Cheukting/mathqa huggingface dataset:
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1500 resolutions ?
Options: a ) 2112 m , b ) 2704 m , c ) 2278 m , d ) 2288 m , e ) 2378 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1500 resolutions . = 1500 * 2 * 22 / 7 * 22.4 = 211200 cm = 2112 m answer : a"
Answer: a
Question (physics): a 300 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 200 m
Rationale: relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 300 / 9 = 500 / 9 x = 200 ans is 200 m answer : e
Answer: e
Question (gain): by selling 12 pens for a rupee a woman loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 8 , e ) 65
Rationale: "d 80 % - - - 12 120 % - - - ? 80 / 120 * 12 = 8"
Answer: d
Question (other): how many of the positive factors of 26 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 26 - 1 , 2 , 13 and 26 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 2 answer : b"
Answer: b
Question (general): find unit digit of n when n = 63 ^ 1 ! + 2 ! + . . . + 63 ! + 18 ^ 1 ! + 2 ! + . . . + 18 ! + 37 ^ 1 ! + 2 ! + . . . 37 !
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: 3,8 and 7 have a power cycle of 4 , i . e . the units digit in each case will repeat after every 4 th power . for eg : 3 ^ 1 = 3 , 3 ^ 2 = 9 , 3 ^ 3 = 27 , 3 ^ 4 = 81 , 3 ^ 5 = 243 all the powers given ( 1 ! + 2 ! + . . . . ) , are multiples of 4 . it is so because the last 2 digits of the total sum will be 00 , for each one of them , which make them divisible by 4 . thus , the given problem boils down to 3 ^ 4 + 8 ^ 4 + 7 ^ 4 = 1 + 6 + 1 = 8 thus , the units digit is 8 . answer : d
Answer: d
Question (probability): 6 students are equally divided into 3 groups , then , the 3 groups were assigned to 3 different topics . how many different arrangements w are possible ?
Options: a ) 30 , b ) 60 , c ) 90 , d ) 180 , e ) 540
Rationale: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks . but now you can order the 3 tasks in 3 ! ways . t 1 t 2 t 3 or t 2 t 1 t 3 . . . . etc etc . i was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements w including the order of tasks . could you explain the highlighted step . . . i ' m getting 90 = 15 * 3 ! suppose the students are numbered 12 , 34 , 56 and tasks are x , y and z one of the 15 possible ways of forming teams is 12 , 34 , 56 . these teams can be assigned to 3 tasks in 3 ! = 6 ways x - - y - - z 12 - - 34 - - 56 12 - - 56 - - 34 34 - - 12 - - 56 34 - - 56 - - 12 56 - - 12 - - 34 56 - - 34 - - 12 so the answer should be 15 * 6 = 90 but now you can fruther decide which task you want to perform first x y or z . . = c
Answer: c
Question (general): find the value of ( √ 1.5 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 3.075
Rationale: "( √ 1.5 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) = > 3.075 answer is e ."
Answer: e
Question (general): a completes a piece of work in 3 / 4 of the time in b does , b takes 4 / 5 of the time in c does . they got a profit of rs . 40000 how much b gets ?
