euclaise/mathqa_programs huggingface dataset:
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 8 sec . what is the length of the platform ?
Options: a ) 287 m , b ) 350 m , c ) 1267 m , d ) 1287 m , e ) 1162.5 m
Rationale: "speed = 300 / 8 = 75 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 75 / 2 = > x = 1162.5 m . answer : e"
Answer: e
Python program:
a = speed * (
b = a - 39
Problem: the rate of increase of the price of sugar is observed to be 3 percent more than the inflation rate expressed in percentage . the price of sugar , on january 1 , 1994 , is rs . 25 per kg . the inflation rate for the years 1994 and 1995 are expected to be 12 % each . the expected price of sugar on january 1 , 1996 would be
Options: a ) 33.06 , b ) 34.1 , c ) 34.2 , d ) 24.6 , e ) none of these
Rationale: explanation : increase in the price of sugar = ( 12 + 3 ) = 15 % hence , price of the sugar on jan 1 , 1996 = > ( 25 * 115 * 115 ) / ( 100 * 100 ) = rs 33.06 . answer : a
Answer: a
Python program:
a = 12 + 3 
b = a + 100 
c = 25 * b
d = 12 + 3 
e = d + 100 
f = c * e
g = 100 * 100
h = f / g
Problem: average weight of 10 people increased by 3 kg when one person of 45 kg is replaced by a new man . then weight of the new man is
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 75
Rationale: explanation : total weight increased is 3 * 10 = 30 . so weight of new person is 45 + 30 = 75 answer : option e
Answer: e
Python program:
a = 3 * 10
b = 45 + a
Problem: find the average of all numbers between 4 and 41 which are divisible by 5
Options: a ) 22.5 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 ) / 8 = 180 / 8 = 22.5 answer : option a"
Answer: a
Python program:
a = 5 * 3
b = 5 * 2
c = 5 + b 
d = a + c 
e = 5 * 4
f = d + e 
g = 4 + 1 
h = g * 5
i = f + h 
j = i / 5
Problem: the value of log 5 ( 1 / 125 ) is
Options: a ) 3 , b ) - 3 , c ) 1 / 3 , d ) - 1 / 3 , e ) none
Rationale: "solution let log 5 ( 1 / 125 ) = n . then , 5 n = 1 / 125 ‹ = › 5 n = 5 - 3 n = - 3 . answer b"
Answer: b
Python program:
a = 4 + 1 
b = a * 1000
c = 1 - b
d = math.log(c)
e = 4 + 1 
f = math.log(e)
g = d / f
h = math.log(g)
Problem: a train 280 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 65 sec , b ) 16 sec , c ) 18 sec , d ) 13 sec , e ) 76 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 280 * 2 / 35 = 16 sec answer : b"
Answer: b
Python program:
a = 63 * 1000
b = 280 / a
c = b * 3600
Problem: at a certain bowling alley , it costs $ 1 to rent bowling shoes for the day and $ 1.25 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 10 , e ) 9
Rationale: "after renting bowling shoes the person is left with $ 12.80 - $ 1 = $ 11.80 , which is enough for 11.8 / 1.25 < 10 = ~ 9 . answer : e ."
Answer: e
Python program:
a = 12 - 80
b = a / 1
Problem: sales price is $ 54 , gross profit is 125 % of cost , what is the value of gross profit ?
Options: a ) 32 , b ) 30 , c ) 39 , d ) 40 , e ) 42
Rationale: "cost + profit = sales cost + ( 125 / 100 ) cost = 54 cost = 24 profit = 54 - 24 = 30 answer ( b )"
Answer: b
Python program:
a = 125 / 100
b = 1 + a 
c = 54 / b
d = 54 - c
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 22 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 288 , b ) 516 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 22 + 21 = 43 t = 12 d = 43 * 12 = 516 answer : b"
Answer: b
Python program:
a = 21 - 22
b = 60 / a
c = b * 22
d = 21 - 22
e = 60 / d
f = e * 21
g = c + f
Problem: marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 10 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 90 ; projected revenue = 120 . actual / projected * 100 = 90 / 120 * 100 = 75 % . answer : e ."
