Cheukting/mathqa huggingface dataset:
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 12 , d ) 16 , e ) 16
Rationale: "t = 9 / 45 * 60 12 answer : c"
Answer: c
Question (general): one - fourth of a number is greater than one - fifth of the number succeeding it by 1 . find the number .
Options: a ) 24 , b ) 42 , c ) 36 , d ) 48 , e ) 50
Rationale: number is 24 as 1 / 4 th of 24 = 6 1 / 5 th of 25 ( 24 + 1 ) = 5 6 = 5 + 1 answer : a
Answer: a
Question (physics): working at their respective constant rates , machine a makes 100 copies in 20 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 675 , d ) 700 , e ) 600
Rationale: "machine a can produce 100 * 30 / 20 = 150 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 600 copies . e is the answer"
Answer: e
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 160 kilometers ?
Options: a ) 8 gallons , b ) 4 gallons , c ) 6 gallons , d ) 5.5 gallons , e ) 10 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 160 kilometers ? 160 / 40 = 4 * 1 gallon = 4 gallons correct answer b"
Answer: b
Question (general): a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: 25 % of 2 litres = 0.5 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.9 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 29 % answer : d
Answer: d
Question (physics): cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 6 hours , how many minutes did it take cole to drive to work ?
Options: a ) 84 , b ) 136 , c ) 172 , d ) 210 , e ) 478
Rationale: "first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 6 hrs therefore , 6 = d / 75 + d / 105 lcm of 75 and 105 = 525 6 = d / 75 + d / 105 = > 6 = 7 d / 525 + 5 d / 525 = > d = 525 / 2 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 2 x 75 ) = > t 1 = ( 7 x 60 ) / 2 - - in minutes = > t 1 = 210 minutes . d"
Answer: d
Question (general): the average of temperatures at noontime from monday to friday is 30 ; the lowest one is 20 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 10
Rationale: "average = 30 , sum of temperatures = 30 * 5 = 150 as the min temperature is 20 , max would be 150 - 4 * 20 = 30 - - > the range = 30 ( max ) - 20 ( min ) = 10 answer : e"
Answer: e
Question (gain): find the c . i . on a sum of rs . 10000 for 6 months at 20 % per annum , interest being compounded halfyearly ?
Options: a ) 3010 , b ) 2010 , c ) 1000 , d ) 3100 , e ) 2100
Rationale: "c . i . = 10000 ( 11 / 10 ) ^ 1 - 10000 = 1000 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 40 minutes ?
Options: a ) 80 , b ) 100 , c ) 160 , 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 40 minutes the population increases by 40 x 4 = 160 people . answer . c ."
Answer: c
Question (general): the average of 10 result is 42 . average of the first 7 of them is 30 and that of the last 7 is 80 . find the 8 th result ?
Options: a ) 35 , b ) 37 , c ) 70 , d ) 75 , e ) 50
Rationale: "sum of all the 10 results = 10 * 42 = 420 sum of the first 7 of them = 7 * 30 = 210 sum of the last 7 of them = 7 * 80 = 560 so , the 8 th number = 420 + 210 - 560 = 70 . c"
Answer: c
Question (general): a certain boxer has agreed to pay his opponent a fee of 3 % of his total purse for every pound over the specified weight limit he weighs in . if the boxer pays his opponent a fee of $ 26250 after weighing in 7 pounds over the specified limit , what was the boxer ' s purse ?
Options: a ) $ 65,625 , b ) $ 105,000 , c ) $ 125,000 , d ) $ 183,750 , e ) $ 1 , 050,000
Rationale: . 03 * 7 = . 21 26250 / . 21 = $ 125,000 answer : c
Answer: c
Question (geometry): what is the maximum number q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options: a ) 36
b ) 32
c ) 24
d ) 21
e ) 15
Rationale: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get q = 24 cubes . ans . c
Answer: c
Question (general): - 64 x 29 + 165 = ?
