euclaise/mathqa_programs huggingface dataset:
Problem: a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations p are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) p = 8
Rationale: "the combinations could be p { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e"
Answer: e
Python program:
a = 240 / 30
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 9,4 ) , and ( 9,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 2 / 9
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 36 . p ( x + y < 4 ) = 8 / 36 = 2 / 9 the answer is e ."
Answer: e
Python program:
a = 4 * 4
b = a / 2
c = 1 + 4 
d = 4 * c
e = b / d
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 = 6 * 0 + 2 * 7.2 + 8 - 6.2 = 0 + 14.4 + 1.8 16.2 answer d"
Answer: d
Python program:
a = 2 * 7
b = 4 / 10
c = 8 - 4
d = a + c 
e = d - 6
Problem: machine a takes 100 hours to complete a certain job and starts that job at 6 am . after ten hour of working alone , machine a is joined by machine b and together they complete the job at 6 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ?
Options: a ) 24.65 , b ) 22.27 , c ) 2.273 , d ) 11.62 , e ) 21.13
Rationale: "let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 10 hr ( so 10 units done ) then a and b finish total work in 12 hours . hence a and b finish 90 units in 2 hours . of these 1 x 2 = 2 units were done by a . hence b did 88 units in 2 hours . hence b ( working rate ) = 44 units / hr hence b takes 100 / 44 = 2.273 hours to complete the job . answer c ."
Answer: c
Python program:
a = 1/(100)
b = a * 2
c = 1 - b
d = 6 * 2
e = d - 6
f = e - 2
g = c / f
h = 1/(100)
i = g - h
j = 1/(i)
Problem: efrida and frazer who live 12 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : d ."
Answer: d
Python program:
a = 12 ** 2
b = 2 ** 2
c = a - b
d = c / 2
e = math.sqrt(d)
f = e + 2
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 7 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 0.07 , b ) 0.049 , c ) 0.7 , d ) 0.49 , e ) 4.9
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 49 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 490 / 10,000 = 49 / 1000 = 0.049 ft the answer is b ."
Answer: b
Python program:
a = volume_cylinder / (
Problem: at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 80 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 44 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 80 = 25 + b + 25 b / 100 b = 44 answer ( e )"
Answer: e
Python program:
a = 100 + 80 
b = 100 + 25 
c = a / b
d = c - 1
e = d * 100
Problem: an article is bought for rs . 1200 and sold for rs . 1300 , find the loss percent ?
Options: a ) 8.33 % , b ) 9.33 % , c ) 10.00 % , d ) 11.11 % , e ) 7.56 %
Rationale: "1200 - - - - 100 100 - - - - ? = > 16 2 / 3 % answer : a"
Answer: a
Python program:
a = 1300 * 100
b = a / 1200
c = 100 - b
Problem: by selling an article for $ 100 a man gains $ 20 then his gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 100 gain = $ 20 c . p . = 100 - 20 = 80 gain % = 20 / 80 * 100 = 25 % answer is a"
Answer: a
Python program:
a = 20 * 100
b = 100 - 20
c = a / b
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 50 miles per hour , what is v in miles per hour ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 50 = > v = 20 ( option a ) .
Answer: a
Python program:
a = 100 - 80
b = 100 / 50
c = 80 / 80
d = b - c
e = a * d
Problem: john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 5 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 50 , e ) s . 290
Rationale: let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . d
Answer: d
Python program:
a = 8000 / 100
b = 10 * a
c = 15000 / 100
d = 5 * c
e = b - d
Problem: the manufacturing cost of a shoe is rs . 230 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 282 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 230 + ( 500 / 100 ) = 235 . gain = 20 % = > sp = 1.2 cp = 1.2 x 235 = 282 answer : a"
Answer: a
Python program:
a = 500 / 100
b = 230 + a 
c = 20 / 100
d = 500 / 100
e = 230 + d 
f = c * e
g = b + f
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 15 , and the difference between the total number of strawberries and the total number of blueberries would increase by 87 . each blue box contains how many blueberries ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "let x be the number of blueberries in each blue box . then there are x + 15 strawberries in each red box . x + ( x + 15 ) = 87 x = 36 the answer is e ."
