Cheukting/mathqa huggingface dataset:
Question (general): if log 8 x + log 8 1 / 6 = 1 / 3 , then the value of x is :
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 – log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a"
Answer: a
Question (general): if the sum of two numbers is 12 and the sum of their squares is 124 , then the product of the numbers is
Options: a ) 10 , b ) 44 , c ) 80 , d ) 88 , e ) 90
Rationale: "sol . let the numbers be x and y . then , ( x + y ) = 12 and x 2 + y 2 = 124 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 12 ) 2 - 124 = 144 - 124 = 20 xy = 10 . answer a"
Answer: a
Question (other): the ratio between the sale price and the cost price of an article is 8 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25
Rationale: "c . p . = rs . 5 x and s . p . = rs . 8 x . then , gain = rs . 3 x required ratio = 3 x : 5 x = 3 : 5 d"
Answer: d
Question (physics): tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 9 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 90 , c ) 30 , d ) 70 , e ) 60
Rationale: "b 90 sum = ( n x n ) + n hence , 9 x 9 = 81 + 9 = 90"
Answer: b
Question (general): in the coordinate plane , points ( x , 1 ) and ( 7 , y ) are on line k . if line k passes through the origin and has slope 1 / 7 , then x - y =
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 3
Rationale: "line k passes through the origin and has slope 1 / 7 means that its equation is y = 1 / 7 * x . thus : ( x , 1 ) = ( 7 , 1 ) and ( 7 , y ) = ( 7,1 ) - - > x - y = 7 - 1 = 6 . answer : a"
Answer: a
Question (geometry): find the perimeter and area of the rectangle of length 15 cm and breadth 13 cm .
Options: a ) 71 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 195 cm 2 , e ) 221 cm 2
Rationale: "length = 15 cm , breadth = 13 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 15 + 13 ) cm = 2 × 28 cm = 56 cm we know that the area of rectangle = length × breadth = ( 15 × 13 ) cm 22 = 195 cm 2 answer : d"
Answer: d
Question (other): out of 400 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 220
Rationale: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 400 - 50 = 350 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 350 = 150 . answer is b"
Answer: b
Question (general): find the sum of first 20 multiples of 12 .
Options: a ) 2520 , b ) 3878 , c ) 2778 , d ) 27 , e ) 911
Rationale: "sum of first 20 multiples of 12 are = ( 12 × 1 ) + ( 12 × 2 ) + ( 12 × 3 ) + . . . . . . + ( 12 × 19 ) + ( 12 × 20 ) . = 12 ( 1 + 2 + 3 + . . . . . + 20 ) use the formula : n ( n + 1 ) 2 ⇒ 12 × ( 20 × 21 ) 2 = 2520 . answer : a"
Answer: a
Question (general): 50 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 200 , c ) 1225 , d ) 220 , e ) 230
Rationale: total no . of handshakes = 49 + 48 + 47 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1225 or , if there are n persons then no . of shakehands = nc 2 = 50 c 2 = 1225 answer : c
Answer: c
Question (physics): if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 10 minutes ?
Options: a ) 40 , b ) 100 , c ) 150 , d ) 240 , e ) 300
Rationale: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 10 minutes the population increases by 10 x 4 = 40 people . answer . a ."
Answer: a
Question (general): real - estate salesman z is selling a house at a 25 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 5 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 30 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 21 / 34 , b ) 55 / 71 , c ) 25 / 34 , d ) 26 / 34 , e ) 27 / 34
Rationale: "let the retail price be = x selling price of z = 0.75 x selling price of x = 0.95 * 0.75 x = 0.71 x selling price of y = ( ( 0.75 x + 0.71 x ) / 2 ) * 0.70 = 0.73 x * 0.75 = 0.55 x 0.55 x = k * 0.71 x k = 0.55 / 0.71 = 55 / 71 answer : b"
Answer: b
Question (general): if p ( a ) = 3 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 6 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 3 / 5 . 2 / 5 p ( a n b ) = 6 / 25 . a"
Answer: a
Question (probability): if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips ?