Options: a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 1601 , e ) none of them
Rationale: "given exp . = - 64 x ( 30 - 1 ) + 165 = - ( 64 x 30 ) + 64 + 165 = - 1830 + 229 = - 1601 answer is d"
Answer: d
Question (general): if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 4 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 3 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 0.5 answer a ( hopefully ) ) )"
Answer: a
Question (physics): two trains of length 100 m and 120 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 11 sec , b ) 70 sec , c ) 21 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 120 = 220 m . the time required = d / s = 220 / 20 = 11 sec . answer : a"
Answer: a
Question (physics): in an examination , a student scores 3 marks for every correct answer and loses 2 marks for every wrong answer . if he attempts all 100 questions and secures 300 marks , the number of questions he attempts correctly , is :
Options: a ) 150 , b ) 250 , c ) 400 , d ) 300 , e ) 100
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 100 â € “ x ) . 3 x â € “ 2 ( 100 â € “ x ) = 300 or 5 x = 500 or x = 100 . answer : e"
Answer: e
Question (geometry): what is the % change in the area of a rectangle when its length increases by 30 % and its width decreases by 30 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 9 % decrease , e ) insufficient data
Rationale: "( 13 / 10 ) * ( 7 / 10 ) = 91 / 100 of original area 91 / 100 is a 9 % decrease from 100 / 100 - > d"
Answer: d
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) rs . 3944
b ) rs . 3942
c ) rs . 3987
d ) rs . 3929
e ) rs . 3938
Rationale: let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 58 = rs . 3944 . answer : a
Answer: a
Question (physics): points a , b , c , and d , in that order , lie on a line . if ab = 3 cm , ac = 4 cm , and bd = 9 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 8 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 3 ( ab = 3 ) c - 4 ( ac = 4 ) d - 12 ( bd = 9 ) cd is 12 - 4 = 8 . ans b"
Answer: b
Question (physics): robert is travelling on his cycle andhas calculated to reach point a at 2 pm . if he travels at 10 kmph , he will reach there at 12 pm if he travels at 15 kmph . at what speed musthe travel to reach a at 1 pm ?
Options: a ) 8 kmph , b ) 10 kmph , c ) 12 kmph , d ) 14 kmph , e ) 16 kmph
Rationale: "let the distance travelled by x km . then , x - x = 2 10 15 3 x - 2 x = 60 x = 60 km . time taken to travel 60 km at 10 km / hr = 60 hrs = 6 hrs . 10 so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . required speed = 60 kmph . = 12 kmph . 5 c"
Answer: c
Question (general): find the value of m 32519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 325157481
Rationale: "32519 x 9999 = 32519 x ( 10000 - 1 ) = 32519 x 10000 - 32519 x 1 = 325190000 - 32519 = 325157481 e"
Answer: e
Question (physics): sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 252 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 252 per week 36 x = 252 x = 7 correct option : e"
Answer: e
Question (physics): a can run 4 times as fast as b and gives b a start of 66 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 88 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 75 m
Rationale: speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 66 m he gains 66 * ( 4 / 3 ) i . e 88 m answer : a
Answer: a
Question (general): how many multiples of 5 are there between 5 to 105 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) none of these , e ) 19
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 , 95 , 100 . answer : e"
Answer: e
Question (physics): a and b go around a circular track of length 600 m on a cycle at speeds of 30 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 360 sec , c ) 178 sec , d ) 187 sec , e ) 189 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 30 * 5 / 18 ) , 600 / ( 54 * 5 / 18 ) } = 360 sec . answer : b"
Answer: b
Question (geometry): the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one of the males and one of the females in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 72 degree
e ) e ) 204 degree
Rationale: let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 of m = 2 x and 1 of f = 3 x . . total preferring that carrer = 5 x now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 d
Answer: d
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 20 % ?
Options: a ) 228 , b ) 480 , c ) 512 , d ) 288 , e ) 276
Rationale: sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 128 sp = cp - loss = 640 - 128 = rs . 512 answer : c
Answer: c
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 9540 , what is the length of the plot in metres ?
Options: a ) 20 , b ) 200 , c ) 300 , d ) 400 , e ) 100
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 9540 [ 4 l - 40 ] = 9540 / 26.50 = 360 4 l = 400 l = 400 / 4 = 100 meters . answer : e"
Answer: e
Question (physics): what is the greatest of 3 consecutive integers whose sum is 36 ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "36 / 3 = 12 the three numbers are 11 , 12 , and 13 . the answer is b ."