Answer: e
Python program:
a = 87 - 15
b = a / 2
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 700 ( before payroll deductions ) ?
Options: a ) 1220 , b ) 1250 , c ) 1280 , d ) 1310 , e ) 1340
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 700 x = 200 / 0.16 = 1250 the answer is b ."
Answer: b
Python program:
a = 12 * 50
b = 700 - a
c = b / 0
Problem: how many positive integers less than 500 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 number of possibilities = 4 * 4 * 4 = 64 . then , just add up the number of 1 digits numbers = 4 , so total is 64 + 4 = 68 . answer : d"
Answer: d
Python program:
a = 4 + 1 
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a rope of which a calf is tied is increased from 12 m to 25 m , how much additional grassy ground shall it graze ?
Options: a ) 1400 , b ) 141.71 , c ) 1210 , d ) 1511.71 , e ) 1500
Rationale: "π ( 252 – 122 ) = 1511.71 answer : d"
Answer: d
Python program:
a = 25 ** 2
b = 10 ** 2
c = a - b
d = 12 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: two pipes a and b can fill a tank in 30 and 60 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 24 , e ) 25
Rationale: "part filled by a in 1 min . = 1 / 30 part filled by b in 1 min . = 1 / 60 part filled by ( a + b ) in 1 min . = 1 / 30 + 1 / 60 = 1 / 20 . both the pipes can fill the tank in 20 minutes . answer : b"
Answer: b
Python program:
a = 30 * 100
b = 1 / 30
c = 1 / 60
d = b + c 
e = d * 2
f = 1 - e
g = f * 30
h = g * const_60
i = a + h
Problem: by selling 22 pencils for a rupee a man loses 40 % . how many for a rupee should he sell in order to gain 40 % ?
Options: a ) 8.56 , b ) 9.35 , c ) 9.43 , d ) 6.56 , e ) 5.5
Rationale: "60 % - - - 22 140 % - - - ? 60 / 140 * 22 = 9.43 answer : c"
Answer: c
Python program:
a = 100 + 40 
b = 100 - 40
c = 1 / b
d = a * c
e = 1 / d
f = e * 22
Problem: the difference between the place values of two threes in the numerical 40378273 is
Options: a ) 29997 , b ) 299997 , c ) 297 , d ) 0 , e ) none of them
Rationale: "required difference = ( 300000 - 3 ) = 299997 . answer is b"
Answer: b
Python program:
a = 40378273 + 1 
b = a / 2
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 22 !
Options: a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 - - - - count 3 ' s = 9 so answer is 9 answer : c"
Answer: c
Python program:
a = 22 / 3
b = math.floor(a)
c = 3 ** 2
d = 22 / c
e = math.floor(d)
f = b + e
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 14 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 114 let marked price be $ x . then , 95 / 100 x = 114 x = 114 / 95 = $ 120 now , s . p . = $ 120 , c . p . = $ 100 profit % = 20 % . b"
Answer: b
Python program:
a = 100 + 14 
b = 100 - 5
c = a / b
d = 100 * c
Problem: three table runners have a combined area of 212 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches
Rationale: "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 212 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 212 - 24 - 140 all three = 24 answer : c"
Answer: c
Python program:
a = 212 - 24
b = 80 / 100
c = 175 * b
d = a - c
e = d / 2
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 75 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 48 , b ) 30 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 45 + 75 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : b"
Answer: b
Python program:
a = 45 + 75
Problem: patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon . if she made no stops during the run and her average speed for the entire marathon was 5 mph , for what fraction of the total time did she run at 3 mph ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 3
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire marathon was 5 mph , she ran at 6 mph for a longer duration . 2 1 3 - - 5 - - - - 6 this shows that you can divide the entire journey in 3 equal parts . thus , 2 / 3 part she ran at 6 mph and 1 / 3 part she ran at 3 mph . answer : e
Answer: e
Python program:
a = 6 - 5
b = 6 - 3
c = a / b
Problem: kamal obtained 66 , 65 , 77 , 62 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: sol . average = 66 + 65 + 77 + 62 + 75 / 5 ) = ( 345 / 5 ) = 69 . answer b
Answer: b
Python program:
a = 66 + 65 
b = a + 77 
c = b + 62 
d = c + 75 
e = 1 + 4 
f = d / e
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 25 % more recliners . what is the percentage increase of the gross ?
