5 . how many 5 digit numbers can be formed using these two sets : 1 , 2 , 3 , 4 , 5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1 , 2 , 4 , 5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , desired # would be total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 4 ! ( 5 - 1 ) = 4 ! * 4 = 96 120 + 96 = 216 = e answer : c .
Answer: c
Question (physics): the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 700 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,400 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 800 ã — 22 ) = rs . 15400 answer : option b"
Answer: b
Question (physics): a car takes 6 hours to cover a distance of 270 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 10 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 27 kmph
Rationale: "time = 6 distence = 270 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 270 / 9 = 30 kmph d )"
Answer: d
Question (general): at a supermarket , john spent 1 / 5 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 11 on candy , how much did john spend at the supermarket ?
Options: a ) $ 20 , b ) $ 30 , c ) $ 50 , d ) $ 90 , e ) $ 110
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 5 of his money on fresh fruits and vegetables , or ( 1 / 5 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 11 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 5 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 11 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 6 t + 10 t + 3 t + 330 = 30 t 19 t + 330 = 30 t 330 = 11 t t = 30 john spent $ 90 at the supermarket . answer : b"
Answer: b
Question (physics): a and b finish the job in 15 days . while a , b and c can finish it in 12 days . c alone will finish the job in
Options: a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days
Rationale: "explanation : 12 = ( 15 * x ) / ( 15 + x ) 180 + 12 x = 15 x 3 x = 180 x = 60 answer : option c"
Answer: c
Question (gain): one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 250 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 250 2.5 h = 250 h = 100 . c is the answer ."
Answer: c
Question (general): a number divided by 44 leaves remainder 17 what is the remainder when same number divided by 8
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: "add 44 + 17 = 61 now 61 divided by 8 so we get 5 as reaminder answer : a"
Answer: a
Question (general): a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6 . if he makes exactly 96 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 42
Rationale: "7 c + 6 p = 96 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 7 * 6 + 6 * 9 = 42 + 54 = 96 hence e is the answer"
Answer: e
Question (gain): in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 30 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.30 = 12 republicans are expected to vote for candidate a . thus total of 45 + 12 = 57 registered voters are expected to vote for candidate a , which is 57 % of the total number of registered voters . answer : e ."
Answer: e
Question (geometry): a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 1520 , b ) $ 1640 , c ) $ 1780 , d ) $ 1850 , e ) $ 1960
Rationale: "the total surface area is 2 ( 2 * 4 + 4 * 5 + 2 * 5 ) = 76 square feet the total cost is 76 * $ 20 = $ 1520 the answer is a ."
Answer: a
Question (gain): a reduction of 10 % in the price of salt enables a lady to obtain 20 kgs more for rs . 400 , find the original price per kg ?
Options: a ) 2.0 , b ) 2.8 , c ) 2.2 , d ) 2.5 , e ) 3.0
Rationale: "answer : 400 * ( 10 / 100 ) = 40 - - - 20 ? - - - 1 = > rs . 2 400 - - - 360 ? - - - 2 = > rs . 2.22 . answer : c"
Answer: c
Question (geometry): in the rectangular coordinate system point o has coordinates ( 0,0 ) and point b has coordinates ( 5,5 ) and if point a is equidistant from points o and b and the area of the triangle oab is 16 , which of the following are the possible coordinates of point a .
Options: a ) ( - 2,6 )
b ) ( 0,4 )
c ) ( 2 , - 6 )
d ) ( 2,6 )
e ) ( 4,0 )
Rationale: area . pngsince a is equidistant from points o and b , then it must be somewhere on the green line ( perpendicular bisector of ob ) . ( 2 , - 6 ) and ( 2,6 ) are not on that line . if a is at ( 0,5 ) or ( 5,0 ) , then the area is 1 / 2 * 5 * 5 = 25 / 2 . thus a must be at ( 2,6 ) . answer : d .
Answer: d
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4528 , b ) s . 1812 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 2 = rs . 1812 answer : b"
Answer: b
Question (other): what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 300 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 300 = 3 ^ 600 * 2 ^ 600 the answer is d ."