Answer: b
Question (geometry): each of the 43 points is placed either inside or on the surface of a perfect sphere . if 16 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 3 , b ) 11 , c ) 13 , d ) 23 , e ) 38
Rationale: "maximum number of points on the surface is 16 % * 43 = 6.88 . . . or 6 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 6 points , so at best we can form 3 pairs ( 6 ) . so , answer is ( a )"
Answer: a
Question (physics): xavier starts from p towards q at a speed of 60 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 60 km , then how much time does he take to cover the distance ?
Options: a ) 48 , b ) 59 , c ) 60 , d ) 56 , e ) 50
Rationale: "first 12 min = 60 * 12 / 60 = 12 km 2 nd 12 min = 70 * 12 / 60 = 14 km 3 rd 12 min = 80 * 12 / 60 = 16 km 4 th 12 min = 90 * 12 / 60 = 18 km total time 12.4 = 48 min a"
Answer: a
Question (general): a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 6000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 42000 , d ) 34000 , e ) none of these
Rationale: explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 6000 = > total profit = 6000 * 7 = 42000 . answer : option c
Answer: c
Question (general): the average of 5 quantities is 11 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 21.5 , b ) 10.6 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 11 - 3 x 4 ) / 2 = 21.5"
Answer: a
Question (gain): 10 % of a number is added to 45 , the result is the same number . find the number ?
Options: a ) 50 , b ) 288 , c ) 270 , d ) 129 , e ) 281
Rationale: "( 10 / 100 ) * x + 45 = x 9 x = 450 x = 50 answer : a"
Answer: a
Question (general): if 4 x + y + z = 80 , 2 x - y - z = 4003 x + y - z = 20 for integers of x , y and z , find x = ?
Options: a ) 10 , b ) 20 , c ) 15 , d ) 26 , e ) 18
Rationale: 4 x + y + z = 80 - - - - - - - - - - 1 ) 2 x - y - z = 40 - - - - - - - - - - - - - 2 ) 3 x + y - z = 20 - - - - - - - - - - - - 3 ) from 1 ) and 2 ) 6 x = 120 x = 20 answer is b
Answer: b
Question (physics): calculate how much time could be saved if the train would run at its usual speed , given that it ran at 5 / 7 of its own speed and got to its destination in 15 hours ?
Options: a ) 1.29 hrs , b ) 2.29 hrs , c ) 4.29 hrs , d ) 5.29 hrs , e ) 3.29 hrs
Rationale: "new speed = 5 / 7 of usual speed new time = 5 / 7 of usual time 5 / 7 of usual time = 15 hrs usual time = 15 * 5 / 7 = 10.71 hrs time saved = 15 - 10.71 = 4.29 hrs answer is c"
Answer: c
Question (general): find the average of first 10 multiples of 7
Options: a ) 35.5 , b ) 37.5 , c ) 38.5 , d ) 40.5 , e ) none of these
Rationale: "explanation : = 7 ( 1 + 2 + 3 + . . . + 10 ) 10 = 7 ( 10 ( 10 + 1 ) ) 10 × 2 = 7 ( 110 ) 10 × 2 = 38.5 answer : option c"
Answer: c
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number ?
Options: a ) 36 , b ) 86 , c ) 27 , d ) 86 , e ) 27
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"
Answer: a
Question (gain): john makes $ 30 a week from his job . he earns a raise and now makes $ 40 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 33.33 %
Rationale: "increase = ( 10 / 30 ) * 100 = 33.33 % . e"
Answer: e
Question (physics): a truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes . the ratio of their speeds is ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 2 : 5 , d ) 3 : 7 , e ) 1 : 3
Rationale: ratio of speeds = ( 550 / 60 ) 18 / 5 : 60 * 33 / 45 = 33 : 44 = 3 : 4 answer is b
Answer: b
Question (gain): a particular library has 150 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 122 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 122 books , thus the number of un - returned books is 150 - 122 = 28 books . 0.35 x = 28 x = 80 the answer is c ."
