euclaise/mathqa_programs huggingface dataset:
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 15400 . how many times did he participate in the competition ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "15400 = 2 * 2 * 2 * 5 * 5 * 7 * 11 john participated 7 times . the answer is c ."
Answer: c
Python program:
a = 11 * 7
b = a * 5
c = b * 2
d = 15400 / c
e = math.sqrt(d)
f = math.floor(e)
Problem: the owner of a furniture shop charges his customer 30 % more than the cost price . if a customer paid rs . 8450 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 5725 , b ) rs . 5275 , c ) rs . 6275 , d ) rs . 6500 , e ) none of these
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8450 ( 100 / 130 ) = rs . 6500 . answer : d"
Answer: d
Python program:
a = 30 / 100
b = 1 + a 
c = 8450 / b
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 6 cups of tea . last week mo drank a total of 22 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 22 t - c = 14 - > t = 18 . c = 2 . mo drinks 6 cups of tea a day then number of days that are not rainy = 18 / 6 = 3 so number of rainy days = 7 - 3 = 4 c is the answer ."
Answer: c
Python program:
a = 4 + 6 
b = 22 + 14 
c = b / 2
d = c / 6
e = a - d
Problem: find the value of 85 p 3 .
Options: a ) 565350 , b ) 595650 , c ) 535950 , d ) 565350 , e ) 575350
Rationale: "85 p 3 = 85 ! / ( 85 - 3 ) ! = 85 ! / 82 ! = 85 * 84 * 83 * 82 ! / 82 ! = 85 * 84 * 83 = 595650 answer : b"
Answer: b
Python program:
a = 3 - 4
b = a * 85
Problem: a certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 12,000 , e ) e ) 11,100
Rationale: let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 142 k x = 12,000 answer : d
Answer: d
Python program:
a = 4 * 2
b = a * 100
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 171 grams of water ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( 2 / 18 ) * 171 = 19 grams the answer is e ."
Answer: e
Python program:
a = 2 + 16 
b = 171 / a
c = 2 * b
Problem: two whole numbers whose sum is 42 can not be in the ratio
Options: a ) 2 : 5 , b ) 1 : 6 , c ) 2 : 4 , d ) 3 : 8 , e ) 2 : 40
Rationale: d ) 3 : 8
Answer: d
Python program:
a = 100 / 0
b = a - 10
c = b / 2
d = 42 / 2
e = d + 10 
f = c / e
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 4 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 24
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 24 days to doing 4 w widgets . answer : e"
Answer: e
Python program:
a = 4 * 2
b = a * 3
Problem: the average of first 32 natural numbers is ?
Options: a ) 16.5 , b ) 17.5 , c ) 18.4 , d ) 15.4 , e ) 15.1
Rationale: "sum of 32 natural no . = 1056 / 2 = 55 average = 528 / 32 = 16.5 answer : a"
Answer: a
Python program:
a = 32 + 1
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 4680 , what will be a ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 2080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 4680 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 4680 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 4680 / 9 = 2080 . correct choice is ( c )"
Answer: c
Python program:
a = 1/(8)
b = 1/(12)
c = 1/(6)
d = 1/(8)
e = c + d 
f = b + e 
g = a / f
h = 4680 * g
Problem: by selling an article at rs . 600 , a profit of 25 % is made . find its cost price ?
Options: a ) 322 , b ) 480 , c ) 287 , d ) 192 , e ) 107
Rationale: "explanation : sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 25 ) ] = 600 * [ 100 / 125 ] = rs . 480 answer : b"
Answer: b
Python program:
a = 600 * 100
b = 100 + 25 
c = a / b
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1200 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 1080 , d ) 900 , e ) 1000
Rationale: let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1200 , loss of pyarelal = 1200 * 9 x / 10 x = 1080 answer : c
Answer: c
Python program:
a = 9 * 1200
b = 1 + 9 
c = a / b
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 20 m wide at the top and 12 m wide at the bottom and the area of cross - section is 800 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 50 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 20 + 12 ) = 800 d = 50 answer : b"
Answer: b
Python program:
a = 20 + 12 
b = a / 2
c = 800 / b
d = c / 12
e = d / 2
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 95 per day . what was his wage on the 8 th day ?
