Cheukting/mathqa huggingface dataset:
Question (gain): working together at their respective constant rates , machine a and machine b can produce 900 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 900 unit total would it produce ?
Options: a ) 30 , b ) 33 , c ) 50 , d ) 67 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 900 units in 24 hrs , so it can produce 900 * 8 / 24 = 300 units is 8 hrs . 300 is 30 % of 900 . a is the answer"
Answer: a
Question (general): sum of the squares of 3 no . ' s is 138 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 * 131 a + b + c = √ 400 = 20 a
Answer: a
Question (physics): a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 10 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 6 pm . the correct answer is d ."
Answer: d
Question (general): if x and y are positive integers and 11 + x + y + xy = 25 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choices . for a : 11 + 3 + xy = 25 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 11 + 5 + xy = 25 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 11 + 6 + xy = 25 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 11 + 8 + xy = 25 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 11 + 9 + xy = 25 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Question (physics): a 6000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 36
Rationale: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 3,000 by that net inflow to get the minutes ) - 36 min . answer e ."
Answer: e
Question (general): rs . 1040 is divided amongst a , b , c so that 2 times a ' s share , 3 times b ' s share and 4 times c ' s share are all equal . find a ' s share ?
Options: a ) 177 , b ) 150 , c ) 817 , d ) 480 , e ) 616
Rationale: a + b + c = 1040 2 a = 3 b = 4 c = x a : b : c = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 6 / 13 * 1040 = rs . 480 answer : d
Answer: d
Question (general): salesperson a ' s compensation for any week is $ 300 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 12,000 , d ) $ 8000 , e ) $ 4000
Rationale: "300 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 240 x = $ 12,000 the answer is c ."
Answer: c
Question (general): if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 6 is subtracted and divided by 8 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 5 , e ) 3
Rationale: explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 6 ) / 8 = ( 54 - 6 ) / 8 = 6 answer : option b
Answer: b
Question (general): ( x + 5 ) is a factor in x ^ 2 - mx - 40 . what is the value of m ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 3 , e ) 5
Rationale: "i solved the second degree equation and found it like this : x ^ 2 - mx - 40 = 0 ( x - 8 ) ( x + 5 ) = 0 x = 8 or x = - 5 substituting both values for x in the equation we find : x ^ 2 - mx - 40 = > ( - 5 ) ^ 2 - m ( - 5 ) = 40 = > 25 + 5 m = 40 = > 5 m = 40 - 25 = 15 = > m = 3 and with 8 , using a similar process we end up with : ( 8 ) ^ 2 - m ( 8 ) = 40 - 8 m = 40 - 64 = - 24 m = 3 ao , ans d"
Answer: d
Question (geometry): in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 4 , - 3 ) , ( 4 , 7 ) , ( 10 , 4 ) , ( 10 , - 7 ) ?
Options: a ) 51 , b ) 54 , c ) 57 , d ) 60 , e ) 63
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 10 + 11 ) × 6 = 63 . the answer is e ."
Answer: e
Question (general): a sum is divided among b , c and d in such a way that for each rupee b gets , c gets 150 paisa and d gets 50 paisa . if the share of c is rs . 40 , what is the total amount ?
Options: a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: b : c : d = 100 : 150 : 100 20 : 30 : 10 30 - - - 40 60 - - - ? = > 80 answer : c
Answer: c
Question (general): find the average marks of all the students in 2 separate classes , if the average marks of students in the first class of 58 students is 67 and that of another class of 52 students is 82 .
Options: a ) 74.1 , b ) 56.3 , c ) 67.8 , d ) 79.7 , e ) 19.4
Rationale: "sum of the marks for the class of 58 students = 58 * 67 = 3886 sum of the marks for the class of 52 students = 52 * 82 = 4264 sum of the marks for the class of 110 students = 3886 + 4262 = 8150 average marks of all the students = 4200 / 80 = 74.1 answer : a"
Answer: a
Question (geometry): four horses are tethered at four corners of a square plot of side 63 metres so that they just can not reach one another . the area left ungrazed is :
Options: a ) 675.5 m 2
b ) 780.6 m 2
c ) 785.8 m 2
d ) 850.5 m 2
e ) 950.5 m 2
Rationale: required area = ( 63 * 63 – 4 * 1 / 4 * 22 / 7 * 63 / 2 * 63 / 2 ) = 850.5 m 2 answer : d
Answer: d
Question (general): mixture contains alcohol and water in the ratio 4 : 3 . if 7 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 5 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 28 x = 4 ( 3 x + 5 ) 16 x = 20 x = 1.25 quantity of alcohol = ( 4 x 1.25 ) litres = 5 litres . answer : c"
Answer: c
Question (general): find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ?
