Cheukting/mathqa huggingface dataset:
Question (physics): kim can do a work in 3 days while david can do the same work in 2 days . both of them finish the work together and get rs . 150 . what is the share of kim ?
Options: a ) 77 , b ) 60 , c ) 99 , d ) 26 , e ) 21
Rationale: kim ' s wages : david ' s wages = kim ' s 1 day work : david ' s 1 day work = 1 / 3 : 1 / 2 = 2 : 3 kim ' s share = 2 / 5 * 150 = rs . 60 answer : b
Answer: b
Question (gain): at what price must an article costing rs . 51.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 60.5 , b ) 69.5 , c ) 67.5 , d ) 67.7 , e ) 22.5
Rationale: "cp = 51.50 sp = 51.50 * ( 125 / 100 ) = 64.375 mp * ( 95 / 100 ) = 64.375 mp = 67.7 answer : d"
Answer: d
Question (general): 4,7 , 11,18 , 29,47 , . . . ? . . , 123,199
Options: a ) 84 , b ) 102 , c ) 76 , d ) 70 , e ) none of the above
Rationale: "the addition of difference between each no . is equal to latter no . so , difference between 47 and 76 is 29 which is previous no . of 47 answer c"
Answer: c
Question (physics): there are two cars . one is 60 miles north of the other . simultaneously , the car to the north is driven westward at 15 miles per hour and the other car is driven eastward at 25 miles per hour . how many miles apart are the cars after 2 hours ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: "here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 60 and a height of 80 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 60 lines up with the ' 3 ' and the 80 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 20 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 60 / 80 / 100 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : c"
Answer: c
Question (other): the diluted wine contains only 8 liters of wine and the rest is water . a new mixture whose concentration is 30 % , is to be formed by replacing wine . how many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : wine water 8 l 32 l 1 : 4 20 % 80 % ( original ratio ) 30 % 70 % ( required ratio ) in ths case , the percentage of water being reduced when the mixture is being replaced with wine . so the ratio of left quantity to the initial quantity is 7 : 8 therefore , \ frac { 7 } { 8 } = \ left [ 1 - \ frac { k } { 40 } \ right ] \ rightarrow \ frac { 7 } { 8 } = \ left [ \ frac { 40 - k } { 40 } \ right ] \ rightarrow k = 5 l answer : b ) 5
Answer: b
Question (geometry): the length of the side of a square is represented by x + 2 . the length of the side of an equilateral triangle is 2 x . if the square and the equilateral triangle have equal perimeter , then the value of x is ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 8 , e ) 6
Rationale: since the side of the square is x + 2 , its perimeter = 4 ( x + 2 ) = 4 x + 8 since the side of the equilateral triangle is 2 x , its perimeter = 3 * 2 x = 6 x also , the perimeters of both are equal . ( i . e . ) 4 x + 8 = 6 x ( i . e . ) 2 x = 8 è x = 4 . answer : c
Answer: c
Question (gain): the cost price of 8 articles is equal to the selling price of 5 articles . what is the profit percent ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "5 * sp = 8 * cp sp = 1.6 * cp the profit percent is 60 % . the answer is d ."
Answer: d
Question (general): a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 20 , e ) 28
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 2 = 2 ( x + 2 ) x + 32 = 2 x + 4 = > x = 28 . answer : e"
Answer: e
Question (other): in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 2 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 7 ) = 5 / 2 answer : b"
Answer: b
Question (general): q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 20 , what is the greatest possible value of q minus r ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 20 . the greatest multiple of 9 which is less than 20 is 18 . the answer is d ."
Answer: d
Question (physics): a 600 meter long train crosses a signal post in 50 seconds . how long will it take to cross a 3 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 5 min
Rationale: "s = 600 / 50 = 12 mps s = 3600 / 12 = 300 sec = 5 min answer : e"
Answer: e
Question (physics): a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 24 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 6 - 1 / x = 1 / 8 , solving 1 / x = 1 / 24 so in 24 hours full cistern will be empty . answer : a"
Answer: a
Question (general): a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is - 8 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 , d ) 4 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = - 8 i . e x ^ 2 + 4 x + 8 = 0 is the quadratic equation which needs to be solved . no solution imo e"
Answer: e
Question (general): if the sum of two positive integers is 20 and the difference of their squares is 40 , what is the product of the two integers ?