Options: a ) 3 / 5 , b ) 1 / 2 , c ) 1 / 5 , d ) 1 / 8 , e ) 1 / 32
Rationale: "on the first three flips , you must get heads . whats the probability of getting heads ? its 1 / 2 so for the first three flips , your probability is ( 1 / 2 ) ^ 3 = 1 / 8 now for the last two , you want to get tails only . whats the prob of getting tails ? well , its the same as prob of getting a heads , namely , 1 / 2 for the last two flips , your probability is ( 1 / 2 ) ^ 2 = 1 / 4 so your overall probability for the event in question is 1 / 8 * 1 / 4 = 1 / 32 answer : e"
Answer: e
Question (general): if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value q of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] q = z - x = x + 9 - x = 9 ans : d"
Answer: d
Question (physics): a piece of work can finish by a certain number of men in 100 days . if however , there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?
Options: a ) 75 , b ) 82 , c ) 100 , d ) 110 , e ) 120
Rationale: originally let there be x men . less men , more days ( indirect ) : . ( x - 10 ) : x : : 100 : 110 or x - 10 / x = 100 / 110 or 11 x - 110 = 10 x or x = 110 so , originally there were 110 men . answer : d
Answer: d
Question (physics): how many seconds will a train 150 meters long take to cross a bridge 200 meters long if the speed of the train is 54 kmph ?
Options: a ) 17 sec , b ) 21 sec , c ) 23.3 sec , d ) 27.5 sec , e ) 29 sec
Rationale: d = 150 + 200 = 350 s = 54 * 5 / 18 = 15 mps t = 350 / 15 = 23.3 sec c ) 23.3 sec
Answer: c
Question (gain): an error 6 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 14.05 % , b ) 14.02 % , c ) 14 % , d ) 13 % , e ) 12.36 %
Rationale: "percentage error in calculated area = ( 6 + 6 + ( 6 ã — 6 ) / 100 ) % = 12.36 % answer : e"
Answer: e
Question (physics): liz drove from point a to point b at 40 km / h . on her way back she drove at 50 km / h and therefore her way back lasted one hour less . what is the distance ( in km ) between a and b ?
Options: a ) 150 , b ) 200 , c ) 450 , d ) 500 , e ) 600
Rationale: distance is same s 1 t 1 = s 2 t 2 40 t = 50 ( t - 1 ) t = 5 distance = speed * time 40 * 5 = 200 answer : b
Answer: b
Question (gain): uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 10 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 3 , e ) 1
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 80 % * total = 36 = > ( 8 / 10 ) total = 36 = > total = 360 / 8 = > total = 45 oz , from there , you must find 10 % of the total 40 oz of the mixture . 20 % * total = > ( 2 / 10 ) ( 45 ) = 9 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 10 - 9 = 1 oz chocolate left over . answer : e"
Answer: e
Question (general): the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?
Options: a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 2 / 7
Rationale: "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 7 / 4 ) * 4 = 2 / 7 the answer is e ."
Answer: e
Question (general): in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2,100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 %
Rationale: ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a
Answer: a
Question (physics): the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 480 / 4 = 12 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 4 miles / gallon is required to match the actual mileage . answer : b"
Answer: b
Question (general): the average age of 22 students in a group is 12 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 31 , b ) 36 , c ) 35 , d ) 53 , e ) 57
Rationale: "age of the teacher = ( 23 * 13 - 22 * 12 ) = 35 years . answer : c"
Answer: c
Question (geometry): a square is drawn inside a right - angled triangle with the two perpendicular sides as 12 cm and 8 cm . what is the side of the largest possible square that can be drawn ?
Options: a ) 4.8 cm
b ) 4.4 cm
c ) 4.9 cm
d ) 5.0 cm
e ) 5.2 cm
Rationale: area of triangle is 1 / 2 * 12 * 8 = 48 side of square = x the entire triangle split into two right angled triangle and one square with dimensions as follows i ) square with side x ii ) right angled triangle with perpendicular sides x and 12 - x iii ) right angled triangle with perpendicular sides 8 - x and x sum of area of all three = 48 = x 2 + 1 / 2 * x * ( 12 - x ) + 1 / 2 * x * ( 8 - x ) = 48 = x = 4.8 cm answer : a
Answer: a
Question (probability): the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be social teachers ?
