Cheukting/mathqa huggingface dataset:
Question (general): how much water must be added to 60 litres of milk at 1.5 litres for rs . 20 so as to have a mixture worth rs . 32 / 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) 21 litres
Rationale: c . p . of 1 litre of milk = rs . 20 × 2 / 3 = rs . 40 / 3 . c . p . of 1 litre of water = rs 0 . mean price = rs . 32 / 3 . by the rule of alligation , we have : c . p of 1 litre c . p of 1 litre of water of milk ( 0 ) ( rs . 40 / 3 ) \ / mean price ( rs . 32 / 3 ) / \ 40 / 3 − 32 / 3 32 / ( 3 − 0 ) 8 / 3 32 / 3 the ratio of water and milk = 8 / 3 : 32 / 3 . = 8 : 32 = 1 : 4 . thus , quantity of water to be added to 60 litres of milk : = ( 1 / 4 ) × 60 litres . = 15 litres . answer : c
Answer: c
Question (gain): a cricket bat is sold for $ 850 , making a profit of $ 255 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 43 %
Rationale: "255 / ( 850 - 255 ) = 255 / 595 = 51 / 119 = 43 % . answer : e ."
Answer: e
Question (physics): a car covers a distance of 624 km in 2 3 / 5 hours . find its speed ?
Options: a ) 104 kmph , b ) 194 kmph , c ) 109 kmph , d ) 174 kmph , e ) 240 kmph
Rationale: 624 / 2 3 / 5 = 240 kmph answer : e
Answer: e
Question (geometry): three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 30 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters , b ) 36 square meters , c ) 42 square meters , d ) 45 square meters , e ) 120 square meters
Rationale: "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 30 = 90 sq m of the wallpaper overlaps in three layers . 90 sq m makes two extra layers hence the area over which it makes two extra layers is 45 sq m . answer ( d ) ."
Answer: d
Question (general): the average of first three prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50
Rationale: "23 + 29 + 31 = 83 / 3 = 27.7 answer : d"
Answer: d
Question (general): if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 40 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 60 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
Options: a ) $ 50 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 3 x + 4 y + 2 z = 40 7 x + 2 y + 2 z = 60 adding both the equations = 10 x + 6 y + 4 z = 100 5 x + 3 y + 2 z = 50 ans a"
Answer: a
Question (general): the heights of 3 individuals are in the ratio 4 : 5 : 6 . if the sum of the heights of the heaviest and the lightest boy is 150 cm more than the height of the third boy , what is the weight of the lightest boy ?
Options: a ) 120 cm , b ) 150 cm , c ) 160 cm , d ) 190 cm , e ) of these
Rationale: let the heights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 150 = > 5 k = 150 = > k = 30 therefore the height of the lightest boy = 4 k = 4 ( 30 ) = 120 cm . answer : a
Answer: a
Question (general): according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 29 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 15 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 29 = 61 - - > c = 5 / 9 * 29 = 16.11 . increase = 16.11 degrees . answer : b ."
Answer: b
Question (general): a man engaged a servant on the condition that he would pay him rs . 900 and auniform after 1 year service . he served only for 9 months and received uniform and rs . 650 , find the price of the uniform ?
Options: a ) rs . 80 , b ) rs . 100 , c ) rs . 120 , d ) rs . 145 , e ) rs . 156
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Question (gain): the sale price of a trolley bag including the sale tax is rs . 1190 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 800 , b ) rs 820 , c ) rs 860 , d ) rs 850 , e ) none of these
Rationale: "explanation : 112 % of s . p . = 1190 s . p . = rs . ( 1190 x 100 / 112 ) = rs . 1062.50 . c . p . = rs ( 100 / 125 x 1062.50 ) = rs 850 answer : d"
Answer: d
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 6 years hence ?
Options: a ) 22 , b ) 77 , c ) 70 , d ) 98 , e ) 72
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 6 years , their ages will be 46 and 26 . sum of their ages = 46 + 26 = 72 . answer : e"
Answer: e
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 5 m wide at the top and 3 m wide at the bottom and the area of cross - section is 3800 sq m , the depth of cannel is ?
