Cheukting/mathqa huggingface dataset:
Question (geometry): the ratio of male to female in a class is 2 : 7 . 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 third of the males and two - third of the females in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 192 degree
e ) e ) 213 degree
Rationale: here is my approach = > males = > 2 x and females = 7 x = > total = 9 x now 9 x = > 360 therefore 16 x / 3 = > 213 degree . p . s = > 16 x / 3 is nothing but total number of students with the given preference answer e
Answer: e
Question (gain): seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 28 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "28 % is 3 % - points above 25 % and 12 % - points below 40 % . thus the ratio of mixture y to mixture x is 4 : 1 . the percent of mixture x is 1 / 5 = 20 % . the answer is b ."
Answer: b
Question (geometry): which is the smallest number divides 2800 and gives a perfect square .
Options: a ) 5
b ) 6
c ) 7
d ) 8
e ) 9
Rationale: 7 is the smallest number which divides 2800 and gives a perfect square . as 2800 = 2 * 2 * 2 * 2 * 5 * 5 * 7 and 7 is not in a pair which gives 400 ( a perfect square of 20 ) on dividing 2800 . answer : c
Answer: c
Question (physics): if a light flashes every 6 seconds , how many times will it flash in 1 / 5 of an hour ?
Options: a ) 81 , b ) 101 , c ) 121 , d ) 141 , e ) 161
Rationale: "in 1 / 5 of an hour there are 12 * 60 = 720 seconds the number of 6 - second intervals = 720 / 6 = 120 after the first flash , there will be 120 more flashes for a total of 121 . the answer is c ."
Answer: c
Question (general): in how many ways can the integer 800 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 7 , c ) 5 , d ) 4 , e ) 2
Rationale: "800 = ( 2 ^ 5 ) * ( 5 ^ 2 ) since 800 is not a perfect square , no of ways = 7 answer b"
Answer: b
Question (gain): from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 15 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 103.5 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 20 % = 90 * 1.15 = 103.5 thus ratio = 103.5 / 100 = 1.03 ( in % terms = 103 % ) . thus b is the correct answer ."
Answer: b
Question (geometry): d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 144 : 25 and de = 13 cm , then find the length of bc .
Options: a ) 5
b ) 13
c ) 14
d ) 11
e ) 15
Rationale: abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 25 / 169 side of abc / side of ade = 5 / 13 so the length of bc = 5 answer - a
Answer: a
Question (gain): at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 15 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 28 , c ) 50 , d ) 68 , e ) 70
Rationale: the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 15 are males , so remaining 90 - 15 = 75 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 75 , 100 % = 75 * 100 / 60 = 125 . . ans 40 % of 125 = 50 c
Answer: c
Question (geometry): a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 34 inches and the width of the wall is 54 inches , what is the length of the wall , in inches ?
Options: a ) 22.8 , b ) 33.8 , c ) 42.8 , d ) 63.8 , e ) 56.8
Rationale: "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 34 ^ 2 = 1156 . area of rectangle is double of that 2 * 1156 = 2312 . now a = lw and we need find w so a / l = w ; 2312 / 54 = 42.8 answer ! answer is c"
Answer: c
Question (general): how many positive integers less than 100 have a remainder of 11 when divided by 13 ?
Options: a ) 11 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have to include 11 also . as 13 * 0 + 11 = 11 if somebody says to divide 11 by 13 , we will be telling we have 0 quotient and remainder as 11 . answer is a"
Answer: a
Question (gain): last year elaine spent 20 % of her annual earnings on rent . this year she earned 25 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 182.5 , b ) 184.5 , c ) 167.5 , d ) 172.5 , e ) 187.5
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 25 % more , or $ 125 . she would ' ve spent 30 % of this on rent , or $ 37.5 do $ 37.5 / $ 20 this will give you 187.5 % e is the correct answer ."
Answer: e
Question (general): how much time does a train 150 metres long running at 90 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 6 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s
Rationale: "explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 150 / t t = 6 s answer : b"
Answer: b
Question (other): a dog takes 4 leaps for every 5 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 12 : 5 , b ) 4 : 3 , c ) 9 : 5 , d ) 9 : 1 , e ) 9 : 2
Rationale: "explanation : dog : hare = ( 4 * 3 ) leaps of hare : 5 leaps of hare = 12 : 5 . answer : a ) 12 : 5"
Answer: a
Question (gain): if an article is sold at 19 % profit instead of 12 % profit , then the profit would be rs . 105 more . what is the cost price ?