Options: a ) 2 / 3 , b ) 1 / 12 , c ) 2 / 9 , d ) 1 / 2 , e ) 1 / 24
Rationale: "probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( b )"
Answer: b
Question (physics): in a 160 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 22 seconds , b ) 12 seconds , c ) 13 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: b runs 56 m in 7 sec . = > b runs 160 m in 7 / 56 * 160 = 20 seconds since a beats b by 7 seconds , a runs 160 m in ( 20 - 7 ) = 13 seconds hence , a ' s time over the course = 13 seconds answer : c
Answer: c
Question (general): . 002 / ? = . 01
Options: a ) . 2 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them
Rationale: let . 002 / x = . 01 ; then x = . 002 / . 01 = . 2 / 1 = . 2 answer is a
Answer: a
Question (physics): a cistern is filled by a tap in 7 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 80 , b ) 100 , c ) 120 , d ) 140 , e ) 160
Rationale: "filling rate - leak rate = net rate 1 / 7.5 - leak rate = 1 / 8 leak rate = 2 / 15 - 1 / 8 = 1 / 120 the answer is c ."
Answer: c
Question (gain): by how much is 70 % of 120 greater than 35 % of 200 .
Options: a ) 15 , b ) 14 , c ) 13 , d ) 16 , e ) 17
Rationale: ( 70 / 100 ) * 120 â € “ ( 35 / 100 ) * 200 84 - 70 = 14 answer : b
Answer: b
Question (general): if 2 ^ k + 2 ^ k = ( 2 ^ 9 ) ^ ( 2 ^ 9 ) - 2 ^ k , then k = ?
Options: a ) 11 / 3 , b ) 11 / 2 , c ) 2 ^ 11 - 1 , d ) 3 ^ 10 , e ) 3 ^ 11 - 1
Rationale: "2 ^ k + 2 ^ k = ( 2 ^ 9 ) ^ 2 ^ 9 - 2 ^ k 2 * ( 2 ^ k ) = 2 ^ ( 4 * 3 ^ 9 ) = 2 ^ ( 2 ^ 2 * 2 ^ 9 ) = 2 ^ ( 2 ^ 11 ) 2 ^ k + 1 = 2 ^ ( 2 ^ 11 ) so k + 1 = 2 ^ 11 so k = 2 ^ 11 - 1 answer is c"
Answer: c
Question (general): in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 5 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42
Rationale: "explanation : let b ' s age = x years . then , as age = ( x + 5 ) years . ( x + 5 + 10 ) = 2 ( x — 10 ) hence x = 35 . present age of b = 35 years answer : option a"
Answer: a
Question (general): if 2 + 7 = 57 ; 3 + 6 = 63 ; 5 + 9 = 206 then 5 + 8 = ?
Options: a ) 185 , b ) 186 , c ) 177 , d ) 168 , e ) 189
Rationale: "2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 5 ^ 3 + 8 ^ 2 = 189 answer : e"
Answer: e
Question (gain): if a man lost 7 % by selling oranges at the rate of 21 a rupee at how many a rupee must he sell them to gain 42 % ?
Options: a ) 12.75 , b ) 11.75 , c ) 8.75 , d ) 15.75 , e ) 13.75
Rationale: "93 % - - - - 21 142 % - - - - ? 93 / 142 * 21 = 13.75 answer : e"
Answer: e
Question (general): what is the greatest prime factor of 5 ^ 6 - 1 ?
Options: a ) 29 , b ) 31 , c ) 37 , d ) 41 , e ) 43
Rationale: "5 ^ 6 - 1 = ( 5 ^ 3 - 1 ) ( 5 ^ 3 + 1 ) = 124 * 126 = 4 * 31 * 3 * 42 the answer is b ."
Answer: b
Question (physics): a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.4 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 4 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 140 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 140 - x ) = 8000 × 1000 = > ( 140 - x ) = 8000 × 1000 / 320 = 100 = > x = 40 cm = 4 dm . answer : b"
Answer: b
Question (physics): a and b can do a piece of work in 10 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 15.5 days , b ) 4.3 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days
Rationale: "c = 1 / 3 – 1 / 10 = 7 / 30 = > 4.3 days answer : b"
Answer: b
Question (physics): a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 40 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 15 / 60 ) = 4 kmhr speed in still water = 1 / 2 ( 2 + 4 ) = 3 kmhr time taken in stationary = 5 / 3 = 1 hrs 40 min answer : e"
Answer: e
Question (physics): a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 16 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 12 days , d ) 24 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 16 x = 24 days answer : option d"
Answer: d
Question (physics): a and b complete a work in 10 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.0875 days , b ) 0.125 days , c ) 0.0675 days , d ) 0.0875 days , e ) 0.0775 days
Rationale: "1 / 10 + 1 / 40 = 0.125 days answer : b"
Answer: b
Question (physics): a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length .