Options: a ) 920 , b ) 930 , c ) 940 , d ) 950 , e ) 960
Rationale: "1 / 2 * d ( 5 + 3 ) = 3800 d = 950 answer : d"
Answer: d
Question (physics): maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 74 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 74 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 70 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 70 / 10 = 7 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 7 = 28 + 4 = 32 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 32 / 4 = 8 hrs . . . answer e"
Answer: e
Question (geometry): the two sides of a triangle are 32 and 68 . the area is 960 sq . cm . find the third side of triangle ?
Options: a ) 45
b ) 50
c ) 60
d ) 70
e ) 80
Rationale: we see 68 ^ 2 - 32 ^ 2 = ( 68 + 32 ) * ( 68 - 32 ) = 100 * 36 = 60 ^ 2 now ( 1 / 2 ) * 60 * 32 = 960 ( match with given options ) ( i . e area of a right angled triangle whose sides are 32 , 60,68 ) third side = 60 answer : c
Answer: c
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 40 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 ) 126 , 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 40 % = 90 * 1.2 = 126 thus ratio = 126 / 100 = 1.26 ( in % terms = 126 % ) . thus b is the correct answer ."
Answer: b
Question (general): if 9 a - b = 10 b + 80 = - 12 b - 2 a , what is the value of 9 a - 11 b ?
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 80
Rationale: "this implies 9 a - b = 10 b + 80 , 9 a - b = - 12 b - 2 a , 10 b + 80 = - 12 b - 2 a manipulating the second equation gives us 9 a - b = 10 b + 80 = = > 9 a - 11 b = 80 answer is e"
Answer: e
Question (gain): john makes $ 50 a week from his job . he earns a raise and now makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 40 %
Rationale: "increase = ( 20 / 50 ) * 100 = 40 % . e"
Answer: e
Question (geometry): the perimeter of one face of a cube is 48 cm . its volume will be :
Options: a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 48 / 4 = 12 cm volume = a * a * a = 12 * 12 * 12 = 1728 cm cube option e"
Answer: e
Question (general): the vertex of a rectangle are ( 1 , 0 ) , ( 5 , 0 ) , ( 1 , 1 ) and ( 5 , 1 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 6 , d ) 3 , e ) 1 / 4
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 3 , 0.5 ) . the slope of a line passing through ( 0,0 ) and ( 3 , 0.5 ) is 0.5 / 3 = 1 / 6 . the answer is c ."
Answer: c
Question (general): on a game show , there are 3 tables . each table has 3 boxes ( one zonk ! , one cash prize , and one grand prize ) . the contestant can choose one box from each table for a total of 3 boxes . if any of the boxes are a zonk ! , the contestant loses everything . what is the probability of getting no zonk ! from any of the 3 boxes chosen ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 8 / 27 , d ) 1 / 27 , e ) 7 / 8
Rationale: no zonk ! : 1 st box = no zonk ! = 2 / 3 2 nd box = no zonk ! = 2 / 3 3 rd box = no zonk ! = 2 / 3 ( 2 / 3 ) ( 2 / 3 ) ( 2 / 3 ) = 8 / 27 8 / 27 is the probability of no zonk ! , so . . . answer : c
Answer: c
Question (general): the average weight of a , b and c is 42 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 40 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 42 x 3 ) = 126 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 40 . b ' s weight = 40 kg . d"
Answer: d
Question (general): dividing by 3 ⁄ 8 and then multiplying by 5 ⁄ 9 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 40 / 27 , e ) 5 ⁄ 16
Rationale: say x / 3 / 8 * 5 / 9 = x * 8 / 3 * 5 / 9 = x * 40 / 27 d
Answer: d
Question (general): how many integers n greater than and less than 100 are there such that , if the digits of n are reversed , the resulting integer is n + 9 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: ( 10 x + y ) = ( 10 y + x ) + 9 = > 9 x - 9 y = 9 = > x - y = 1 and only 8 numbers satisfy this condition and the numbers are 21,32 , 43,54 , 65,76 , 87,98 answer : d
Answer: d
Question (physics): a runs twice as fast as b and gives b a start of 50 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 50 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 50 m is 50 / 1 = 50 m so the total time taken by a and b to reach = 2 * 50 = 100 m answer : d"
Answer: d
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 12 % ?