Answer: c
Question (general): a batsman in his 12 th innings makes a score of 48 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 26 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 48 ∴ x = 26 answer a"
Answer: a
Question (general): the average of 1 st 3 of 4 numbers is 7 and of the last 3 are 5 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 3.5 , d ) 7 , e ) 8
Rationale: "a + b + c = 21 b + c + d = 15 a + d = 13 a – d = 6 a + d = 13 2 d = 7 d = 3.5 answer : c"
Answer: c
Question (geometry): the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 24 - inch flat - screen television than a square 17 - inch flat - screen television ?
Options: a ) 143.5 , b ) 154 , c ) 160 , d ) 148.75 , e ) 142.25
Rationale: "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 24 - inch flat - screen television the diagonal ( hypotenuse ) = 24 so , we can apply the pythagorean theorem to get x ² + x ² = 24 ² simplify : 2 x ² = 24 ² divide both sides by 2 to get : x ² = 24 ² / 2 since the area of the square = x ² , we can see that the area of this square is 24 ² / 2 square 17 - inch flat - screen television the diagonal ( hypotenuse ) = 17 so , we can apply the pythagorean theorem to get x ² + x ² = 17 ² simplify : 2 x ² = 17 ² divide both sides by 2 to get : x ² = 17 ² / 2 since the area of the square = x ² , we can see that the area of this square is 17 ² / 2 difference in areas = 24 ² / 2 - 17 ² / 2 = 288 - 144.5 i . e = 143.5 a"
Answer: a
Question (general): the average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 76.5 kg , c ) 85 kg , d ) 90 kg , e ) none
Rationale: "sol . total weight increased = ( 8 × 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer c"
Answer: c
Question (general): a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 6 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 8 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 6 / 8 * c : ( b + c ) / 2 = ( 6 / 8 ) * c b = ( 1 / 2 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 2 * c ) / 2 = ( 1 / 4 ) * c median = ( a + c ) / 2 = ( 1 / 4 * c + c ) / 2 = ( 5 / 4 ) * c / 2 = ( 5 / 8 ) * c ( answer d )"
Answer: d
Question (general): line q has the equation 5 y – 3 x = 75 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 48 , b ) 52 , c ) 56 , d ) 60 , e ) 64
Rationale: "5 y - 3 x = 75 and so y = 3 x / 5 + 15 when x = 0 , then y = 15 . when y = 0 , then x = - 25 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 25 , 0 ) , 0 = - 5 ( - 25 ) / 3 + c the y - intercept is c = - 125 / 3 < - 41 . thus the perpendicular line s can have y - intercepts from - 41 up to 14 . the number of possible lines is 41 + 14 + 1 = 56 the answer is c ."
Answer: c
Question (geometry): a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 1100 , b ) $ 1240 , c ) $ 1360 , d ) $ 1480 , e ) $ 1550
Rationale: "the total surface area is 2 ( 2 * 3 + 3 * 5 + 2 * 5 ) = 62 square feet the total cost is 62 * $ 20 = $ 1240 the answer is b ."
Answer: b
Question (physics): two concentric circles form a ring . the inner and outer circumference of the ring are 352 / 7 m and 528 / 7 m respectively . find the width of the ring .
Options: a ) 2
b ) 4
c ) 5
d ) 6
e ) 78
Rationale: explanation : let the inner and outer radii be r and r meters then , \ inline { \ color { black } 2 \ prod r } = 352 / 7 = > r = ( 352 / 7 ) * ( 7 / 22 ) * ( 1 / 2 ) = 8 m \ inline { \ color { black } 2 \ prod r } = 528 / 7 = > r = ( 528 / 7 ) * ( 7 / 22 ) * ( 1 / 2 ) = 12 m width of the ring = r - r = 12 - 8 = 4 m answer : b ) 4
Answer: b
Question (gain): a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2300
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 12 %
Rationale: "explanation : gain % = ( 264.36 * 100 / 2300 ) = 11.49 % = 12 % approx option e"
Answer: e