Cheukting/mathqa huggingface dataset:
Question (general): the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length q of a cube whose surface area is equal to 6 z ?
Options: a ) q = 16 , b ) q = 8 √ 2 , c ) q = 8 , d ) q = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Question (general): find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 10 of money ?
Options: a ) 1500 , b ) 1992 , c ) 9921 , d ) 1000 , e ) 2789
Rationale: "p = 10 ( 100 / 10 ) 2 = > p = 1000 answer : d"
Answer: d
Question (general): 5 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.1388 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 5 / 36 = . 1388 answer ( b )"
Answer: b
Question (general): a room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 144 , c ) 175 , d ) 165 , e ) 130
Rationale: "let us calculate both the length and width of the room in centimeters . length = 7 meters and 68 centimeters = 768 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 768 and 432 = 48 thus , the number of square tiles required = ( 768 x 432 ) / ( 48 x 48 ) = 16 x 9 = 144 answer : b"
Answer: b
Question (physics): there is enough provisions for 600 men in an army camp for 25 days . if there were 300 men less , how long will the provision last ?
Options: a ) 35 days , b ) 40 days , c ) 45 days , d ) 50 days , e ) 55 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 300 * d 2 d 2 = 600 * 25 / 300 = 50 days . answer : d"
Answer: d
Question (physics): two cars start from the opposite places of a main road , 140 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 55 , e ) 21
Rationale: answer : d ) 55 km
Answer: d
Question (general): 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = ?
Options: a ) 5 / 3 , b ) 4 / 3 , c ) 2 / 3 , d ) 1 / 3 , e ) 1 / 5
Rationale: explanation : 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ 1 } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 } ] = 1 ÷ [ 1 + 1 ÷ 2 ] = 1 ÷ [ 1 + ( 1 / 2 ) ] = 1 ÷ 3 / 2 = 1 × 3 / 2 = 1 × 2 / 3 = 2 / 3 answer : option c
Answer: c
Question (general): in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 15 and 150 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 12 , d ) 4 and 14 , e ) 5 and 14
Rationale: given : 15 < x ( x + 1 ) < 170 . now , it ' s better to test the answer choices here rather than to solve : if x = 4 then x ( x + 1 ) = 20 > 15 - - > so , the least value is 4 . test for the largest value : if x = 12 then x ( x + 1 ) = 12 * 13 = 156 > 150 answer : c .
Answer: c
Question (gain): john had a stock of 1000 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 59.8 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1000 - n = 1000 - 402 = 598 percentage books not sold / total number of books = 598 / 1000 = 59.8 = 59.8 % correct answer a"
Answer: a
Question (general): a line that passes through ( – 1 , – 4 ) and ( 2 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 2 + 1 ) = > 3 k = k + 4 = > k = 2 ans d it is !"
Answer: d
Question (general): p , q and r have $ 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 2403 , c ) 3200 , d ) 2539 , e ) 1930
Rationale: "c 3200 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 ."
Answer: c
Question (general): a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes bil can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Question (general): of the 3,600 employees of company x , 16 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 57 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 16 / 25 are clerical out of 3600 so 2304 are clerical 2304 reduced by 1 / 4 is 2304 * 1 / 4 so it reduced 576 people , so there is 1728 clerical people left but since 576 people left , it also reduced from the total of 3600 so there are 3024 people total since 1728 clerical left / 3024 people total you get ( a ) 57 %"
Answer: a
Question (general): the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
Options: a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) none
Rationale: "solution let the numbers be x and x ( x + 1365 ) . then , x + 1365 = 6 x + 15 ‹ = › 5 x = 1350 . ‹ = › x = 270 . answer d"
Answer: d
Question (general): the sum of present age of abe and the age before 7 years is 33 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 33 2 x - 7 = 33 2 x = 33 + 7 x = 40 / 2 x = 20 z = x + 7 = 20 + 7 = 27 answer : c"
Answer: c
Question (general): if 100 < x < 199 and 9 < y < 100 , then the product xy can not be equal to :
Options: a ) 19,104 , b ) 19,303 , c ) 19 , 956.732 , d ) 19,502 , e ) 19,809
Rationale: "correct answer : ( c ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 100 * 9 . the largest value must be less than 199 * 100 . this means that 900 < xy < 19,900 . ( c ) is outside of this range , so it is not a possible product of xy ."
Answer: c
Question (general): positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 9 . what is the value of x ?
Options: a ) 20 , b ) 60 , c ) 100 , d ) 120 , e ) 150
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 9 ( y / 100 ) * x = 9 ( x / 400 ) * x = 9 x ^ 2 = 9 * 400 x = 60 the answer is b ."
Answer: b
Question (physics): a train running at a speed of 60 kmph crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 120 m , b ) 300 m , c ) 190 m , d ) 150 m , e ) 160 m
Rationale: 60 kmph = 50 / 3 m / sec 50 / 3 * 18 = 300 m answer : b
Answer: b
Question (other): a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number w of people surveyed by the company ?
Options: a ) 46 , b ) 80 , c ) w . 90 , d ) w . 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Question (general): when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )"
Answer: a
Question (general): the average earning of a person for the first 4 days of a week is rs 18 and for the last 4 days is rs 22 . if he earns rs 20 on the fourth day , his average earning for the whole week is ?