Options: a ) 1890 , b ) 2790 , c ) 1990 , d ) 1500 , e ) 1701
Rationale: "let the cost price of an article be rs . x . ( 19 % of x ) - ( 12 % of x ) = 105 19 x / 100 - 12 x / 100 = 105 = > 7 x = 105 * 100 = > x = 1500 cost price = rs . 1500 answer : c"
Answer: c
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 130 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 260 , b ) 620 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 130 ) = 2 + 2 ( extra ) = > 2 x - 260 = x = > x = 260 . answer : a"
Answer: a
Question (physics): an intern wants to label folders with numbers using digit stickers only . if the intern uses 999 stickers , how many folders have been numbered ? ( the numbers of the folders are consecutive and the number of the first folder is 1 ) .
Options: a ) 287 , b ) 369 , c ) 370 , d ) 371 , e ) 430
Rationale: for the first 9 folders we need 9 stickers . for the next 90 we need 2 stickers each or 180 stickers . for the next 900 folders we need 3 stickers each . the first 99 folders correspond to 189 stickers . subtract 189 from the total number of stickers ( 999 ) . this leaves 810 stickers for folders that use 3 stickers each . so , divide 810 by 3 to get 270 folders . add 99 folders to 270 folders to get the total number of folders , 369 . answer : b
Answer: b
Question (gain): each month a retailer sells 100 identical items . on each item he makes a profit of $ 50 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 50 sell price = $ 500 + $ 50 thus , the sell price is $ 550 for each item . selling all 100 items gives the retailer . . . 100 ( $ 50 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 550 ) = $ 27.5 discount $ 522.5 = $ 500 + $ 22.5 now , the retailer makes a profit of just $ 22.5 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 22.5 ( x ) = $ 2,000 x = 2,000 / 22.5 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Question (geometry): the perimeter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 23.57 , b ) 25.54 , c ) 26.5 , d ) 26.55 , e ) 26.71
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 20 + 14 ) = 68 cm perimeter of the square = 68 cm i . e . 4 a = 68 a = 17 diameter of the semicircle = 17 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 17 ) = 1 / 2 ( 22 / 7 ) ( 17 ) = 26.71 cm to two decimal places answer : e"
Answer: e
Question (general): working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 12 , and 8 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 5 / 2 , b ) 7 / 4 , c ) 8 / 5 , d ) 10 / 3 , e ) 12 / 5
Rationale: the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 12 + 1 / 8 = 5 / 24 the time it takes y and z is 24 / 5 the ratio of times is 16 / ( 24 / 5 ) = 5 * 16 / 24 = 10 / 3 the answer is d .
Answer: d
Question (physics): a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is
Options: a ) 3.496 kg , b ) 3.696 kg , c ) 3.690 kg , d ) 9.696 kg , e ) 3.296 kg
Rationale: explanation : external radius = 4 cm , internal radius = 3 cm . volume of iron = = weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg answer : b ) 3.696 kg
Answer: b
Question (geometry): in may , the grounds keeper at spring lake golf club built a circular green with an area of 49 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 80 , e ) 90
Rationale: "area of circle 49 pi sq feet = pi r ^ 2 therefore r = 7 now green radi doubled i . e r = 14 area = 196 pi c"
Answer: c
Question (gain): j is 25 % less than p and 20 % less than t . t is r % less than p . what is the value of r ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( r / 100 ) ] * p i . e . 100 - r = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . r = 6.25 answer : option d"
Answer: d
Question (general): if k is the greatest positive integer such that 3 ^ k is a divisor of 21 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "21 / 3 = 7 21 / 9 = 2.33 = 2 7 + 2 = 9 k = 9 answer : e"
Answer: e
Question (gain): a chemist mixes one liter of pure water with x liters of a 30 % salt solution , and the resulting mixture is a 20 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 2
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 30 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 30 - 20 ) / ( 20 - 0 ) = 1 / 2 1 / x = 1 / 2 x = 2 answer : e"
Answer: e
Question (gain): in an examination 35 % of the students passed and 546 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 650 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 546 65 x / 100 = 546 x = 546 * 100 / 65 = 840 answer is e"
Answer: e
Question (general): what is the unit digit in 15 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: unit digit in 15 ^ 100 = unit digit in [ ( 15 ^ 4 ) ^ 25 ] but unit digit in 15 ^ 4 = 5 unit digit 15 ^ 100 = 5 answer is e
Answer: e
Question (physics): a person walks from one end to the other of a 90 - meter long moving walkway at a constant rate in 30 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 30 ( v + x ) = 90 then 120 ( v + x ) = 360 120 ( v - x ) = 90 when we add the two equations : 240 v = 450 v = 15 / 8 time = 90 / ( 15 / 8 ) = 48 seconds the answer is c ."