Options: a ) 108 , b ) 99 , c ) 128 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 20 - - 1 x ^ 2 - y ^ 2 = 40 = > ( x + y ) ( x - y ) = 40 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 11 y = 9 product = 11 * 9 = 99 answer b"
Answer: b
Question (physics): 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 20 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 4 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 20 women ’ s 1 day ’ s work = 1 / 192 × 20 = 5 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 10 men + 20 women + 10 children ) ’ s 1 day ’ s work = 5 / 48 + 5 / 48 + 1 / 24 = 1 / 4 the required no . of days = 4 days answer : option d"
Answer: d
Question (general): what is the remainder when 3 ^ 86 is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 0 , e ) 3
Rationale: "3 ^ 0 = 1 3 ^ 1 = 3 3 ^ 2 = 9 3 ^ 3 = 27 3 ^ 4 = . . . 1 3 ^ 5 = . . . . 3 3 ^ 6 = . . . . . . 9 and so on . 86 / 4 = 21 ( with a remainder 2 ) so the last number is a 9 . so when 3 ^ 86 is divided by 5 the remainder is 4 , ans = c"
Answer: c
Question (other): if the ratio of two number is 2 : 5 and lcm of the number is 160 then what is the number .
Options: a ) 15 , b ) 20 , c ) 16 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 2 x * 5 x = 160 * x x = 16 answer : c"
Answer: c
Question (physics): the moon revolves around the earth at a speed of approximately 1.03 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,708 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.03 * 3600 = 3708 kilometers per hour . option d is correct"
Answer: d
Question (general): the average marks obtained by 100 candidates in an examination is 50 . find how many candidates have passed in the examination , if the average marks of candidates who passed is 70 and that of failed candidates is 20 .
Options: a ) 33 , b ) 77 , c ) 60 , d ) 29 , e ) 11
Rationale: explanation : let the number of students who passed the examination be x number of students failed = ( 100 - x ) total marks of students who have passed = 70 x total marks of 100 students = 100 * 50 = 5000 total marks of students who have failed = 20 ( 100 – x ) 20 ( 100 – x ) + 70 x = 5000 2000 – 20 x + 70 x = 5000 50 x = 3000 x = 60 answer : c
Answer: c
Question (general): set v consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set v , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: v = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 016 , - 59 } y > 21 so l = median of v = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c
Answer: c
Question (general): in 1982 and 1983 , company b ’ s operating expenses were $ 11.0 million and $ 14.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 16 2 / 3 % , c ) 25 % , d ) 4 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 11 = 4.6 million $ profit in 1983 = 18.8 - 14 = 4.8 million $ percentage increase in profit = ( 4.8 - 4.6 ) / 4.6 * 100 % = 4 1 / 3 % answer d"
Answer: d
Question (general): how many integers between 1 and 1,800 are divisible by 20 , 30,40 ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "lcm of the given numbers = 120 therefore , number of integers = 1800 / 120 = 15 option b is answer"
Answer: b
Question (gain): a sum of rs . 2704 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1672 , b ) 1664 , c ) 1677 , d ) 1698 , e ) 1679
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2704 - x ) * 3 * 5 ) / 100 24 x / 100 = 40560 / 100 - 15 x / 100 39 x = 40560 = > x = 1040 second sum = 2704 â € “ 1040 = 1664 answer : b"
Answer: b
Question (gain): 150 is increased by 40 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 180 , d ) 190 , e ) 220
Rationale: "final number = initial number + 40 % ( original number ) = 150 + 40 % ( 150 ) = 150 + 60 = 210 . answer b"
Answer: b
Question (gain): a person ' s salary is getting reduced by 20 % . what percentage should be added to get back his original salary ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 85 % , e ) 95 %
Rationale: salary he get after reduced 20 % = 100 - 20 % = 80 % so , percentage should be added to get back his salary = ( 20 / 80 ) * 100 = 25 % answer : a
Answer: a
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 18 white marbles . how many red marbles could be in bag a ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 18 = 6 k + 4 p = > k = 1 , p = 3 total red ' s in bag a will be 2 k = 2 a"
Answer: a
Question (general): the price of lunch for 10 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.8 , d ) 14 , e ) 18
Rationale: clearly e is the answer i used poe here lets consider option ( e ) 10 * 18 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo e
Answer: e
Question (general): in an office , totally there are 1800 employees and 60 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 756 , b ) 750 , c ) 600 , d ) 760 , e ) none of these
Rationale: "number of male employees = 1800 * 60 / 100 = 1080 required number of male employees who are less than 50 years old = 1080 * ( 100 - 30 ) % = 1080 * 70 / 100 = 756 . answer : a"
Answer: a
Question (physics): if 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 2300 , b ) 600 , c ) 250 , d ) 300 , e ) none of these
Rationale: "1 st line - 0 points 2 nd line - new 1 point 3 td line - new 2 points + old 1 point 4 th line - new 3 points + old 2 + 1 points 5 th line - new 4 points + old 3 + 2 + 1 points n - th line - ( n - 1 ) points + ( n - 2 ) . . . . 3 + 2 + 1 therefore , s = 1 + 2 + 3 . . . ( n - 1 ) s = ( n - 1 ) n / 2 = 24 * 25 / 2 = 300 ans ; d"
Answer: d
Question (general): in a renowned city , the average birth rate is 5 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 ) 85,400 , b ) 86,400 , c ) 87,400 , d ) 88,400 , e ) 89,400
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 5 - 3 = 2 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 2 = 86,400 . hence b ."