Options: a ) 00 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 25 % more ie . , 125 recliners hence her sales tields 125 * 80 = $ 10000 increase in sales = 10000 - 10000 = $ 0 so % increase = 0 * 100 / 10000 = 0 % a is the answer"
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 25 / 100
d = 1 + c 
e = b * d
f = e * 100
g = f - 100
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 750 more than that by the previous schema , his sales were worth ?
Options: a ) s . 4,000 , b ) s . 6,000 , c ) s . 30,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 750 x = 6000 answer : b"
Answer: b
Python program:
a = 5 * 4
b = a - 12
Problem: what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 22 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 1 : 2 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3 : 6 = 1 : 2"
Answer: c
Python program:
a = 25 - 22
b = 22 - 16
c = a / b
Problem: calculate how long it will take a swimmer to swim a distance of 7 km against the current of a river which flows at 2.5 km / hr , given that he can swim in still water at 4.4 km / h
Options: a ) 6.67 , b ) 1.67 , c ) 2.67 , d ) 3.67 , e ) 4.67
Rationale: "swim in still water at = 4.4 speed of river = 2.5 us = 4.4 - 2.5 = 1.9 distance = 7 t = 7 / 1.9 = 3.67 answer : d"
Answer: d
Python program:
a = 4 - 4
b = 7 / a
Problem: a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 200 . the cost for 1 bat and 6 balls is $ 220 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 210 for the purchase ?
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: imo it should be c that is 3 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 200 1 b + 6 c = 220 solving both we get b that is bat = 40 and c that is ball = 30 new equation 210 to be divided in equal 3 b + 3 c = 210 3 * 40 + 3 * 30 = 210 120 + 90 = 210
Answer: c
Python program:
a = 200 / 2
b = 220 - a
c = b / 4
d = 6 * c
e = 220 - d
f = 200 / 2
g = 220 - f
h = g / 4
i = e + h 
j = 210 / i
Problem: if the product of the integers from 1 to n is divisible by 686 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "686 = 7 x 7 x 7 x 2 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c ."
Answer: c
Python program:
a = 686 / 3
b = 3 + 4 
c = a / b
d = 3 + 4 
e = c / d
f = e * 3
Problem: find the area of a parallelogram with base 12 cm and height 18 cm .
Options: a ) 200 , b ) 216 , c ) 345 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 12 * 18 = 216 cm 2 answer : option b"
Answer: b
Python program:
a = 12 * 18
Problem: if a number p is prime , and 2 p + 4 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "1 / 6 = 0.1666666 . . . ( a repeating pattern one digit long ) a"
Answer: a
Python program:
a = 166 + 1 
b = a - 4
c = b / 2
d = 166 + 1 
e = d - 4
f = e / 2
g = f - 1
h = c - g
Problem: a train 110 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: speed of train relative to man : 110 / 6 * 18 / 5 km / hr = 66 km / hr let speed of train = x therefore x + 6 = 66 x = 66 - 6 x = 60 km / hr answer : b
Answer: b
Python program:
a = 6 * const_0_2778
b = a * 6
c = 110 - b
d = c / 6
e = d / const_0_2778
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , the how old is b ?
Options: a ) 10 years , b ) 12 years , c ) 14 years , d ) 15 years , e ) 16 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 x = 6 . hence , b ' s age = 2 x = 12 years . b )"
Answer: b
Python program:
a = 32 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 45000 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 90000 , c ) 85000 , d ) 190000 , e ) 250000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 45000 - > x = 150000 answer : b"
Answer: b
Python program:
a = 2 / 3
b = 3 / 4
c = a * b
d = 45000 / c
Problem: in a certain company , the formula for maximizing profits is p = - 25 x ^ 2 + 7500 x , , where p is profit and x is the number of machines the company operates in its factory . what value for x will maximize p ? this one is from integratedlearning . here ' s what i did : the oa states : to find a maximum or minimum value of an equation with an exponent in it , you take the derivative of the equation , set it to zero , and solve . i dont really get what that means . so whoever solves it , could you plz post explanation of what the above sentence mean as well ?