Answer: c
Question (other): right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 34 years . what is molly ' s age right now ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "now , sandy is 34 - 6 = 28 molly ' s age is ( 3 / 4 ) * 28 = 21 the answer is d ."
Answer: d
Question (physics): a 420 meter long train crosses a platform in 60 seconds while it crosses a signal pole in 30 seconds . what is the length of the platform ?
Options: a ) 120 , b ) 840 , c ) 350 , d ) 420 , e ) 210
Rationale: "speed = [ 420 / 30 ] m / sec = 14 m / sec . let the length of the platform be x meters . then , x + 420 / 60 = 14 x + 420 = 840 è x = 420 m . answer : d"
Answer: d
Question (general): a , b and c rents a pasture for rs . 435 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?
Options: a ) 180 , b ) 227 , c ) 268 , d ) 198 , e ) 176
Rationale: 12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 435 = 180 answer : a
Answer: a
Question (gain): a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 15000 . a ' s share is ?
Options: a ) 2999 , b ) 2778 , c ) 6000 , d ) 5000 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 15000 = 5000 answer : d"
Answer: d
Question (general): a car traveled 80 % of the way from town x to town y at an average speed of 80 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 20
Rationale: assume total distance = 100 miles time taken for 80 miles = 80 / 80 = 1 hour time taken for the rest of the 20 miles = 20 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 20 / v hence v = 20 mph answer : e
Answer: e
Question (general): a guy was asked to specify his age in years . he said , “ take my age 8 years hence , multiply it by 8 and subtract 8 times of my age 8 years ago and get the half of the result and you will know my age . ” what was the age of that guy ?
Options: a ) 18 , b ) 55 , c ) 63 , d ) 64 , e ) 70
Rationale: current age of the guy = a years . then , 8 ( a + 8 ) – 8 ( a – 8 ) = a ( 8 a + 64 ) – ( 8 a – 64 ) = a a = 128 / 2 = 64 d
Answer: d
Question (general): there are 12 students in a class . on the day the test was given , ella was absent . the other 11 students took the test and their average was 74 . the next day , ella took the test , and with this grade included , the new average was 75 . what was ella ' s grade on the test ?
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: 11 * 74 + ella ' s grade = 12 * 75 ella ' s grade is 12 * 75 - 11 * 74 = 86 . the answer is e .
Answer: e
Question (gain): at what price must an book costing $ 47.50 be marked in order that after deducting 20 % 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 ) 64.2 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 80 / 100 ) = 59.375 mp = 74.2"
Answer: c
Question (geometry): three fifth of the square of a certain number is 126.15 . what is the number ?
Options: a ) 210.25
b ) 75.69
c ) 14.5
d ) 145
e ) 150
Rationale: let the number be x given , 3 / 5 x ^ 2 = 126.5 x ^ 2 = 126.15 * 5 / 3 x ^ 2 = 42.05 * 5 = 210.25 x = 14.5 answer c .
Answer: c
Question (physics): one woman and one man can build a wall together in one hour , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them two hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 7 , b ) 6 / 7 , c ) 10 / 7 , d ) 12 / 7 , e ) 22 / 7
Rationale: solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 1 - - > ( 1 ) , w + 2 g = 1 / 1 - - > ( 2 ) and m + g = 1 / 2 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 6 , m = 1 / 3 and w = 2 / 3 . so , n = 1 / ( 7 / 6 ) = 6 / 7 option , b
Answer: b
Question (geometry): in a certain circle there are 10 points . what is the number of the triangles connecting 4 points of the 10 points ?