Options: a ) 20 % , b ) 25 % , c ) 13 1 / 30 % , d ) 32 % , e ) 13 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 88 2 / 3 sp 1 = 88 sp 1 = 132 100 - - - 32 = > 32 % answer : d"
Answer: d
Question (general): reeya obtained 65 , 67 , 76 , 80 and 95 out of 100 in different subjects , what will be the average
Options: a ) 76.6 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: explanation : ( 65 + 67 + 76 + 80 + 95 / 5 ) = 76.6 option a
Answer: a
Question (general): an ant walks an average of 600 meters in 12 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 2.215 . , b ) 2.55 , c ) 2.775 . , d ) 3.2 . , e ) 3.5 .
Rationale: "the ant walks an average of 600 meters in 12 minutes 600 meters in 1 / 5 hours the beetle walks 15 % less distance = 600 - 90 = 510 meters in 12 minutes 0.510 km in 12 / 60 = 1 / 5 hours speed = 0.510 * 5 = 2.55 km / h correct answer b = 2.55"
Answer: b
Question (physics): an aeroplane covers a certain distance of 450 kmph in 4 hours . to cover the same distance in 3 2 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 490 , c ) 640 , d ) 740 , e ) 250
Rationale: "speed of aeroplane = 450 kmph distance travelled in 4 hours = 450 * 4 = 1800 km speed of aeroplane to acver 1800 km in 11 / 3 = 1800 * 3 / 11 = 490 km answer b ."
Answer: b
Question (general): when the number 72 y 6139 is exactly divisible by 11 , then the smallest whole number that can replace y is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "the given number = 72 y 6139 sum of the odd places = 9 + 1 + y + 7 sum of the even places = 3 + 6 + 2 = 11 ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) ( 16 + y ) - ( 11 ) = divisible by 11 y � 5 = divisible by 11 . y must be 6 , to make given number divisible by 11 . d"
Answer: d
Question (general): a 12 month project had a total budget of $ 42000 . after 8 months , the project had spent $ 23700 . at this point , how much was the project under budget ?
Options: a ) $ 4100 , b ) $ 4300 , c ) $ 4500 , d ) $ 4700 , e ) $ 4900
Rationale: each month , the project should spend $ 42,000 / 12 = $ 3500 . in 8 months , the project should spend 8 * $ 3500 = $ 28,000 . the project is under budget by $ 28,000 - $ 23,700 = $ 4300 . the answer is b .
Answer: b
Question (general): a is the average ( arithmetic mean ) of the first 7 positive multiples of 4 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 16 , which also equals b . b is the second positive multiple of n , thus n = 16 / 2 = 8 . the answer is d ."
Answer: d
Question (physics): a cistern 8 m long and 6 m wide contains water up to a breadth of 1 m 85 cm . find the total area of the wet surface .
Options: a ) 102 m sqaure , b ) 100 m sqaure , c ) 152 m sqaure , d ) 164 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 1.85 + 8 * 1.85 ) ] + 8 * 6 = 100 m square option b"
Answer: b
Question (other): the ratio of buses to cars on river road is 1 to 13 . if there are 60 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 65 , b ) 60 , c ) 55 , d ) 40 , e ) 45
Rationale: "b / c = 1 / 13 c - b = 60 . . . . . . . . . > b = c - 60 ( c - 60 ) / c = 1 / 13 testing answers . clearly eliminate bcde put c = 65 . . . . . . . . . > ( 65 - 60 ) / 65 = 5 / 65 = 1 / 13 answer : a"
Answer: a
Question (physics): if a takes x days to do a work then b takes 2 x days to do the same work then with in how many day ' s a will alone complete this work ?
Options: a ) 27 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: 1 / x + 1 / 2 x = 1 / 18 = > 3 / 2 x = 1 / 18 = > x = 27 days . hence , a alone can finish the work in 27 days . answer : a
Answer: a
Question (geometry): 62 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 128 , c ) 152 , d ) 154 , e ) 256
Rationale: "62 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 62 = 154 hence , d is the answer ."
Answer: d
Question (probability): if you throw two dice at a same time . can you find the probability of getting sum as 10 of the two numbers shown ?