Options: a ) $ 76 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 95 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 95 * 7 ) = 1350 - ( 609 + 665 ) = 1350 - 1274 = 76 answer a
Answer: a
Python program:
a = 90 * 15
b = 87 * 7
c = 95 * 7
d = b + c 
e = a - d
Problem: what is the rate percent when the simple interest on rs . 1500 amount to rs . 250 in 5 years ?
Options: a ) 3.33 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 1 %
Rationale: "interest for 5 yrs = 250 interest for 1 yr = 50 interest rate = 50 / 1500 x 100 = 3.33 % answer : a"
Answer: a
Python program:
a = 100 * 250
b = 1500 * 5
c = a / b
Problem: nd the area of trapezium whose parallel sides are 20 cm and 15 cm long , and the distance between them is 14 cm ?
Options: a ) 230 cm 2 , b ) 245 cm 2 , c ) 255 cm 2 , d ) 260 cm 2 , e ) 280 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 15 ) * ( 14 ) = 245 cm 2 answer : b"
Answer: b
Python program:
a = 20 + 15 
b = 14 * a
c = b / 2
Problem: if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 7 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 17 / 140 , b ) 29 / 180 , c ) 26 / 143 , d ) 1 / 5 , e ) 39 / 121
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 7 * 2 = 14 hours ; in 1 hour 15 journeymen can finish 1 / 14 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 14 = 17 / 140 of the job . answer : a"
Answer: a
Python program:
a = 50 * 4
b = a / 10
c = 1 / b
d = 30 * 7
e = d / 15
f = 1 / e
g = c + f
Problem: a sum of money lent out at s . i . amounts to a total of $ 420 after 2 years and to $ 595 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 310 , b ) $ 320 , c ) $ 330 , d ) $ 340 , e ) $ 350
Rationale: "s . i for 5 years = $ 595 - $ 420 = $ 175 the s . i . is $ 35 / year s . i . for 2 years = $ 70 principal = $ 420 - $ 70 = $ 350 the answer is e ."
Answer: e
Python program:
a = 595 - 420
b = 2 / 5
c = a * b
d = 420 - c
Problem: donovan and michael are racing around a circular 300 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 6 , b ) 9 , c ) 8 , d ) 7 , e ) 10
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 300 / 45 = > 60 / 9 2 . speed / rate of michael = distance / time = > 300 / 40 = > 30 / 4 relative speed between them = 30 / 4 - 60 / 9 = > 270 - 240 / 36 = 30 / 36 = 5 / 6 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 300 , relative rate = 5 / 6 total time taken by micheal to surpass donovan = distance / rate = > 300 * 6 / 5 = > 1800 / 5 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . b"
Answer: b
Python program:
a = 300 / 40
b = 300 / 45
c = a - b
d = 300 / c
e = d / 40
Problem: the average age of a group of persons going for picnic is years . fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is
Options: a ) 5 , b ) 10 , c ) 15 , d ) 40 , e ) 50
Rationale: solution let the initial number of persons be x . then 16 x + 15 x 15 = 15.5 ( x + 20 ) = 0.5 x = 7.5 x = 15 . answer c
Answer: c
Python program:
a = 15 * 15
b = a / 15
Problem: the average of 10 numbers was calculated as 19 . it is discovered later on that while calculating the average , one number , namely 76 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "10 * 19 - 26 + 76 = 240 240 / 10 = 24 the answer is d ."