Options: a ) 10 , b ) 50 , c ) 150 , d ) 200 , e ) 300
Rationale: recognize that 25 is a factor of 7500 . if we take this out , we have two parts to the equation : - x ^ 2300 x one part of the equation brings our value down , whereas the other part brings our value up . at this point , we can test the numbers in the answer choice . notice that they are very straight forward to square , and multiplication by 300 is very easy . a ) 10 - 3000 - 100 = 2900 b ) 50 - 15000 - 2500 = 12500 c ) 150 - 45000 - 22500 = 22500 d ) 200 - 60000 - 40000 = 20000 e ) 300 - recognize that this is zero therefore , answer is 150 . hope this helps those - like myself - who have n ' t thought about calculus for over half a decade . c
Answer: c
Python program:
a = math.sqrt(25)
b = 2 * a
c = 7500 / b
d = math.sqrt(25)
e = c / d
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 5 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ?
Options: a ) 100 , b ) 225 , c ) 169 , d ) 256 , e ) 324
Rationale: "one point ( - 5 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 5 - 3 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 d"
Answer: d
Python program:
a = 5 * 3
b = 5 * 3
c = a * b
Problem: the cost of the paint is rs . 30 per kg . if 1 kg of paint covers 18 sq . ft , how much will it cost to paint outside of a cube having 6 feet each side
Options: a ) rs . 962 , b ) rs . 672 , c ) rs . 540 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 6 ^ 2 = 216 sq . ft quantity of paint required = ( 216 / 18 ) = 12 kg cost of painting = 30 x 18 = rs . 540 answer : c"
Answer: c
Python program:
a = surface_cube / (
b = a * 18
Problem: what is the smallest number which when diminished by 18 , is divisible 8 , 14 , 26 and 28 ?
Options: a ) 746 , b ) 750 , c ) 789 , d ) 678 , e ) 897
Rationale: "required number = ( lcm of 8 , 14 , 26 and 28 ) + 18 = 728 + 18 = 746 option a"
Answer: a
Python program:
a = math.lcm(8, 14)
b = math.lcm(26, 28)
c = math.lcm(a, b)
d = c + 18
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 11 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 9 / 5 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 11 ) = 36 / 20 = 9 / 5 . answer : d ."
Answer: d
Python program:
a = 4 + 1 
b = 45 / a
c = 45 - b
d = 4 + 1 
e = 45 / d
f = e + 11 
g = c / f
Problem: two men started from the same place walk at the rate of 5 kmph and 5.5 kmph respectively . what time will they take to be 8.5 km apart , if they walk in the same direction ?
Options: a ) 10 hours , b ) 12 hours , c ) 17 hours , d ) 15 hours , e ) 20 hours
Rationale: "to be 0.5 km apart they take 1 hour to be 8.5 km apart they take = 1 / 0.5 * 8.5 = 17 hours answer is c"
Answer: c
Python program:
a = 5 - 5
b = a / 8
Problem: ? % of 360 = 162
Options: a ) 277 , b ) 36 , c ) 45 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 162 or , ? = 162 × 100 / 360 = 45 answer c"
Answer: c
Python program:
a = 162 * 100
b = a / 360
Problem: how many factors does 35 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 6 * 4 = 24 answer c ."
Answer: c
Python program:
a = 10 * 2
b = 35 / a
Problem: at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the men are married ?
Options: a ) 3 / 4 , b ) 2 / 5 , c ) 4 / 5 , d ) 2 / 3 , e ) 1 / 4
Rationale: - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married man / total man , so 10 / 40 = 1 / 4 e
Answer: e
Python program:
a = 3 / 4
b = 1 - a