Answer: e
Python program:
a = 100 - 10
b = 20 + 100 
c = a / b
d = c * 100
Problem: if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers
Options: a ) 23 , b ) 28 , c ) 48 , d ) 25 , e ) 99
Rationale: "explanation : h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d"
Answer: d
Python program:
a = 18750 / 750
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 12 . if the shop carries 375 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 75 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 12 x total dogs and bunnies = 15 x . and we are given that 15 x = 375 . hence x = 25 . dogs = 3 x = 3 * 25 = 75 ( option c )"
Answer: c
Python program:
a = 3 + 12 
b = 375 / a
c = b * 3
Problem: 30 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 120 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "30 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 30 ) * 100 = 120 square feet answer : option b"
Answer: b
Python program:
a = 4 * 9
b = 30 / 100
c = a / b
Problem: a sum of money at simple interest amounts to rs . 830 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 698 , c ) 758 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 830 ) = rs . 24 . s . i . for 3 years = rs . ( 24 x 3 ) = rs . 72 . principal = rs . ( 830 - 72 ) = rs . 758 . answer : c"
Answer: c
Python program:
a = 854 - 830
b = a * 3
c = b / 4
d = 830 - c
Problem: a person p takes 4 hrs time to complete a job and q takes 6 hrs to complete the same job if they work together how much time will they require to complete the job ?
Options: a ) 1.2 hrs , b ) 1.8 hrs , c ) 2.4 hrs , d ) 3.0 hrs , e ) none of these
Rationale: explanation : p ’ s 1 hr work = 1 / 4 q ’ s 1 hr work = 1 / 6 ( p + q ) ’ s 1 hr work = 1 / 4 + 1 / 6 = 5 / 12 = > time = 12 / 5 = 2.4 hrs answer : option c
Answer: c
Python program:
a = 1 / 4
b = 1 / 6
c = a + b 
d = 1/(c)
Problem: a shopkeeper fixes the marked price of an item 35 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 20 % , b ) 27 % , c ) 31 % , d ) 43 % , e ) none
Rationale: solution let c . p = rs . 100 then , marked price = rs . 135 , s . p = rs . 108 . discount % = ( 27 / 135 × 100 ) % = 20 % answer a
Answer: a
Python program:
a = 8 + 100 
b = 35 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: if the cost price of 22 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 37.5 % profit , c ) 37.5 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 22 articles = rs . 22 . selling price of 16 articles = rs . 22 therefore , selling price of 22 articles is : - = > 22 / 16 ã — 22 = > 30.25 . therefore , profit = selling price - cost price . = > 30.25 â ˆ ’ 22 = 8.25 hence , the percentage of profit = profit x 100 / c . p . = > 8.25 / 22 ã — 100 . = > 37.5 % profit . answer : b"
Answer: b
Python program:
a = 100 * 16
b = a / 22
c = 100 - b
d = 100 * 16
e = d / 22
f = c / e
g = 100 * f
Problem: six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) none
Rationale: "l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d"
Answer: d
Python program:
a = 2 + 3 
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / 10
g = 10 / f
Problem: at what rate percent per annum will the simple interest on a sum of money be 4 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 7 % , c ) 8 % , d ) 3 % , e ) 1 %
Rationale: "let sum = x . then , s . i . = 4 x / 5 , time = 10 years . rate = ( 100 * 4 x ) / ( x * 5 * 10 ) = 8 % answer : c"
Answer: c
Python program:
a = 4 / 5
b = a * 100
c = b / 10
Problem: the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length of this rectangle .
