euclaise/mathqa_programs huggingface dataset:
Problem: in an examination , a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 30 questions and secures 130 marks , the no of questions he attempts correctly is :
Options: a ) a ) 35 , b ) b ) 40 , c ) c ) 90 , d ) d ) 88 , e ) e ) 37
Rationale: let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 3 x – ( 30 – x ) = 130 = > 4 x = 160 = > x = 40 answer : b
Answer: b
Python program:
a = 130 + 30 
b = 3 + 1 
c = a / b
Problem: a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 2.3 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 2.0 , b ) 2.5 , c ) 3.0 , d ) 3.5 , e ) 4.0
Rationale: 72 km / hr = 1.2 km / min the total distance is 2.4 km . 2.4 / 1.2 = 2 minutes the answer is a .
Answer: a
Python program:
a = 100 / 1000
b = 2 + 3 
c = b / 72
d = c * const_60
Problem: a garrison of 2000 men has provisions for 40 days . at the end of 20 days , a reinforcement arrives , and it is now found that the provisions will last only for 10 days more . what is the reinforcement ?
Options: a ) 1888 , b ) 2766 , c ) 2999 , d ) 2000 , e ) 1712
Rationale: 2000 - - - - 40 2000 - - - - 20 x - - - - - 10 x * 10 = 2000 * 20 x = 4000 2000 - - - - - - - 2000 answer : d
Answer: d
Python program:
a = 2000 * 40
b = 2000 * 20
c = a - b
d = c / 10
e = d - 2000
Problem: five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 seconds respectively . in 20 minutes , how many times do they toll together ?
Options: a ) 11 , b ) 10 , c ) 15 , d ) 16 , e ) 17
Rationale: "l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 20 min they will toll 10 times . as they have initially tolled once , the answer will be 10 + 1 = 11 . answer : a"
Answer: a
Python program:
a = 2 + 3 
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / 10
g = 10 / f
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 600 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 90 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 600 . 6 ( 85 - g ) + 7 g = 600 . 510 - 6 g + 7 g = 600 . g = 600 - 510 = 90 . the answer is b ."
Answer: b
Python program:
a = 85 * 6
b = 600 - a
Problem: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 750 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 1160 , b ) 1190 , c ) 1220 , d ) 1250 , e ) 1280
Rationale: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 750 x = 1250 the answer is d ."
Answer: d
Python program:
a = 60 / 100
b = 750 / a
Problem: if the price of 357 apples is rs . 1517.25 , what will be the approximate price of 49 dozens of such apples
Options: a ) rs . 2500 , b ) rs . 2300 , c ) rs . 2200 , d ) rs . 1400 , e ) none of these
Rationale: "let the required price be x more apples , more price ( direct proportion ) hence we can write as apples 357 : ( 49 × 12 ) } : : 1517.25 : x ⇒ 357 x = ( 49 × 12 ) × 1517.25 ⇒ x = ( 49 × 12 × 1517.25 ) / 357 = ( 7 × 12 × 1517.25 ) / 51 = ( 7 × 4 × 1517.25 ) / 17 = 7 × 4 × 89.25 ≈ 2500 . answer a"
Answer: a
Python program:
a = 49 * 12
b = 1517 / 25
c = a * b
Problem: if 9 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 237 , c ) 387 , d ) 400 , e ) 481
Rationale: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 9 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 9 * 30 / 24 * 80 x = 400 answer : d"
Answer: d
Python program:
a = 36 * 30
b = 9 * 24
c = b / 80
d = a / c
Problem: two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 144 seconds . the length of each train is :
Options: a ) 82 m , b ) 150 m , c ) 172 m , d ) 200 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 144 secs the total distance traveled is 144 x 25 / 9 = 400 m . therefore the length of each train is = 400 / 2 = 200 m . answer d"
Answer: d
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 144
e = d / 2
Problem: if an investor puts $ 900 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 986.25 , b ) $ 988.25 , c ) $ 990.25 , d ) $ 992.25 , e ) $ 994.25
Rationale: 1.05 * 1.05 * 900 = $ 992.25 the answer is d .