Options: a ) 80 , b ) 96 , c ) 108 , d ) 120 , e ) 210
Rationale: "imo : e here we have to select 4 points out of 10 points . order is not important so the answer will be 10 c 4 = 210"
Answer: e
Question (physics): two trains of length 400 m and 200 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 36 kmph . after how much time will the trains meet ?
Options: a ) 8 sec , b ) 20 / 7 sec , c ) 33 / 7 sec , d ) 21 / 7 sec , e ) 32 / 7 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 36 ) * 5 / 18 = 25 mps . the time required = d / s = 200 / 25 = 8 sec . answer : a"
Answer: a
Question (geometry): the diagonals of two squares are in the ratio of 3 : 7 then find the ratio of its areas ?
Options: a ) 7 : 37 , b ) 6 : 46 , c ) 9 : 49 , d ) 8 : 68 , e ) 6 : 61
Rationale: "let the diagonals of the squares be 3 x and 7 x ratio of their areas = 1 / 2 ( 3 x ) ^ 2 : 1 / 2 ( 7 x ) ^ 2 = 9 x ^ 2 : 49 x ^ 2 = 9 : 49 answer is c"
Answer: c
Question (general): the average marks of a class of 30 students is 40 and that of another class of 50 students is 90 . find the average marks of all the students ?
Options: a ) 71.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 90 = 4500 sum of the marks for the class of 80 students = 1200 + 4500 = 5700 average marks of all the students = 5700 / 80 = 71.25 answer : a"
Answer: a
Question (general): in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 8 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 900 , c ) 1500 , d ) 1600 , e ) 1750
Rationale: "sugar : flour = 3 : 8 = 15 : 40 ; flour : soda = 10 : 1 = 40 : 4 ; thus we have that sugar : flour : soda = 15 x : 40 x : 4 x . also given that 40 x / ( 4 x + 60 ) = 8 / 1 - - > x = 60 - - > sugar = 15 x = 900 . answer : b ."
Answer: b
Question (general): jacob is 18 years old . he is 2 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 36 , b ) 38 , c ) 33 , d ) 32 , e ) 38
Rationale: j = 18 ; j = 2 b ; b = 18 / 2 = 9 ; twice as old so b = 9 ( now ) + ( 9 ) = 18 ; jacob is 18 + 18 = 36 answer : a
Answer: a
Question (general): 3897 x 999 = ?
Options: a ) 3883203 , b ) 3893103 , c ) 3639403 , d ) 3791203 , e ) none of them
Rationale: "= 3897 x 999 = 3897 x ( 1000 - 1 ) = 3897 x 1000 - 3897 x 1 = 3897000 - 3897 = 3893103 answer is b"
Answer: b
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 600 . what is the manager ' s monthly salary ?
Options: a ) rs . 16003 , b ) rs . 16029 , c ) rs . 11288 , d ) rs . 14100 , e ) rs . 16011
Rationale: "explanation : manager ' s monthly salary rs . ( 2100 * 21 - 1500 * 20 ) = rs . 14100 . answer : d"
Answer: d
Question (physics): noelle walks from point a to point b at an average speed of 5 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 8 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 7.25 , d ) 7.5 , e ) 20
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 8 = 2 * 5 * x / 5 + x x = 20 e is the answer"
Answer: e
Question (gain): a man buy a book in rs 50 & sale it rs 90 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 80 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: cp = 50 sp = 90 profit = 90 - 50 = 40 % = 40 / 50 * 100 = 80 % answer : b
Answer: b
Question (physics): in what time will a train 250 metres long cross an electric pole , if its speed be 162 km / hr ?
Options: a ) 4 sec , b ) 5 sec , c ) 5.55 sec , d ) 6.55 sec , e ) 4.55 sec
Rationale: "solution speed = ( 162 x 5 / 18 ) m / sec = 45 m / sec time taken = ( 250 / 45 ) sec = 5.55 sec . answer c"
Answer: c
Question (physics): an ant is climbing 30 meters tall pole . it climbs 3 meter during the day and slips down 2 meters down during night in sleep , how many days it takes to reach the top of the pole ?
Options: a ) a - 30 , b ) b - 29 , c ) c - 28 , d ) d - 27 , e ) e - 26
Rationale: ants overall distance covered is 3 - 2 = 1 meter per day . in 27 days it will climb 27 meters . on 28 th day it will reach the top of the pole . answer : c
Answer: c