Options: a ) 12765 , b ) 121227 , c ) 26887 , d ) 19977 , e ) 26992
Rationale: assume c takes 20 days . now b takes 4 / 5 ( 20 ) = 16 days . a takes 3 / 4 ( 16 ) = 12 now their efficiencies ratio = 1 / 20 : 1 / 16 : 1 / 12 = 12 : 15 : 20 b ' s share in the profit of rs . 40000 = 15 / 47 ( 40000 ) = rs . 12765 answer : a
Answer: a
Question (physics): the sum of two consecutive number is 87 . which is the larger number ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 87 2 x + 1 = 87 2 x = 86 x = 43 therefore larger number is x + 1 = 44 answer : c"
Answer: c
Question (geometry): right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x and y coordinates of p , q and r are to be integers that satisfy the inequalitites - 4 ≤ x ≤ 5 and 6 ≤ y ≤ 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100
Rationale: total values for x = 10 ; y = 11 x 1 , y 1 = 10 * 11 . . . . . . . . . . . . . . . . . . . . . . . coordinates of 1 st pnt x 2 , y 2 = 9 * 1 ( y 2 = y 1 ) . . . . . . . . . . . . . . . coordinates of 2 nd pnt y coordinates will be same as that of 1 st pnt bcoz it is parallel to x axis x 3 , y 3 = 1 * 10 ( x 2 = x 3 ) . . . . . . . . . . coordinates of 3 rd pt . x coordinates will be same as that of 2 nd point bcoz to make a right angle it has to be parallel to y axis tot ways = 10 * 11 * 9 * 1 * 1 * 10 = 9900 ans : c
Answer: c
Question (general): when a student joe , weighing 40 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 40 + 30 = 70 so , the average the two persons = 35 that gives the answer 40 - 35 = 5 answer a"
Answer: a
Question (general): a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 33 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 50 , c ) c . 48 , d ) d . 69 , e ) e . 44
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 33 seconds . thus x = 3 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 69 seconds . answer d"
Answer: d
Question (general): john bought a total of 20 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 20 mangoes and oranges that john originally purchased was 69 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let number of mangoes be x , number of oranges be 12 - x 0.80 x + ( 20 - x ) 0.60 / 20 = 0.69 solving for x , we get x = 9 - - > mangoes 9 , oranges 11 now , number of oranges to be returned be y 0.80 * 9 + ( 11 - y ) * 0.60 / 20 - y = 0.72 solving for y , y = 5 ans : b"
Answer: b
Question (physics): a goods train runs at a speed of 72 kmph and crosses a 240 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 280 m
Rationale: "s = 240 + x / t 72 * 5 / 18 = 240 + x / 26 x = 280 answer : e"
Answer: e
Question (other): a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 15 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 4 , d ) 7 / 10 , e ) 9 / 10
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 15 - 2 cmb = 100 b - cb - mb - 2 cmb = 25 hence the probability = 25 / 100 = 1 / 4 . c"
Answer: c
Question (gain): when the price of an article was reduced by 40 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 8 % increase , b ) 4 % decrease , c ) 6 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 40 % , the new price is 0.6 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.6 p ) ( 1.8 n ) = 1.08 np , which is 1.08 times the old revenue , so is 8 % greater . answer : a"
Answer: a
Question (general): how many integers from 101 to 900 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 8 = 8 9 is not possible here because it would result in a number greater than 9 ( i . e 909 , 919 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 8 * 10 = 80 answer is d ."
Answer: d
Question (general): what is the units digit of 2222 ^ ( 333 ) * 4444 ^ ( 222 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 10
Rationale: "each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 4444 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 8 . final answer : e"
Answer: e
Question (general): the ratio of petrol and kerosene in the container is 3 : 2 when 10 liters of the mixture is taken out and is replaced by the kerosene , the ratio become 2 : 3 . then total quantity of the mixture in the container is :
Options: a ) 33 , b ) 30 , c ) 38 , d ) 37 , e ) 27
Rationale: explanation : pool : kerosene 3 : 2 ( initially ) 2 : 3 ( after replacement ) \ frac { remaining \ : ( or \ : left ) \ : quantity } { initial \ : quantity } = \ left ( 1 - \ frac { replaced \ : quantity } { total \ : quantity } \ right ) ( for petrol ) \ frac { 2 } { 3 } = \ left ( 1 - \ frac { 10 } { k } \ right ) \ rightarrow \ frac { 1 } { 3 } = \ frac { 10 } { k } \ rightarrow k = 30 l therefore the total quantity of the mixture in the container is 30 liters . answer : b ) 30
Answer: b
Question (geometry): abcd is a square . e , f , g , h is the midpoint of the sides of square . j and k is the midpoint of the sides hg and fg . l is a point on sides ef such that lf = 1 / 3 ef . find the ratio of area of triangle jkl to the area of square abcd .
Options: a ) 5 : 46
b ) 5 : 44
c ) 4 : 48
d ) 5 : 48
e ) 5 : 4
Rationale: ratio = 5 : 48 answer : d
Answer: d
Question (general): what is the greatest 6 - digit number when divided by 6 , 7 , 8 , 9 , and 10 leaves a remainder of 3 , 4 , 5 , 6 and 7 respectively ?
Options: a ) 456780 , b ) 678910 , c ) 997479 , d ) 997917 , e ) 997920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 7 when we divide by 10 , so d is the only possible answer .