Answer: d
Question (geometry): huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 8 inches on a side and costs $ 10 , and a large pizza that measures 12 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches , b ) 10 square inches , c ) 16 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 8 * 8 = 64 ) for the small pizza and ( 12 * 12 = 144 ) for the large pizza . in total sq inches that would be ( 64 + 144 ) * 2 = 416 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 144 = 432 sq inches . hence , the difference is 16 square inches more ( 432 - 416 ) . the correct answer is c"
Answer: c
Question (physics): 30 men can do a work in 40 days . when should 16 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 14 days , c ) 55 days , d ) 44 days , e ) 22 days
Rationale: "total work to be done = 30 * 40 = 1200 let 16 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 16 * 40 ) = 1200 40 p = 560 = > p = 14 days answer : b"
Answer: b
Question (gain): what is the normal price of an article sold at $ 126 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 155 , b ) $ 165 , c ) $ 175 , d ) $ 185 , e ) $ 195
Rationale: "0.8 * 0.9 * cost price = $ 126 cost price = $ 175 the answer is c ."
Answer: c
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 40 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 33 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Question (general): there are 280 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 600 , b ) 650 , c ) 700 , d ) 750 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 280 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 280 = 2 / 5 t , or 2 / 5 ( t - m ) = 280 , from here we get that t - m = 700 , that would be total number of female employees and the answer ( c )
Answer: c
Question (general): the average monthly income of p and q is rs . 2050 . the average monthly income of q and r is rs . 5250 and the average monthly income of p and r is rs . 6200 . the monthly income of p is :
Options: a ) 3050 , b ) 3000 , c ) 4000 , d ) 4050 , e ) 3100
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 2050 x 2 ) = 4100 . . . . ( i ) q + r = ( 5250 x 2 ) = 10500 . . . . ( ii ) p + r = ( 6200 x 2 ) = 12400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 27000 or p + q + r = 13500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 3000 . p ' s monthly income = rs . 3000 . answer : b"
Answer: b
Question (gain): running at the same constant rate , 16 identical machines can produce a total of 32 shirt per minute . at this rate , how many shirt could 8 such machines produce in 10 minutes ?
Options: a ) 911 , b ) 100 , c ) 101 , d ) 160 , e ) 785
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 32 / 16 = 2 shirt per minute per machine . 8 machines = 16 per minute . 10 minutes worth = 160 shirt . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d ."
Answer: d
Question (geometry): a certain cube floating in a bucket of water has between 70 and 85 percent of its volume below the surface of the water . if between 8 and 20 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 70 % = 240.1 , 85 % = 291.55 so vol above water , between 102.9 and 51.45 - - > too big if side are 4 , vol = 64 70 % = 44.8 , 85 % = 54.4 vol above water between 19.2 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 70 % = 87.5 , . 85 % = 106.25 vol above water between 18.75 - 37.5 ( sides are 4 cubic centimeters ) a"
Answer: a
Question (general): the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 14 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 77 / 2 , b ) 1 / 7 , c ) 78 / 85 , d ) 1 / 5 , e ) 47 / 85
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 14 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 14 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 14 * 2 b * b 3 b - 2 b ^ 2 = 28 b ^ 2 3 b = 30 b ^ 2 b = 3 / 30 = 1 / 10 so , a = 2 b = 1 / 5 the correct answer is d ."
Answer: d
Question (other): three numbers are in the ratio of 3 : 4 : 6 and their product is 1944 . the largest of these numbers is
Options: a ) 6 , b ) 12 , c ) 18 , d ) 26 , e ) 28
Rationale: "solution let the numbers be 3 x , 4 x and 6 x . then , 3 x × 4 x × 6 x = 1944 ‹ = › 72 x 3 = 1944 ‹ = › x 3 = 27 ‹ = › x = 3 therefore , largest number = 6 x = 18 . answer c"
Answer: c
Question (physics): two stations p and q are 200 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10 am , b ) 12 noon , c ) 10.30 am , d ) 12.30 am , e ) 11 am
Rationale: "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 200 = > 20 x + 25 ( x - 1 ) = 200 = > 45 x = 225 = > x = 5 means , they meet after 5 hours after 7 am , ie , they meet at 12 noon answer is b ."
Answer: b
Question (physics): walking at 1 / 3 th of its usual speed a cab is 20 mnts late . find its usual time to cover the journey ?
Options: a ) 10 m , b ) 15 m , c ) 20 m , d ) 25 m , e ) 12 m
Rationale: "new speed = 1 / 3 th of usual speed new time = 3 of usual time 3 ut - ut = 20 m 2 ut = 20 m ut = 10 m answer is a"
Answer: a