Options: a ) 40 , b ) 70 , c ) 20 , d ) 80 , e ) 60
Rationale: "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c"
Answer: c
Python program:
a = 70 / 2
b = 70 / 2
c = 70 / 2
d = b * c
e = 4 * 300
f = d - e
g = math.sqrt(f)
h = a - g
i = h / 2
Problem: a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 1 km , b ) 1.5 km , c ) 5 km , d ) 3.2 km , e ) 2.4 km
Rationale: speed of down stream = 5 + 1 = 6 kmph speed of upstream = 5 - 1 = 4 kmph let the required distance be xkm x / 6 + x / 4 = 1 2 x + 3 x = 12 x = 2.4 km answer is e
Answer: e
Python program:
a = 5 - 1
b = a * 3
c = b / 5
Problem: a sum fetched a total simple interest of $ 4106.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8927
Rationale: "e 8927 principal = $ 100 x 4106.25 / 9 x 5 = $ 410625 / 45 = $ 8927 ."
Answer: e
Python program:
a = 4106 * 25
b = a / 9
c = b / 5
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 75 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1733.33 , d ) 1800 , e ) 2025
Rationale: 300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 75 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 75 = 1733.33 c is the answer
Answer: c
Python program:
a = 300 * 100
b = a / 30
c = b + 300 
d = 75 / 100
e = c / d
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 45 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 928 , d ) $ 870 , e ) $ 660
Rationale: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 145 % of $ 640 = $ 928 . c"
Answer: c
Python program:
a = 832 + 448 
b = a / 2
c = b * 45
d = c / 100
e = 832 + 448 
f = e / 2
g = d + f
Problem: a motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . his average speed for the whole journey in km / hr is ?
Options: a ) 37.9 , b ) 37.53 , c ) 37.5 , d ) 37.1 , e ) 37.4
Rationale: explanation : average speed = ( 2 xy ) / ( x + y ) km / hr = ( 2 * 50 * 30 ) / ( 50 + 30 ) km / hr . 37.5 km / hr . answer : c
Answer: c
Python program:
a = 50 * 30
b = 2 * a
c = 50 + 30 
d = b / c
Problem: 4685 * 999
Options: a ) 4680250 , b ) 4685850 , c ) 4680315 , d ) 4685975 , e ) none of these
Rationale: "explanation : 4685 * ( 1000 - 1 ) = 4685000 - 4685 = 4680315 option c"
Answer: c
Python program:
a = 4685 / 999
b = a * 100
Problem: 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 5 like all . how many people like apple ?
Options: a ) 48 , b ) 46 , c ) 54 , d ) 58 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 5 40 + 10 + 5 - 7 = 48 like apple answer : a"
Answer: a
Python program:
a = 40 - 3
b = a + 7 
c = 10 - 7
d = b + c
Problem: a textile manufacturing firm employees 56 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 56 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 ) 6250 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 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 ã — ( 55 / 56 ) â ˆ ’ 150000 ã — ( 55 / 56 ) â ˆ ’ 75000 . = > rs 2 , 68,750 decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 68,750 = > rs . 6,250 answer : b"
Answer: b
Python program:
a = 5 * 1000
b = a * 100
c = 75000 * 2
d = c + 75000 
e = b - d
f = 56 - 1
g = f / 56
h = 5 * 1000
i = h * 100
j = g * i
k = 75000 * 2
l = 56 - 1
m = l / 56
n = k * m
o = j - n
p = o - 75000
q = e - p
Problem: a factory produces 5505 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 1101 toys , d ) 2354 toys , e ) 1375 toys
Rationale: to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 5505 / 5 = 1101 toys correct answer c
Answer: c
Python program:
a = 5505 / 5
Problem: 8 men , working 8 hours a day can complete a work in 24 days . how many hours a day must 12 men work to complete the same work in 16 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 8 * 24 = 1536 12 × 16 × ( x ) = 1536 x = 8 the answer is c ."
Answer: c
Python program:
a = 8 * 8
b = a * 24
c = 12 * 16
d = b / c
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 9 , 1 ) , ( 1 , 1 ) , ( 1 , - 8 ) and ( - 9 , - 8 ) ?