Answer: d
Python program:
a = 10 / 2
b = a / 100
c = 1 + b 
d = c ** 2
e = 900 * d
Problem: if the wheel is 21 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 8 , b ) 27 , c ) 10 , d ) 7 , e ) 19
Rationale: "2 * 22 / 7 * 21 * x = 1056 = > x = 8 answer : a"
Answer: a
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 21
h = 1056 / g
Problem: for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 60 color copies at print shop y than at print shop x ?
Options: a ) $ 80 , b ) $ 90 , c ) $ 100 , d ) $ 110 , e ) $ 120
Rationale: "the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 60 * $ 1.50 = $ 90 the answer is b ."
Answer: b
Python program:
a = 2 * 75
b = 1 * 25
c = a - b
Problem: a train 180 m long running at 75 kmph crosses a platform in 40 sec . what is the length of the platform ?
Options: a ) 687 , b ) 638 , c ) 683 , d ) 726 , e ) 267
Rationale: "d = 75 * 5 / 18 = 40 = 833 â € “ 150 = 683 answer : c"
Answer: c
Python program:
a = 75 * const_0_2778
b = 40 * a
c = b - 180
Problem: a train is 327 meter long is running at a speed of 40 km / hour . in what time will it pass a bridge of 122 meter length ?
Options: a ) 32.7 , b ) 41 , c ) 50.29 , d ) 40.41 , e ) 20.28
Rationale: "speed = 40 km / hr = 40 * ( 5 / 18 ) m / sec = 100 / 9 m / sec total distance = 327 + 122 = 449 meter time = distance / speed = 449 * ( 9 / 100 ) = 40.41 seconds . answer : d"
Answer: d
Python program:
a = 327 + 122 
b = 40 * 1000
c = b / 3600
d = a / c
Problem: if x + y = 2 x - 2 z , x - 2 y = 4 z and x + y + z = 21 , what is the value of z / y ?
Options: a ) - 4.5 . , b ) - 2 . , c ) - 0.5 . , d ) 3 . , e ) 2.5 .
Rationale: "x + y = 2 x - 2 z x - y = 2 z - - - - - - - - - - 1 x - 2 y = 4 z - - - - - - - - - 2 subtracting equation 1 from equation 2 2 z = - y z / y = - 0.5 c is the answer"
Answer: c
Python program:
a = 21 * 2
Problem: if a person walks at 16 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 60 km , d ) 70 km , e ) 33.3 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 16 16 x = 10 x + 200 6 x = 200 x = 33.3 km . answer : e"
Answer: e
Python program:
a = 16 - 10
b = 20 / a
c = 10 * b
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind coe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of coe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . coe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d
Answer: d
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 2 : 4 . a has a start of 300 m . then , a wins by :
Options: a ) 60 m , b ) 20 m , c ) 43 m , d ) 20 m , e ) 100 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 300 ) m , i . e . , 200 m . while a covers 2 m , b covers 4 m . while a covers 200 m , b covers 4 x 200 / 2 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 100 m behind . a wins by 100 m . answer : e"
Answer: e
Python program:
a = 500 - 300
b = a * 4
c = b / 2
d = 500 - c
Problem: the two lines y = x and x = - 8 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "the point of intersection is ( - 8 , - 8 ) . the triangle has a base of length 8 and a height of 8 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 8 * 8 = 32 the answer is b ."
Answer: b
Python program:
a = 8 * 8
b = a / 2
Problem: a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 377.78
Rationale: "let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 60 % of total amount . so total amount = 16000 * 100 / 60 remaining amount is 40 % of total amount . 40 % of total amount = 16000 * ( 100 / 60 ) * ( 40 / 100 ) = 32000 / 3 this amount has to be divided by 60 ( remaining people are 60 ) so per head amount is 32000 / 3 / 60 = 32000 / 180 = 1600 / 9 = $ 177.78 ; answer : b"
Answer: b
Python program:
a = 40 / 100
b = a * 400
c = 60 / 100
d = b / c
e = 40 / 100
f = d * e
g = 60 / 100
h = f / g
Problem: the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ?