Answer: d
Python program:
a = 10 * 19
b = 76 - 26
c = a + b 
d = c / 10
Problem: of the 3,600 employees of company x , 3 / 4 are clerical . if the clerical staff were to be reduced by 4 / 5 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 37 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 3 / 4 are clerical out of 3600 so 2700 are clerical 2700 reduced by 4 / 5 is 2700 * 4 / 5 so it reduced 2160 people , so there is 540 clerical people left but since 2160 people left , it also reduced from the total of 3600 so there are 1440 people total since 540 clerical left / 1440 people total you get ( a ) 37 %"
Answer: a
Python program:
a = 3 / 4
b = 4 / 5
c = 4 - b
d = a * c
e = 3 / 4
f = 4 / 5
g = 4 - f
h = e * g
i = 3 / 4
j = 4 - i
k = h + j 
l = d / k
m = l * 100
Problem: the sum of the squares of three numbers is 41 , while the sum of their products taken two at a time is 20 . their sum is :
Options: a ) 10 , b ) 5 , c ) 9 , d ) 15 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 138 xy + yz + zx = 131 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 41 + ( 2 * 20 ) ( x + y + z ) ^ 2 = 81 so x + y + z = 9 answer : c"
Answer: c
Python program:
a = 41 - 20
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 41 - 20
f = e / 2
g = 41 - f
h = math.sqrt(g)
i = d + h
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ?
Options: a ) $ 1940 , b ) $ 2150 , c ) $ 2360 , d ) $ 2570 , e ) $ 2780
Rationale: let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d .
Answer: d
Python program:
a = 7 / 100
b = 109 / 9
c = 1000 + b
Problem: a cyclist rides a bicycle 9 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.5 , b ) 9.8 , c ) 10.1 , d ) 10.6 , e ) 11.2
Rationale: "distance = 21 km time = 9 / 12 + 12 / 9 = ( 81 + 144 ) / 108 = 225 / 108 = 25 / 12 hours average speed = ( 21 * 12 ) / 25 = 10.1 km / h the answer is c ."
Answer: c
Python program:
a = 9 + 12 
b = 9 / 12
c = 12 / 9
d = b + c 
e = a / d
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 173 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 195.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 173 / 22.50 = 1 = â € º x - 173 = 22.50 = â € º x = 195.50 . hence , price of the third variety = rs . 195.50 per kg . answer c"
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 173 * b
d = 126 + 126 
e = c - d
f = e / 2
Problem: 110 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 150 , d ) 155 , e ) 165
Rationale: "final number = initial number + 50 % ( original number ) = 110 + 50 % ( 110 ) = 110 + 55 = 165 . answer e"
Answer: e
Python program:
a = 50 / 100
b = 110 * a
c = 110 + b
Problem: in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 8 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 24 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 24 / 8 = 6 ans b"
Answer: b
Python program:
a = 36 * 24
b = a * 4
c = b / 72
d = c / 8
Problem: a textile manufacturing firm employees 50 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 50 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 − ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 × ( 49 / 50 ) − 150000 × ( 49 / 50 ) − 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 − 2 , 68,000 = > rs . 7,000 . answer : b"
Answer: b
Python program:
a = 5 * 1000
b = a * 100
c = 75000 * 2
d = c + 75000 
e = b - d
f = 50 - 1
g = f / 50
h = 5 * 1000
i = h * 100
j = g * i
k = 75000 * 2
l = 50 - 1
m = l / 50
n = k * m
o = j - n
p = o - 75000
q = e - p
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 4 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1815
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 4 x + 15 3 x = 1350 x = 450 large number = 450 + 1365 = 1815 e"
Answer: e
Python program:
a = 1365 - 15
b = 4 - 1
c = a / b
d = c * 4
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 216 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 6
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 216 per week 36 x = 216 x = 6 correct option : e"
Answer: e
Python program:
a = 8 * 3
b = 6 * 2
c = a + b 
d = 216 / c
Problem: by selling 15 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 2.15 , b ) 4.2 , c ) 5.18 , d ) 3.75 , e ) 4.2
Rationale: "40 % - - - 15 160 % - - - ? 40 / 160 * 15 = 3.75 answer : d"
Answer: d
Python program:
a = 100 + 60 
b = 100 - 60
c = 1 / b
d = a * c
e = 1 / d
f = e * 15
Problem: find the area of a cuboid of length 10 cm , breadth 8 cm . and height 6 cm .