Options: a ) 20 seconds , b ) 27 seconds , c ) 30 seconds , d ) 40 seconds , e ) 50 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds answer : d"
Answer: d
Question (general): if a 2 - b 2 = 9 and a * b = 4 , find a 4 + b 4 .
Options: a ) 32 , b ) 90 , c ) 113 , d ) 92 , e ) 81
Rationale: "a 2 - b 2 = 9 : given a 4 + b 4 - 2 a 2 b 2 = 92 : square both sides and expand . a * b = 4 : given a 2 b 2 = 42 : square both sides . a 4 + b 4 - 2 ( 16 ) = 81 : substitute a 4 + b 4 = 113 correct answer c"
Answer: c
Question (physics): a work as fast as b . if b can complete a work in 20 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 6 2 / 3 days
Rationale: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 10 + 1 / 20 = 3 / 20 = > 20 / 3 = 6 2 / 3 a and b can finish the work in 6 2 / 3 days answer is e"
Answer: e
Question (general): there are 9 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 540 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 9 c 2 number of ways of selecting 2 non fiction books = 6 c 2 9 c 2 * 6 c 2 = 36 * 15 = 540 answer : c"
Answer: c
Question (physics): a train 120 m long is running with a speed of 62 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going
Options: a ) 5 sec , b ) 6 sec , c ) 7 sec , d ) 8 sec , e ) 9 sec
Rationale: "explanation : speed of the train relative to man = ( 62 - 8 ) kmph = ( 54 × 5 / 18 ) m / sec = 15 m / sec time taken by the train to cross the man = time taken by it to cover 120 m at 15 m / sec = 120 × 1 / 15 sec = 8 sec answer : option d"
Answer: d
Question (gain): a chemist mixes one liter of pure water with x liters of a 50 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3 / 7
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 50 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 50 - 15 ) / ( 15 - 0 ) = 7 / 3 1 / x = 7 / 3 x = 3 / 7 answer : e"
Answer: e
Question (physics): the cyclist going at a constant rate of 18 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 48 miles per hour . the motor - cyclist stops to wait for the cyclist 15 minutes after passing cyclist , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: for the 15 minutes the motor - cyclist continues to overtake the cyclist , she is going at 30 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 18 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 30 / 18 * 15 or 25 minutes answer is ( a )
Answer: a
Question (general): a number is doubled and 9 is added . if the resultant is trebled , it becomes 81 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 9
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 81 2 x = 18 = > x = 9 answer : e"
Answer: e
Question (general): what is difference between biggest and smallest fraction among 1 / 3 , 3 / 4 , 4 / 5 and 5 / 6
Options: a ) 2 / 5 , b ) 1 / 2 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 1 / 3 = . 33 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 1 / 3 their difference is 5 / 6 - 1 / 3 = 3 / 6 = 1 / 2 option b"
Answer: b
Question (general): in a renowned city , the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 6 persons are added ( 9 - 3 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e"
Answer: e
Question (general): 894.7 – 573.07 – 95.007 = ?
Options: a ) 226.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 894.7 - ( 573.07 + 95.007 ) = 894.7 - 668.077 = 226.623 . answer a"
Answer: a
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 1800 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 1800 x = 30 the numbers are 3 * 30 , 4 * 30 , 5 * 30 hence required h . c . f . = 30 answer is b"
Answer: b
Question (physics): john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 65 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 65 = > v = 55 ( option d ) ."
Answer: d
Question (gain): a man walking at a rate of 15 km / hr crosses a bridge in 35 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1750 m , c ) 950 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 35 minutes = 15 / 18 * 35 * 60 = 1750 m answer is b"
Answer: b
Question (geometry): the squared value of the diagonal of a rectangle is ( 64 + b 2 ) sq cm , where b is less than 8 cm . what is the breadth of that rectangle ?
Options: a ) 6 cm
b ) 10 cm
c ) 8 cm
d ) data inadequate
e ) none of these
Rationale: diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a
Answer: a