Answer: b
Question (gain): population is 21000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 27951 , c ) 36621 , d ) 26621 , e ) 26821
Rationale: "population after 1 st year = 21000 * 10 / 100 = 2100 = = = > 21000 + 2100 = 23100 population after 2 nd year = 23100 * 10 / 100 = 2310 = = = > 23100 + 2310 = 25410 population after 3 rd year = 254100 * 10 / 100 = 2541 = = = > 25410 + 2541 = 27951 answer : b"
Answer: b
Question (physics): a , b , c hired a car for rs . 720 and used it for 9 , 10 and 13 hours respectively . hire charges paid by b are :
Options: a ) rs 220 , b ) rs . 225 , c ) rs . 230 , d ) rs . 235 , e ) rs . 255
Rationale: "a : b : c = 9 : 10 : 13 . hire charges paid by b = rs . 720 * 10 / 32 = rs . 225 . answer : b"
Answer: b
Question (gain): at what price must an book costing $ 47.50 be marked in order that after deducting 12 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 67.5 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 88 / 100 ) = 59.375 mp = 67.5 c"
Answer: c
Question (general): the average of 45 results is 13 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 695
Rationale: "23 th result = sum of 45 results - sum of 44 results 13 * 45 - 15 * 22 + 20 * 22 = 585 - 330 + 440 = 695 answer is e"
Answer: e
Question (other): if log 1087.5 = 5.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 70 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 5.9421 + 1 ) = 10 ( 6.9421 ) = 69.421 x = antilog ( 69.421 ) therefore , number of digits in x = 70 . answer : b"
Answer: b
Question (gain): a japanese rock band made ¥ 3 million on their first album with sales of ¥ 12 million , and made ¥ 5 million on their second album with sales of ¥ 30 million . by approximately what percent did the ratio of profit to sales decrease from the first album to second album ?
Options: a ) 24 % , b ) 27 % , c ) 30 % , d ) 33 % , e ) 36 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first album , and the second ratio will be for the next album . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first album profit / sales = 3 / 12 = 1 / 4 second album profit / sales = 5 / 30 = 1 / 6 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 12 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first album profit / sales = ( 1 / 4 ) x 12 = 3 next 2 million profit / sales = ( 1 / 6 ) x 12 = 2 we can plug 3 and 2 into our percent change formula : ( 2 – 3 ) / 3 x 100 = - 1 / 3 x 100 so approximately a 33 % decrease . answer d .
Answer: d
Question (gain): an inspector rejects 0.05 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 4000
Rationale: "let the number of meters to be examined be x then , 0.05 % of x = 2 ( 5 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 4000 answer is e"
Answer: e
Question (general): a number is doubled and 9 is added . if resultant is trebled , it becomes 69 . what is that number
Options: a ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 69 = > 2 x + 9 = 23 = > x = 7 answer : option a"
Answer: a
Question (physics): a motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance . what is the time taken by boat in still water ?