Options: a ) 1 / 16 , b ) 2 / 14 , c ) 1 / 12 , d ) 1 / 19 , e ) 1 / 17
Rationale: c 1 / 12 all possible cases can be 36 ( 6 * 6 ) case we need : [ ( 4,6 ) , ( 5,5 ) , ( 6,4 ) ] = 3 probability = > 3 / 36 = 1 / 12
Answer: c
Question (gain): in an office , 30 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 480 , b ) 48 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 30 / 100 ) * workers = x + 16 = > x = 48 answer b"
Answer: b
Question (general): the least number which must be subtracted from 820 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 1 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 820 by 9 , we get remainder = 1 therefore , required number to be subtracted = 1 answer : c"
Answer: c
Question (geometry): can n and can в are both right circular cylinders . the radius of can n is twice the radius of can b , while the height of can n is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can n with the same brand of gasoline ?
Options: a ) $ 1
b ) $ 2
c ) $ 4
d ) $ 8
e ) $ 16
Rationale: let x be the radius of b and 2 h be the height of b . therefore , radius of n = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
Answer: e
Question (physics): a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 120 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 27 % , e ) 40 %
Rationale: "total time for travelling 120 miles @ 60 mph = 120 / 60 = 2 hour = 120 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 120 minutes it will use = 3 gallons . thus , full tank = 3 + 8 = 11 gallons - - - > 3 / 11 = 27 % of the fuel used . d is the correct answer ."
Answer: d
Question (geometry): if the sides of a triangle are 39 cm , 36 cm and 15 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 765 cm 2 , c ) 216 cm 2 , d ) 270 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 39 cm , 36 cm and 15 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : d"
Answer: d
Question (general): what is the dividend . divisor 19 , the quotient is 7 and the remainder is 6
Options: a ) 136 , b ) 137 , c ) 138 , d ) 139 , e ) 140
Rationale: "d = d * q + r d = 19 * 7 + 6 d = 133 + 6 d = 139"
Answer: d
Question (geometry): obra drove 120 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 18.75 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 120 π / 480 π = 25 % hence , answer is d ."
Answer: d
Question (physics): some persons can do a piece of work in 20 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "20 / ( 2 * 2 ) = 5 days answer : c"
Answer: c
Question (geometry): if paint costs $ 3.20 per quart , and a quart covers 1200 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60
b ) $ 16.00
c ) $ 96.00
d ) $ 108.00
e ) $ 196.00
Rationale: total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 1200 = 0.5 cost will be 0.5 * 3.2 = $ 1.6 ans : a
Answer: a
Question (physics): the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 33 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft
b ) 25 ft
c ) 750 ft
d ) 900 ft
e ) 1650 ft
Rationale: point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 33 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 50 . sub x = 50 either in ( x + 5 ) * 30 or in x * 33 to get the distance , which is 1650 . so the correct choice is e .
Answer: e
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 w of a cube whose surface area is equal to 6 z ?
Options: a ) w = 16 , b ) w = 8 √ 2 , c ) w = 8 , d ) w = 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): if 50 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 42.8 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %
Rationale: "50 % of ( x - y ) = 20 % of ( x + y ) 50 / 100 ( x - y ) = 20 / 100 ( x + y ) 3 x = 7 y required percentage = y / x * 100 = 3 y / 7 y * 100 = 42.85 % answer is b"
Answer: b
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 34 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "34 % is 9 % - points above 25 % and 6 % - points below 40 % . thus the ratio of mixture y to mixture x is 2 : 3 . the percent of mixture x is 3 / 5 = 60 % . the answer is d ."
Answer: d
Question (geometry): in a triangle abc , ab = 6 , bc = 8 and ac = 10 . a perpendicular dropped from b , meets the side ac at d . a circle of radius bd ( with centre b ) is drawn . if the circle cuts ab and bc at p and q respectively , then ap : qc is equal to
Options: a ) 1 : 1
b ) 3 : 2
c ) 4 : 1
d ) 3 : 8
e ) 2 : 5
Rationale: explanation : triangle abc and triangle adb are similar , ac / ab = bc / bd 10 / 6 = 8 / r r = 24 / 5 bp = bq = bd = r = 24 / 5 ap = ab - r = 6 - 24 / 5 = 6 / 5 cq = bc - r = 8 - 24 / 5 = 16 / 5 ap : cq = 6 / 16 = 3 : 8 answer : d
Answer: d
Question (general): find the mean proportional between 49 & 81 ?
Options: a ) 59 , b ) 61 , c ) 63 , d ) 65 , e ) 67
Rationale: formula = √ a × b a = 49 and b = 81 √ 49 × 81 = 7 × 9 = 63 c
Answer: c