Options: a ) 72 , b ) 180 , c ) 70 , d ) 90 , e ) 140
Rationale: "length of side 1 = 9 + 1 = 10 length of side 2 = 8 + 1 = 9 area of rectangle = 10 * 9 = 90 d is the answer"
Answer: d
Python program:
a = 9 + 1 
b = 1 + 8 
c = a * b
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 1 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 14 / 19 , e ) 1 / 2
Rationale: "# of basic stereos was 1 / 3 of total and # of deluxe stereos was 2 / 3 of total , let ' s assume total = 15 , then basic = 5 and deluxe = 10 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 5 * 1 = 5 and total time for deluxe would be 10 * 7 / 5 = 14 - - > total time for both of them would be 5 + 14 = 19 - - > deluxe / total = 14 / 19 . answer : d ."
Answer: d
Python program:
a = 3 + 1 
b = a / 10
Problem: a train is 460 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 48 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 460 + 140 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : d"
Answer: d
Python program:
a = 460 + 140 
b = 45 * 1000
c = b / 3600
d = a / c
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 6 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 135 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 6 ) * 270 = 45 gallons total paint used = 135 gallons . option b"
Answer: b
Python program:
a = 360 / 4
b = a * 1
c = 360 / 4
d = c * 1
e = 360 - d
f = e / 6
g = b + f
Problem: a train 100 m long crosses a platform 180 m long in 14 sec ; find the speed of the train ?
Options: a ) 72 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph
Rationale: "d = 100 + 180 = 280 t = 14 s = 280 / 14 * 18 / 5 = 72 kmph answer : a"
Answer: a
Python program:
a = 180 * const_0_2778
b = 14 * a
c = b - 100
Problem: a meal cost $ 48.75 adn there was no tax . if the tip was more than 5 pc but less than 20 pc of the price , then the total amount paid should be :
Options: a ) 60 - 65 , b ) 55 - 58 , c ) 51 - 59 , d ) 39 - 41 , e ) 38 - 40
Rationale: "5 % ( 48.75 ) = 2.4375 20 % ( 48.75 ) = 9.75 total amount could have been 48.75 + 2.4375 and 48.75 + 9.75 = > could have been between 51.1875 and 58.5 = > approximately between 51 and 59 answer is c ."
Answer: c
Python program:
a = 48 * 75
b = a / 100
c = b + 48
Problem: on a map , 1 inch represents 28 miles . how many c inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "c inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Python program:
a = 383 / 6
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples f did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons f = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Python program:
a = 10 + 10 
b = a + 2 
c = 1430 / b
d = c + 45 
e = 1430 / d
f = e + 9
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1232 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 1232 = > x = 14 answer : c"
Answer: c
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 1232 / g
Problem: what is the volume of an tetrahedron with edge length of 1 ?