Options: a ) rs 18.95 , b ) rs 16 , c ) rs 20 , d ) rs 25.71 , e ) none of these
Rationale: total earning for the week = rs ( 4 × 18 + 4 × 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c
Answer: c
Question (physics): mary can do a piece of work in 12 days . rosy is 50 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 11 , e ) 10
Rationale: ratio of times taken by mary and rosy = 150 : 100 = 3 : 2 suppose rosy takes x days to do the work . 3 : 2 : : 12 : x = > x = 8 days . hence , rosy takes 8 days to complete the work . answer : b
Answer: b
Question (general): the largest 3 digit number exactly divisible by 88 is ?
Options: a ) a ) 9944 , b ) b ) 9954 , c ) c ) 9967 , d ) d ) 9969 , e ) e ) 9970
Rationale: "largest 4 - digit number = 999 88 ) 999 ( 113 88 - - - - 119 88 - - - - 319 264 - - - 55 - - - required number = ( 999 - 55 ) = 9944 . a )"
Answer: a
Question (geometry): points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 812 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a
Answer: a
Question (physics): a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 174 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 10
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 174 - $ 120 = $ 54 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 54 / $ 6 = 9 ans is c"
Answer: c
Question (gain): the price of rice falls by 25 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 26.67 kg , d ) 30 kg , e ) none
Rationale: solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 25 % of 100 ) = 75 new price of rice = 75 / 20 = rs . 3.75 per kg . rice can bought now at = 100 / 3.75 = 26.67 kg . answer : option c
Answer: c
Question (general): in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50000 a year , and engineers make an average of $ 80000 . what is the average salary for managers if the average for all employees is also $ 80000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 370,000 , e ) $ 320,000
Rationale: for sake of ease , let ' s say there are 10 employees : 7 marketers , 1 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 50,000 ) and the engineers ( $ 80,000 ) > > > $ 800,000 - $ 350,000 - $ 80,000 = $ 370,000 . the correct answer is d .
Answer: d
Question (general): john purchased 1370 large bottles at $ 1.99 per bottle and 690 small bottles at $ 1.50 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.83
Rationale: "( 1370 * 1.99 + 690 * 1.50 ) / ( 1370 + 690 ) = ~ 1.83 - option ( e )"
Answer: e
Question (other): find the ratio in which rice at rs . 7.30 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 3 : 5 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 100 = 3 : 5 answer : c"
Answer: c
Question (physics): 3 different containers contain 50 litres , 100 litres and 150 litres of mixture of milk and water respectively . what is the biggest measure can measure all the different quantities exactly ?
Options: a ) 120 litres , b ) 57 litres , c ) 60 litres , d ) 50 litres , e ) 100 litres
Rationale: m 1 = 50 litres m 2 = 100 litres m 3 = 150 litres required measurement = h . c . f . of m 1 , m 2 , m 3 = 50 litres answer is d
Answer: d
Question (general): 2034 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 2982 , d ) 2981 , e ) 1984
Rationale: 2034 - 50 = 1984 answer : e
Answer: e
Question (probability): x , y , and z are all unique numbers . if x is chosen randomly from the set { 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 8 , d ) 3 / 10 , e ) 1 / 10
Rationale: p ( x is prime ) = 1 / 2 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 2 * 1 / 4 = 1 / 8 the answer is c .
Answer: c
Question (geometry): marty ' s pizza shop guarantees that their pizzas all have at least 75 % of the surface area covered with toppings , with a crust of uniform width surrounding them . if you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust ?
Options: a ) 0.8 inches
b ) 1.1 inches
c ) 1.6 inches
d ) 2.0 inches
e ) 2.5 inches
Rationale: total area = 8 * 8 * pi radius = 64 pi surface = . 75 * 64 * pi = 48 pi radius of surface = 4 sqrt ( 3 ) ~ 6.8 radius width = 8 - 6.8 = 1.2 answer : b
Answer: b
Question (general): compute all real solutions to 16 x + 4 x + 1 - 96 = 0
Options: a ) 3 / 2 , b ) 3 / 3 , c ) 2 / 4 , d ) 4 / 4 , e ) 4 / 5
Rationale: if we substitute y = 4 x , we have y 2 + 4 y - 96 = 0 , so y = - 4 or y = 8 . the first does not map to a real solution , while the second maps to x = 3 / 2 correct answer a
Answer: a
Question (general): virginia , adrienne , and dennis have taught history for a combined total of 87 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 38 , d ) 41 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 87 = > 3 d = 87 + 27 = 114 = > d = 38 answer c"
Answer: c
Question (physics): the edges of a cuboid are 4 cm , 5 cm and 7 cm . find the volume of the cuboid ?
Options: a ) 140 , b ) 278 , c ) 378 , d ) 368 , e ) 367
Rationale: "4 * 5 * 7 = 120 answer : a"
Answer: a
Question (other): what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 20 nor by 35 ?