Options: a ) 13 / 89 , b ) 15 / 87 , c ) 27 / 89 , d ) 27 / 87 , e ) 89 / 27
Rationale: "1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 c )"
Answer: c
Question (physics): 18 men can complete a piece of work in 20 days . in how many days can 15 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 20 , d ) 24 , e ) 11
Rationale: "18 * 20 = 15 * x = > x = 24 days answer : d"
Answer: d
Question (gain): the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 9000 , brokerage being 1 / 4 % , is :
Options: a ) 113.2 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 9000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 9000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 125 . = market value of rs . 100 stock = rs . 125 - re . 0.25 . = market value of rs . 100 stock = rs . 124.75 . answer : e"
Answer: e
Question (other): a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 3 , b ) 3 : 10 , c ) 2 : 3 , d ) 6 : 3 , e ) 10 : 3
Rationale: "explanation : dog : hare = ( 2 * 5 ) leaps of hare : 3 leaps of hare = 10 : 3 answer : e"
Answer: e
Question (general): if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 55 , how much more remains to be paid ?
Options: a ) $ 455 , b ) $ 495 , c ) $ 525 , d ) $ 550 , e ) $ 585
Rationale: "90 % remains to be paid so the remaining amount is 9 * 55 = $ 495 . the answer is b ."
Answer: b
Question (general): if two times of the daughter ’ s age in years is included to the mother ’ s age , the total is 70 and if two times of the mother ’ s age is included to the daughter ’ s age , the total is 95 . so the mother ’ s age is ,
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 39
Rationale: b 40 let daughter ’ s age = a and mother ’ s age = b given : 2 a + b = 70 and , a + 2 b = 95 solving b , we will get b = 40 .
Answer: b
Question (general): an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many r ways can the assembly line be arranged ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720
Rationale: c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want r = 6 c ! / 2 - > 720 / 2 = 360
Answer: c
Question (gain): a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 140 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 8 : 7 , b ) 7 : 5 , c ) 1 : 3 , d ) 8 : 7 , e ) 9 : 10
Rationale: "explanation : 3 : 4 a = 3 / 7 * 140 = 60 360 : 400 39 : 40 answer : e"
Answer: e
Question (gain): the difference between the compound interest and simple interest on a certain sum at 10 % per annum for 2 years is $ 631 . find the sum ?
Options: a ) $ 52000 , b ) $ 61000 , c ) $ 71540 , d ) $ 63100 , e ) $ 56210
Rationale: let the sum be $ x c . i . = x ( 1 + 10 / 100 ) ^ 2 - x = 21 x / 100 s . i . = ( x * 10 * 2 ) / 100 = x / 5 c . i . - s . i . = ( 21 x / 100 ) - ( x / 5 ) = x / 100 x / 100 = 631 x = 63100 answer is d
Answer: d
Question (general): what is the smallest number which when diminished by 16 , is divisible 4 , 6 , 8 and 10 ?
Options: a ) 136 , b ) 192 , c ) 198 , d ) 122 , e ) 142
Rationale: required number = ( lcm of 4 , 6,8 , and 10 ) + 16 = 120 + 16 = 136 option a
Answer: a
Question (general): in a room with 10 people , 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 5 , d ) 5 / 7 , e ) 16 / 21
Rationale: ( 6 / 10 ) ( 7 / 9 ) + ( 5 / 10 ) ( 6 / 9 ) if you choose one of the 6 with one other friend , then you have a 7 / 9 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 9 chance of not picking one of their friends second . add them up . 42 / 90 + 30 / 90 72 / 90 = 4 / 5 c . 4 / 5
Answer: c
Question (general): there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 79 . how tall is the fourth person ?
Options: a ) 85 , b ) 87 , c ) 89 , d ) 91 , e ) 93
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 79 ) = 316 x = 75 and the fourth person has a height of 75 + 10 = 85 inches the answer is a ."
Answer: a
Question (physics): a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 17 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 5 : 34 pm . the correct answer is b .
Answer: b
Question (other): if both 5 ^ 3 and 3 ^ 4 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ^ 2 ) , what is the smallest possible positive value of n ?
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) has two appearances of 3 ( in 12 ^ 2 ) and two appearances of 5 ( in 10 ^ 2 ) . thus n must include at least 3 ^ 2 * 5 = 45 the answer is b ."
Answer: b
Question (gain): the profit earned by selling an article for 812 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 945 , e ) none of these
Rationale: "let the profit or loss be x and 812 – x = 448 + x or , x = 364 ⁄ 2 = 182 \ cost price of the article = 812 – x = 448 + x = 630 \ sp of the article = 630 × 150 ⁄ 100 = 945 answer d"
Answer: d
Question (gain): if w is 40 percent less than e , e is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 e , e = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Question (physics): what is the angle between the minute hand and the hour hand when the time is 1540 hours ?
Options: a ) 150 , b ) 160 , c ) 140 , d ) 130 , e ) none
Rationale: solution : the total angle made by the minute hand during an hour is 360 o . if it takes 360 o for an hour , it will take ( 40 / 60 ) * 360 = 240 o . the angle between the hour hand the minute hand will therefore , be somewhere between 240 - 90 = 150 o , as the hour hand is between 3 and 4 . the angle made by the hour hand when it moves from say 3 to 4 will be 30 o . that is the hour hand makes 30 o during the course of an hour . the hour hand will therefore , move ( 40 / 60 ) * 30 = 20 o . therefore , the net angle between the hour hand and the minute hand will be 150 - 20 = 130 o . answer d
Answer: d
Question (general): what is the sum of the multiples of 3 from 33 to 60 , inclusive ?