Options: a ) 3.11545466
b ) 0.76678113
c ) 0.11785113
d ) 2.11785113
e ) 0.11786667
Rationale: the answer is sqr ( 2 ) / 12 = 0.11785113 the following can be derived using the pythagorean theorem : the height of a face is 3.5 / 2 . the area of any face is 3.5 / 4 . the distance from any corner to the center of a joining face is 1 / 3.5 . the height of the tetrahedron is ( 2 / 3 ) . 5 the area is 1 / 3 * base * height = ( 1 / 3 ) * 3.5 / 4 * ( 2 / 3 ) . 5 = 21 / 2 / 12 . the above cube has sides of length 1 / sqr ( 2 ) . the area formed by the diagonals along four of the faces as shown in the diagram is a tetrahedrom . left over are four pyramids . the base of each pyramid is half of the side of the cube and the height is the height of the cube . thus the area of each pyramid is : 1 / 2 * ( 1 / sqr ( 2 ) ) 2 * 1 / sqr ( 2 ) * 1 / 3 = ( 12 * sqr ( 2 ) ) - 1 the total area of the cube is ( 1 / sqr ( 2 ) ) 3 = ( 2 * sqr ( 2 ) ) - 1 the area of the tetrahedrom is thus ( 2 * sqr ( 2 ) ) - 1 - 4 * ( 12 * sqr ( 2 ) ) - 1 = 3 / ( 6 * sqr ( 2 ) ) - 2 / ( 6 * sqr ( 2 ) ) = 1 / ( 6 * sqr ( 2 ) ) = sqr ( 2 ) / 12 correct answer c
Answer: c
Python program:
a = math.sqrt(2)
b = 10 + 2 
c = a / b
Problem: an exam consists of 2 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 1 / 16 . a"
Answer: a
Python program:
a = 1 / 2
b = a ** 2
c = 1 / 2
d = c ** 2
e = 2 * d
f = b + e 
g = 2 * 3
h = 1 / 2
i = h ** 2
j = g * i
k = f + j 
l = 1 - k
m = l / 10
n = 1 / 2
o = n ** 2
p = 1 / 2
q = p ** 2
r = 2 * q
s = o + r 
t = 2 * 3
u = 1 / 2
v = u ** 2
w = t * v
x = s + w 
y = 1 - x
z = m + y
Problem: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 28 years . find the average age of the women ?
Options: a ) 87 , b ) 98 , c ) 32 , d ) 28 , e ) 37
Rationale: "20 + 28 + 8 * 2 = 64 / 2 = 32 answer : c"
Answer: c
Python program:
a = 20 + 28 
b = 8 * 2
c = a + b 
d = c / 2
Problem: a girl was riding her scooter . her father wanted to calculate her speed . he knew that the street was 600 meters from end to end . he saw his daughter make the roundtrip 6 times . it took her 20 minutes to complete those 6 trips . how fast was the girl riding her scooter in kilometers per hour ?
Options: a ) 2 , b ) 2.4 , c ) 1.2 , d ) 2.1 , e ) 2.7
Rationale: the distance of the street was 600 meters . the made the roundtrip 6 times , which would be 2 trips for each roundtrip . multiply 12 times 600 to get the total distance . 600 * 12 = 7200 meters of 7.2 km . the question asked for the speed in km / hour and 20 minutes is one third of an hour . multiply 7200 by 1 / 3 to get approximately 2400 meters . correct answer is b
Answer: b
Python program:
a = 600 * 6
b = a / 1000
c = 20 / const_60
d = b / c
e = d - 1
f = e / 4
Problem: the ratio of two quantities is 2 : 3 . if each of the quantities is increased by 6 , what is the ratio of the new quantities ?
Options: a ) 2 : 3 , b ) 6 : 7 , c ) 8 : 9 , d ) 8 : 3 , e ) it can not be determined from the information given
Rationale: "let quantities are 2 x and 3 x ratio of quantities after each is increased by 6 = ( 2 x + 6 ) / ( 3 x + 6 ) for x = 1 , ( 2 x + 6 ) / ( 3 x + 6 ) = 8 / 9 for x = 2 , ( 2 x + 6 ) / ( 3 x + 6 ) = 10 / 12 the value of final expression is dependent on the value of x which ca n ' t be determined as per given information . hence , the answer can not be determined answer : option e"
Answer: e
Python program:
a = 2 + 6 
b = 3 + 6 
c = a / b
Problem: a rower whose speed is 2.5 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 0.5 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 2.2 , b ) 2.3 , c ) 2.4 , d ) 2.5 , e ) 2.6
Rationale: time upstream = d / 2 time downstream = d / 3 total time = d / 2 + d / 3 = 5 d / 6 average speed = 2 d / ( 5 d / 6 ) = 2.4 km / hr the answer is c .
Answer: c
Python program:
a = 2 - 5
b = 2 + 5 
c = a + b 
d = c / 2