Options: a ) 26 h , b ) 16 h , c ) 86 h , d ) 96 h , e ) 66 h
Rationale: explanation : if t 1 and t 2 are the upstream and down stream times . then time taken in still water is given by \ inline \ frac { 2 \ times t 1 \ times t 2 } { t 1 + t 2 } = \ frac { 2 \ times 12 \ times 24 } { 36 } = 16 h answer : b
Answer: b
Question (general): if x is a positive integer , then the least value of x for which x ! is divisible by 100000 is ? can someone please explain intuitively what the question is asking ?
Options: a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30
Rationale: in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d .
Answer: d
Question (general): a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 30 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 1080 , b ) $ 1180 , c ) $ 1280 , d ) $ 1380 , e ) $ 1480
Rationale: a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 30 a = 30 + b ( 1 ) = = = > c = 90 + 3 b - b = 2 b + 90 = = > 2 b - c = - 90 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 30 = 2.5 b - 30 = = > 2.5 b - c = 30 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 120 b = $ 240 a = $ 270 c = 810 - 240 = $ 570 total amount = 270 + 240 + 570 = $ 1080 answer : a
Answer: a
Question (other): if 0.25 of a number is equal to 0.05 of another number , the ratio of the numbers is :
Options: a ) 2 : 5 , b ) 3 : 4 , c ) 1 : 5 , d ) 20 : 5 , e ) 30 : 7
Rationale: "0.25 a = 0.05 b - > a / b = 0.05 / 0.25 = 5 / 25 = 1 / 5 : . a : b = 1 : 5 answer : c"
Answer: c
Question (gain): what is the compound interest on rs : 50,000 for 4 months at the rate of 5 % per annum
Options: a ) 1058.24 , b ) 2006.24 , c ) 838.55 , d ) 848.55 , e ) 858.55
Rationale: "it is monthly compound rate = 5 / 12 % per month 50000 * ( 1 + 5 / 1200 ) ^ 4 - 50000 = 838.55 answer : c"
Answer: c
Question (geometry): if k and w are the dimensions of a rectangle that has area 20 and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two
b ) three
c ) four
d ) five
e ) six
Rationale: kw = 20 = 20 * 1 = 10 * 2 = 5 * 4 - - > k can take 3 values , answer : b
Answer: b
Question (geometry): danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 648 , what is the area of the side face of the box ?
Options: a ) 32
b ) 78
c ) 84
d ) 90
e ) 72
Rationale: lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 648 l * 1.5 l * 2 l = 648 l = 6 side face area = l * d = l * 2 l = 6 * 2 * 6 = 72 e is the answer
Answer: e
Question (physics): the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 30 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 492 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 30 + 32 + 34 + . . . . . upto 12 terms ) this is an a . p with first term , a = 30 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 30 + { 12 - 1 ) x 2 ] = 6 ( 82 ) = 492 kms . answer : c"
Answer: c
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 54 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 16.7 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 54 * 5 / 18 = 15 mps t = 250 / 15 = 16.7 sec answer : c"
Answer: c
Question (general): if x and g are integers and 2 x – g = 11 , then 4 x + g can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - g = 11 . . . . g = 2 x - 11 4 x + g = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Question (general): a fair 8 - sided dice labeled 1 to 8 is tossed 3 times . what is the probability the value of the dice shown is 3 at least once ?
Options: a ) 57 / 512 , b ) 7 / 512 , c ) 55 / 512 , d ) 9 / 512 , e ) 11 / 512
Rationale: this is a fair dice with 8 fair sides , so the probability of the dice landing on any sides is equal . the question ask if the value of the dice is shown 3 at least once so the calculation of the first possible outcomes is 1 / 8 * 1 / 8 * 1 / 8 ( all of the dice thrown shown the value of 3 ) this is follow by the second possible outcomes if the dice thrown show the value of 3 2 times ( 1 / 8 * 1 / 8 * 7 / 8 ) * 7 here referring to any number besides 3 the third possible outcomes is that the dice show the value 3 one time ( 1 / 8 * 7 / 8 * 7 / 8 ) so the answer is 1 / 512 + 7 / 512 + 49 / 512 = 57 / 512 answer : a
Answer: a
Question (physics): in what time will a train 100 m long cross an electric pole , it its speed be 216 km / hr ?
Options: a ) 2.5 sec , b ) 2.9 sec , c ) 1.7 sec , d ) 7.5 sec , e ) 2.4 sec
Rationale: "speed = 215 * 5 / 18 = 60 m / sec time taken = 100 / 60 = 1.7 sec . answer : c"
Answer: c