Answer: d
Question (general): a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent q should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked will be q = 25 % greater than the original number . the answer is c ."
Answer: c
Question (general): if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } is used exactly once , in how many ways can the digits be arranged ?
Options: a ) 4830 , b ) 5040 , c ) 5250 , d ) 5460 , e ) 5680
Rationale: "7 ! = 5040 the answer is b ."
Answer: b
Question (geometry): if the sum of a number and its square is 20 , what is the number ?
Options: a ) 15 , b ) 26 , c ) 28 , d ) 4 , e ) none of these
Rationale: "let the number be x . then , x + x 2 = 20 ( x + 5 ) ( x - 4 ) = 0 x = 4 answer : d"
Answer: d
Question (general): roy is now 8 years older than julia and half of that amount older than kelly . if in 4 years , roy will be twice as old as julia , then in 4 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 172 , b ) 180 , c ) 192 , d ) 200 , e ) 216
Rationale: "r = j + 8 = k + 4 r + 4 = 2 ( j + 4 ) ( j + 8 ) + 4 = 2 j + 8 j = 4 r = 12 k = 8 in 4 years ( r + 4 ) ( k + 4 ) = 16 * 12 = 192 the answer is c ."
Answer: c
Question (gain): an investor deposited $ 5,000 to open a new savings account that earned 4 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 5050.50 , b ) $ 5100.50 , c ) $ 5200.50 , d ) $ 5300.50 , e ) $ 5400.50
Rationale: the amount in the account after 6 months is 1.01 * 1.01 ( $ 5,000 ) = $ 5100.50 the answer is b .
Answer: b
Question (other): in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 48 people were made to stand in a column , how many columns could be formed ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 16 * 30 = 48 * n n = 10 the answer is a .
Answer: a
Question (physics): 18 buckets of water fill a tank when the capacity of each bucket is 60 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 5 litres ?
Options: a ) 216 , b ) 200 , c ) 212 , d ) 220 , e ) 210
Rationale: "capacity of the tank = ( 18 ã — 60 ) litre number of buckets required of capacity of each bucket is 17 litre = 18 ã — 60 / 5 = 18 ã — 12 = 216 answer is a"
Answer: a
Question (general): a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 50 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 55 , b ) 60 , c ) 75 , d ) 80 , e ) 90
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 100 + ( d / 2 ) / v d / 150 = d / 2 v and so v = 75 km / hr the answer is c ."
Answer: c
Question (physics): james took a 3 - hour bike ride . in the second hour he traveled 36 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 111.0 , d ) 157.0 , e ) 163.0
Rationale: "let the distance travelled in the first hour be x . thus , 1.2 x = 36 , x = 30 . now , the distance travelled in the 3 rd hour = 36 + 1 / 4 â ˆ — 36 = 45 . 36 + 30 + 45 = 111 answer : c"
Answer: c
Question (physics): a large tanker can be filled by two pipes a and b in 30 and 15 hours respectively . how many hours will it take to fill the tanker from empty state if a and b fill it together ?
Options: a ) 8 hr , b ) 10 hr , c ) 12 hr , d ) 9 hr , e ) 5 hr
Rationale: part filled by a in 1 hr = 1 / 30 part filled by b in 1 hr = 1 / 15 part filled by a + b = 1 / 30 + 1 / 15 = 1 / 10 both the pipes can fill the tank in = 10 hours answer is b
Answer: b
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 440 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 64 , d ) 88 , e ) 92
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 440 breadth = 22 feet area to be fenced = 2 b + l = 2 ( 22 ) + 20 = 64 feet answer : c"
Answer: c
Question (geometry): the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 3600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) 280
Rationale: "given that the area of the square = 3600 sq . units = > side of square = √ 3600 = 60 units the radius of the circle = side of the square = 60 units length of the rectangle = 2 / 5 * 60 = 24 units given that breadth = 10 units area of the rectangle = lb = 24 * 10 = 240 sq . units answer : option a"
Answer: a
Question (geometry): a certain rectangular window is four times as long as it is wide . if its perimeter is 50 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2 , b ) 11 by 3 , c ) 20 by 5 , d ) 10 by 4 , e ) 9 by 3
Rationale: "2 x + 2 y = 50 x + y = 25 x + 4 x = 25 5 x = 25 x = 5 answer c"
Answer: c
Question (general): if l is the least positive integer that is divisible by every integer from 1 to 9 inclusive , then l / 2 is =
Options: a ) 5040 , b ) 2520 , c ) 1890 , d ) 1260 , e ) 630
Rationale: the integer should be divisible by : 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 , that is 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 and 3 ^ 2 . the least common multiple of these integers is the product of 7 , 5 , 3 ^ 2 and 2 ^ 3 . then , l / 2 is ( 7 * 5 * 3 ^ 2 * 2 ^ 3 ) / 2 = 7 * 5 * 9 * 4 = 1260 . answer : d .
