euclaise/mathqa_programs huggingface dataset:
Problem: 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
Python program:
a = 29 * 5
b = a / 9
Problem: 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
Python program:
a = 1 * 900
b = 3 * 4
c = b * 9
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: 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
Python program:
a = 12 / 100
b = 1190 * a
c = 1190 - b
d = 25 / 100
e = d + 1 
f = c / e
Problem: 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
Python program:
a = 60 / 6
b = a * 2
c = b + 6 
d = 60 / 6
e = d + 6 
f = c + e
Problem: 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
Python program:
a = 5 + 3 
b = a / 2
c = 3800 / b
d = c / 3
e = d / 2
Problem: 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
Python program:
a = 74 + 6 
b = 4 + 6 
c = a / b
Problem: 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
Python program:
a = 68 + 32 
b = a ** 2
c = 68 * 32
d = c ** 2
e = 960 ** 2
f = e * 4
g = d - f
h = math.sqrt(g)
i = 68 * 32
j = h + i 
k = j / 2
l = k * 4
m = b - l
n = math.sqrt(m)
o = 68 + 32 
p = n + o 
q = p / 2
r = q * 2
s = 68 + 32 
t = r - s
Problem: 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
Python program:
a = 100 + 20 
b = a / 100
c = 100 * b
d = 100 - 25
e = d / 100
f = c * e
g = 100 + 40 
h = g / 100
i = f * h
Problem: 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
Python program:
a = 80 / 2
b = a * 2
c = negate * (
Problem: 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
Python program:
a = 70 - 50
b = a / 50
c = b * 100
Problem: 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
Python program:
a = 5 - 1
b = a + 1 
c = b / 1
d = 1 / c
Problem: 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
Python program:
a = 2 ** 3
b = 3 ** 3
c = a / b
Problem: 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
Python program:
a = 40 * 2
b = 43 * 2
c = a + b 
d = 42 * 3
e = c - d
Problem: 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
Python program:
a = 8 / 3
b = 5 / 9
c = a * b
Problem: 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
Python program:
a = 100 / 10
b = a - 2
Problem: 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
Python program:
a = 50 * 2
Problem: 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
Python program:
a = 100 - 12
b = 2 / 3
c = a / b
d = c - 100
Problem: 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
Python program:
a = 65 + 67 
b = a + 76 
c = b + 80 
d = c + 95 
e = 4 + 1 
f = d / e
Problem: 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
Python program:
a = 600 / 1000
b = 12 / const_60
c = a / b
d = 15 / 100
e = 1 - d
f = c * e
Problem: 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
Python program:
a = 450 * 4
b = 3 * 3
c = b + 2 
d = c / 3
e = a / d
Problem: 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
Python program:
a = 72 - 72
Problem: 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
Python program:
a = 23700 / 8
b = a * 12
c = 42000 - b
d = c / 12
e = d * 8
Problem: 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
Python program:
a = 4 * 4
b = a / 2
Problem: 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
Python program:
a = 85 / 100
b = a + 1 
c = b * 6
d = 85 / 100
e = d + 1 
f = e * 8
g = c + f 
h = 2 * g
i = 6 * 8
j = h + i
Problem: 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
Python program:
a = 13 - 1
b = 60 / a
c = b * 13
Problem: 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
Python program:
a = 3 * 3
b = 2 * 2
c = a * b
d = 3 * 3
e = 2 * 2
f = d + e 
g = c - f
h = 2 * 2
i = g + h
Problem: 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
Python program:
a = cube_edge_by_volume + ( 
b = volume_cube - (
Problem: 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
Python program:
a = 6 ** 2
b = 1 / a
c = 6 ** 2
d = 1 / c
e = b + d 
f = 6 ** 2
g = 1 / f
h = e + g
Problem: 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
Python program:
a = 10 / 100
b = 16 / a
c = b * 90
d = c / 100
e = 10 / 100
f = 16 / e
g = 1 / 2
h = f * g
i = d - h
j = 2 * 4
k = i / j
Problem: 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
Python program:
a = 4 + 1 
b = a * 10
c = 4 + 2 
d = b + c 
e = d * 9
f = 820 - e
Problem: 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
Python program:
a = 4 * 2
b = 2 ** 2
c = b / 2
d = a * c
Problem: 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
Python program:
a = 40 * 60
b = 120 * 60
c = a / b
d = 40 * 60
e = 120 * 60
f = d / e
g = f + 8 
h = c / g
Problem: 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
Python program:
a = 36 * 15
b = a / 2
Problem: 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
Python program:
a = 19 * 7
b = a + 6
Problem: 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
Python program:
a = circumface / (
b = a * 120
c = b * 3
d = c - 2
e = d - 4
Problem: 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
Python program:
a = 1 / 2
b = 20 * a
c = 1 / 2
d = b * c
Problem: 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
Python program:
a = 3 / 2
b = a * surface_cube
Problem: 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
Python program:
a = 10 / 2
b = 30 * a
c = b / 3
d = 10 / 2
e = c + d 
f = 30 * e
Problem: 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
Python program:
a = 4 * 4
b = a / 2
c = math.sqrt(b)
Problem: 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
Python program:
a = 50 - 20
b = 50 + 20 
c = a / b
d = c * 100
Problem: 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
Python program:
a = 25 + 1 
b = 34 - a
c = 40 / 100
d = 25 + 1 
e = d / 100
f = c - e
g = b / f
Problem: 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
Python program:
a = 8 * 6
b = a / 10
c = 6 - b
d = 8 * 6
e = d / 10
f = 8 - e
g = c / f
Problem: 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
Python program:
a = 49 + 81 
b = a / 2
Problem: the average monthly income of p and q is rs . 6050 . the average monthly income of q and r is rs . 7050 and the average monthly income of p and r is rs . 8000 . the monthly income of p + q + r is :
Options: a ) 41100 , b ) 42000 , c ) 21100 , d ) 42200 , e ) 21000
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 6050 x 2 ) = 12100 . . . . ( i ) q + r = ( 7050 x 2 ) = 14100 . . . . ( ii ) p + r = ( 8000 x 2 ) = 16000 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 42200 or p + q + r = 21100 . . . . ( iv ) ( p + q + r ) ' s monthly income = rs . 21100 . answer : c"
Answer: c
Python program:
a = 6050 + 8000 
b = a - 7050