Options: a ) 465 , b ) 470 , c ) 452 , d ) 450 , e ) 460
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 60 / 3 ) - ( 33 / 3 ) + 1 multiply these together so what we show average * total numbers = sum ( 33 + 60 ) / 2 * ( 60 / 3 ) - ( 33 / 3 ) + 1 = sum 93 / 2 * 10 = 465 a"
Answer: a
Question (general): 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 15 , 25 and 30 , what is the minimum possible range in scores of the 3 test - takers ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 15 , e ) 10
Rationale: i simply looked at the 3 different possible scores for each individual test : 15 , 30,25 we have to find the minimum range : 30 - 15 = 15 30 - 25 = 5 25 - 15 = 10 the find the minimum range , you have to make the set of the 5 scores as small as possible . which means that 4 of the 5 scores of each individual person is zero . 5 * 5 = 25 . answer : a
Answer: a
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 250 m , c ) 643 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 270 / 26 = 20 x + 270 = 520 x = 250 . answer : b"
Answer: b
Question (general): rebecca ' s annual income is $ 15000 and jimmy ' s annual income is $ 18000 . by how much must rebecca ' s annual income increase so that it constitutes 50 % of rebecca and jimmy ' s combined income ?
Options: a ) 7000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: total rebecca = x + 15000 ; total = x + 15000 + 18000 x + 15000 / x + 33000 = 50 / 100 therefore x = 3000 e
Answer: e
Question (geometry): a cubic object 3 ' ' x 3 ' ' x 3 ' ' is painted blue on all the outside surfaces , including the top and bottom . if the cube is cut into 27 cubes of 1 ' ' x 1 ' ' x 1 ' ' , how many 1 ' ' cubes do have any painted surfaces ?
Options: a ) 15
b ) 22
c ) 26
d ) 33
e ) 44
Rationale: c 26 only the box in the very centre of the stack will not suffer the strokes of the paint brush , whereas all the other 26 boxes will have at least one side painted .
Answer: c
Question (general): the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of charlie 10 years from now ?
Options: a ) 17 , b ) 25 , c ) 45 , d ) 47 , e ) 50
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of charlie = 7 * 5 = 35 charlie ' s age 10 years hence = 35 + 10 = 45 answer = c"
Answer: c
Question (other): how many of the positive factors of 17 are not factors of 34 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 17 - 1 , 17 factors of 34 - 1 , 2 , 17 , 34 , comparing both , we have three factors of 17 which are not factors of 34 - no factors the answer is a"
Answer: a
Question (geometry): rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 5 / 3
b ) 9 / 5
c ) 9 / 25
d ) 3 / 5
e ) 25 / 9
Rationale: the area of rectangle a is ab . c = 5 a / 3 and d = 5 b / 3 . the area of rectangle b is cd = 25 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 9 ) = 9 / 25 . the answer is c .
Answer: c
Question (physics): j is faster than p . j and p each walk 24 km . sum of the speeds of j and p is 7 kmph . sum of time taken by them is 14 hours . then j speed is equal to
Options: a ) 22 , b ) 14 , c ) 6 , d ) 8 , e ) 16
Rationale: given j > p j + p = 7 , only options are ( 6 , 1 ) , ( 5 , 2 ) , ( 4 , 3 ) from the given options , if j = 4 the p = 3 . times taken by them = 244 + 243 = 14 answer : b
Answer: b
Question (general): 2 ^ 8 × 39 + 31 = ?
Options: a ) 34545 , b ) 65657 , c ) 65567 , d ) 45677 , e ) 56782
Rationale: "256 * 39 + 31 65567 c"
Answer: c
Question (physics): a river 5 m deep and 35 m wide is flowing at the rate of 2 kmph , calculate the amount of water that runs into the sea per minute ?
Options: a ) 5832.75 , b ) 5839.75 , c ) 5837.75 , d ) 5222.75 , e ) 5835.75
Rationale: "rate of water flow - 2 kmph - - 2000 / 60 - - 33.33 m / min depth of river - - 5 m width of river - - 35 m vol of water per min - - 33.33 * 5 * 35 - - - 5832.75 answer a"
Answer: a
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 15 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 11.7 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is a . this question is in the og and thus well explained by ets . those who exceed : x so x = 10 % + 0,15 x id est x = 11,7 %"
Answer: a
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 23 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 288 , b ) 195 , c ) 881 , d ) 1277 , e ) 121
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 23 = 345 m . let the length of the platform be x m . then , ( x + 345 ) / 36 = 15 = > x = 195 m . answer : b"
Answer: b
Question (geometry): the area of a square field is 4802 m ( power ) 2 the length of its diagonal is :
Options: a ) 98 m
b ) 102 m
c ) 95 m
d ) 105 m
e ) 96 m
Rationale: let the diagonal be d metres , then 1 / 2 d ( power ) 2 = 4802 d 2 = 9604 d = √ 9604 d = 98 m answer is a .
Answer: a