Options: a ) 567 , b ) 850 , c ) 560 , d ) 923 , e ) 240
Rationale: "in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 20 * 35 i . e . 700 = 1000 / 700 = 1 number of integers from 1 to 1000 that are divisible by neither 20 nor by 35 = 1000 - ( 50 + 28 - 1 ) { using the concept of sets here ) = 923 answer is d"
Answer: d
Question (gain): the population of a town is 10000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 6400 , b ) 4500 , c ) 5120 , d ) 5230 , e ) 5366
Rationale: "10000 × 80 / 100 × 80 / 100 = 6400 answer : a"
Answer: a
Question (geometry): in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 4 , 1 ) , ( 1 , 1 ) , ( 1 , - 3 ) and ( - 4 , - 3 ) ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 25 , e ) 30
Rationale: "length of side 1 = 4 + 1 = 5 length of side 2 = 3 + 1 = 4 area of rectangle = 5 * 4 = 20 b is the answer"
Answer: b
Question (other): each person in a group of 110 investors has investments in either equities or securities or both . exactly 25 of the investors in equities have investments in securities , and exactly 40 of the investors in securities have investments in equities . how many have investments in equities ?
Options: a ) 65 , b ) 80 , c ) 120 , d ) 180 , e ) 190
Rationale: explanation : the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let x , y , and z denote the number of people in the respective categories . since the total number of investors is 110 , we have : - = > x + y + z = 110 - - - - - - - - - - - - - ( 1 ) . also , the number of people with investments in equities is x + z and the number of people with investments in securities is y + z . since exactly 25 % of the investors in equities have investments in securities , we have the equation = > ( 25 / 100 ) × ( x + z ) = z . = > ( 25 / 100 ) × x = 75 z / 100 . = > x = 3 z . - - - - - - - - - - - - - - ( 2 ) since exactly 40 % of the investors in securities have investments in equities , we have the equation = > ( 40 / 100 ) × ( y + z ) = z . = > ( y + z ) = 5 z / 2 . = > y = 3 z / 2 . - - - - - - - - - - - - - - - - - ( 3 ) substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) gives : - = > 3 z + ( 3 z / 2 ) + z = 110 . = > 11 z / 2 = 110 . = > z = 110 × 2 / 11 = 20 . hence , the number of people with investments in equities is : = > x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 = 80 . answer : b
Answer: b
Question (geometry): the area of a triangle will be when a = 1 m , b = 4 m , c = 5 m , a , b , c being lengths of respective sides ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 4
Rationale: "s = ( 1 + 4 + 5 ) / 2 = 5 answer : c"
Answer: c
Question (general): a certain number of two digits is 3 times the sum of its digits and if 45 be added to it , the degits are reversed . the number is .
Options: a ) 23 , b ) 27 , c ) 32 , d ) 72 , e ) 46
Rationale: let the ten ' s digit be x and unit ' s digit be y . then 10 x + y = 3 ( x + y ) = = > 7 x - 2 y = 0 = = > 7 x - 2 y = 0 - - - - > ( i ) 10 + y + 45 = 10 y + x = = > y - x = 5 = = = > - 2 x + 2 y = 10 - - - - - - ( ii ) by adding ( i ) and ( ii ) we get 5 x = 10 so x = 2 and y = 7 so the required number is 27 . so the correct option is b ) 27 .
Answer: b
Question (physics): steve traveled the first 2 hours of his journey at 35 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 62 mph , e ) 66.67 mph
Rationale: "distance traveled in 2 hours = 2 * 35 = 70 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 70 = 310 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 310 / 5 = 62 mph answer : d"
Answer: d
Question (physics): tom , working alone , can paint a room in 16 hours . peter and john , working independently , can paint the same room in 8 hours and 4 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 2 / 7 , d ) 1 / 7 , e ) 3 / 7
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 16 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 8 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 4 * t part of the job : 1 / 16 * ( t + 4 ) + 1 / 8 * ( t + 2 ) + 1 / 4 * t = 1 - - > multiply by 16 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 16 - - > t = 10 / 7 ; hence peter has done 1 / 8 * ( 10 / 7 + 2 ) = 1 / 8 * 24 / 7 = 3 / 7 answer : e"
Answer: e
Question (general): an angry arjun carried some arrows for fighting with bheeshm . with half the arrows , he cut down the arrows thrown by bheeshm on him and with 6 other arrows he killed the chariot driver of bheeshm . with one arrow each he knocked down respectively the chariot , the flag and the bow of bheeshm . finally , with one more than 4 times the square root of arrows he laid bheeshm unconscious on an arrow bed . find the total number of arrows arjun had .
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: x / 2 + 6 + 3 + 1 + 4 sqrt ( x ) = x x / 2 + 10 + 4 sqrt ( x ) = x 4 sqrt ( x ) = x / 2 - 10 squaring on both sides 16 x = x ² / 4 + 100 - 10 x simplifying x ² - 104 x + 400 = 0 x = 100 , 4 x = 4 is not possible therefore x = 100 answer : b
Answer: b
Question (physics): find the distance covered by a man walking for 10 min at a speed of 6 km / hr ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 1.5 km , e ) 4 km
Rationale: "distance = 6 * 10 / 60 = 1 km answer is a"
Answer: a