Options: a ) 400 cm cube , b ) 410 cm cube , c ) 420 cm cube , d ) 430 cm cube , e ) 480 cm cube
Rationale: "area of a cuboid = lxbxh = 10 cm x 8 cm x 6 cm = 480 cm cube answer : e"
Answer: e
Python program:
a = 10 * 8
b = a * 6
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 8 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 87.8 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 8 % of 400 = 8 / 100 × 400 = 3200 / 100 = 32 therefore , total number of rotten fruits = 90 + 32 = 122 therefore number of fruits in good condition = 1000 - 122 = 878 therefore percentage of fruits in good condition = ( 878 / 1000 × 100 ) % = ( 87800 / 1000 ) % = 87.8 % answer : b"
Answer: b
Python program:
a = 600 + 400 
b = 15 / 100
c = 600 * b
d = 8 / 100
e = 400 * d
f = c + e 
g = a - f
h = 600 + 400 
i = g / h
j = i * 100
Problem: in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate
Options: a ) 356000 , b ) 356500 , c ) 357000 , d ) 400000 , e ) none of these
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 c )"
Answer: c
Python program:
a = 15 / 100
b = 1 - a
c = 560000 * b
d = 75 / 100
e = c * d
Problem: of 30 applicants for a job , 12 had at least 4 years ' experience , 19 had degrees , and 6 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 30 - 6 = 24 aub = a + b - aib aib = 19 + 12 - 24 = 7 answer d"
Answer: d
Python program:
a = 12 + 19 
b = 30 - 6
c = a - b
d = 19 - 12
e = c + d
Problem: the circumferences of two circles are 264 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29960 sq m , b ) 33880 sq m , c ) 43120 sq m , d ) 27680 sq m , e ) 12786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 704 s = 264 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 132 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 132 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 132 - 352 ) ( 132 + 352 ) / ∏ = ( 220 ) ( 484 ) / ( 22 / 7 ) = 33880 sq m answer : b"
Answer: b
Python program:
a = 2 * math.pi
b = 704 / a
c = circle_area - (
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.25 km and 1.00 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 48 , b ) 9 , c ) 7 , d ) 67 , e ) 54
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.25 + 1.0 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : e"
Answer: e
Python program:
a = 1 * 25
b = 60 * 1000
c = b / 3600
d = a / c
e = 1 * 0
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: a reduction of 25 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.8 , b ) 2.3 , c ) 2.5 , d ) 3.3 , e ) 2.9
Rationale: "100 * ( 25 / 100 ) = 25 - - - 10 ? - - - 1 = > rs . 2.5 100 - - - 75 ? - - - 2.5 = > rs . 3.3 answer : d"
Answer: d
Python program:
a = 25 / 100
b = a * 100
c = b / 10
d = 25 / 100
e = d * 100
f = c / e
g = f * 100
Problem: if 15 % of 30 % of 50 % of a number is 90 , then what is the number ?
Options: a ) 4000 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 4000 . answer : a"
Answer: a
Python program:
a = 50 / 100
b = 30 / 100
c = a * b
d = 15 / 100
e = c * d
f = 90 / e
Problem: a certain box has 9 cards and each card has one of the integers from 1 to 9 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 9 cards ?
Options: a ) 1 / 36 , b ) 1 / 15 , c ) 1 / 18 , d ) 1 / 9 , e ) 2 / 9
Rationale: "the average of the numbers is 5 . the total number of ways to choose 2 cards from 9 cards is 9 c 2 = 36 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } the probability is 2 / 36 = 1 / 18 the answer is c ."
Answer: c
Python program:
a = math.factorial(9)
b = math.factorial(2)
c = 9 - 2
d = math.factorial(c)
e = b * d
f = a / e
g = 4 / f
Problem: what is the 6 th digit to the right of the decimal point in the decimal equivalent of 16 / 45 ?
Options: a ) 5 , b ) 12 , c ) 2 , d ) 35 , e ) 4
Rationale: "16 / 45 = 0.3555 . . . . 35 is non - terminating repeating decimal . the 22 nd digit to the right of decimal point will be 5 . answer a"
Answer: a
Python program:
a = 16 / 45