Answer: d
Question (gain): rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 82 . how much was lent at 5 % ?
Options: a ) 899 , b ) 866 , c ) 878 , d ) 800 , e ) 877
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 82 5 x / 100 + 90 – 6 x / 100 = 82 x / 100 = 8 = > x = 800 answer : d"
Answer: d
Question (physics): an athlete runs 200 metres race in 24 seconds . what is his speed ?
Options: a ) 20 km / hr , b ) 30 km / hr , c ) 25 km / hr , d ) 35 km / hr , e ) 40 km / hr
Rationale: speed = dist / time = 200 / 24 200 / 24 * 18 / 5 = 40 * 3 / 4 = 30 km / hr answer b
Answer: b
Question (general): if the average ( arithmetic mean ) of a and b is 115 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) − 90 , d ) 135 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 115 = = = > a + b = 230 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 230 - 320 = = = > a + b - b - c = - 90 = = = > a - c = - 90 answer : c"
Answer: c
Question (geometry): in a certain parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle ?
Options: a ) 65 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 50 ) = 180 - - > x = 65 . answer : a ."
Answer: a
Question (gain): jim is able to sell a hand - carved statue for $ 550 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 407.41 , b ) $ 412.40 , c ) $ 455.40 , d ) $ 474.90 , e ) $ 488.20
Rationale: "550 = 1.35 * x x = 550 / 1.35 = 407.407407 . . . which rounds to $ 407.41 , which is ( a ) ."
Answer: a
Question (physics): pipe b that can fill a tank in an hour and pipe a that can fill the tank in half an hour are opened simultaneously when the tank is empty . pipe a is shut 15 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 32 mins , b ) 35 mins , c ) 40 mins , d ) 30 mins , e ) 36 mins
Rationale: the last 15 minutes only pipe b was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : d
Answer: d
Question (physics): working together , tim and tom can type 12 pages in one hour . if they would be able to type 15 pages in one hour if tom increases his typing speed by 30 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 1 / 5 , b ) 5 / 1 , c ) 4 / 1 , d ) 1 / 4 , e ) 1 / 3
Rationale: lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 12 tom increase speed by 30 % means he will type 1.3 y pages an hour . so we get x + 1.3 y = 15 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 : 0.3 y = 3 so y = 10 . . . so x = 2 ( y / x ) = 10 / 2 = 5 / 1 answer is ( b )
Answer: b
Question (gain): the interest on a certain deposit at 5 % per annum is rs . 101.20 in one year . how much will the additional interest in one year be on the same deposit at 6 % per annum ?
Options: a ) rs . 20.8 , b ) rs . 19.74 , c ) rs . 20.24 , d ) rs . 19.5 , e ) rs . 19.00
Rationale: explanation : principal , p = 100 × si / rt = 100 × 101.20 / 5 × 1 = 20 × 101.20 = rs . 2024 simple interest for rs . 2024 at 6 % per annum for 1 year , si = 2024 × 6 × 1100 = 121.44 additional interest = rs . 121.44 - rs . 101.20 = rs . 20.24 answer : option c
Answer: c
Question (gain): in an election , candidate a got 65 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 309400 , c ) 347000 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 65 % therefore , the number of valid votes polled in favour of candidate a = 65 % of 476000 = 65 / 100 × 476000 = 30940000 / 100 = 309400 b )"
Answer: b
Question (gain): the profit obtained by selling an article for rs . 86 is the same as the loss obtained by selling it for rs . 42 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) rs . 64
Rationale: "s . p 1 - c . p = c . p – s . p 2 86 - c . p = c . p - 42 2 c . p = 86 + 42 ; c . p = 128 / 2 = 64 answer : e"
Answer: e