Options: a ) 78 , b ) 65 , c ) 58 , d ) 62 , e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 60 = 78 answer is a"
Answer: a
Python program:
a = 6 * 58
b = 6 * 65
c = a + b 
d = 11 * 60
e = c - d
Problem: each month a retailer sells 100 identical items . on each item he makes a profit of $ 30 that constitutes 16 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 157 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 16 % of the cost : sell price = cost + $ 20 sell price = $ 125 + $ 20 thus , the sell price is $ 145 for each item . selling all 100 items gives the retailer . . . 100 ( $ 20 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 145 ) = $ 7.25 discount $ 137.75 = $ 125 + $ 12.75 now , the retailer makes a profit of just $ 12.75 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 12.75 ( x ) = $ 2,000 x = 2,000 / 12.75 x = 156.8627 = 157 items a
Answer: a
Python program:
a = 100 * 30
b = 100 * 30
c = b / 16
d = c + 30 
e = d * 5
f = e / 100
g = 30 - f
h = a / g
Problem: 4 dice are thrown simultaneously on the board . find the probability show the same face .
Options: a ) 1 / 213 , b ) 1 / 215 , c ) 1 / 216 , d ) 2 / 113 , e ) 3 / 114
Rationale: "the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 × 6 × 6 × 6 = 64 = 6 × 6 × 6 × 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c"
Answer: c
Python program:
a = 3 + 3 
b = 3 / a
c = 3 + 3 
d = 3 / c
e = b * d
Problem: if a 3 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 40 % , b ) 100 % , c ) 150 % , d ) 200 % , e ) 300 %
Rationale: "the area a of the large cube is 3 * 3 * 6 = 54 square cm . the area of the 27 small cubes is 27 * 6 = 54 * 3 = 3 a , an increase of 200 % . the answer is d ."
Answer: d
Python program:
a = surface_cube * (
b = a / surface_cube
c = 100 * b
Problem: the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 5100 , b ) 5120 , c ) 5200 , d ) 5400 , e ) 6480
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 ã — 90 / 100 = 6480 answer : e"
Answer: e
Python program:
a = 10 / 100
b = 8000 * a
c = 8000 - b
d = 10 / 100
e = 8000 * d
f = 8000 - e
g = 10 / 100
h = f * g
i = c - h
Problem: jim ’ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.15 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 3.60 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 15 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 15 = 2.25 + 9 * . 15 = 3.6 $ answer c"
Answer: c
Python program:
a = 2 / 5
b = 3 / 6
c = 0 * 15
d = 2 + 25
Problem: in a certain city , 70 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 80 percent of the registered voters who are democrats and 30 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 65 % , b ) 52 % , c ) 85 % , d ) 69 % , e ) 75 %
Rationale: "say there are total of 100 registered voters in that city . thus 70 are democrats and 30 are republicans . 70 * 0.80 = 56 democrats are expected to vote for candidate a ; 30 * 0.30 = 9 republicans are expected to vote for candidate a . thus total of 56 + 9 = 65 registered voters are expected to vote for candidate a , which is 65 % of the total number of registered voters . answer : a"
Answer: a
Python program:
a = 80 / 100
b = 70 * a
c = 100 - 70
d = 30 / 100
e = c * d
f = b + e
Problem: a and b can do a piece of work in 7 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 9 1 / 3 , c ) 30 , d ) 88 , e ) 11
Rationale: "c = 1 / 4 â € “ 1 / 7 = 3 / 28 = > 28 / 3 = 9 1 / 3 days answer : b"
Answer: b
Python program:
a = 4 / 7
b = 4 - a
c = 1/(b)
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 80 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 26 % , e ) 80 %
Rationale: "the actual answer is obtained by multiplying 180 % by 70 % and subtracting 100 % from this total . that is : 180 % × 70 % = 126 % ; 126 % − 100 % = 26 % . answer : d"
Answer: d
Python program:
a = 80 / 100
b = 1 + a 
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: pipe a can fill a tank in 16 hrs and pipe b can fill it in 24 hrs . if both the pipes are opened in the empty tank . in how many hours will it be fill 5 / 4 th of that tank ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: part filled a in 1 hr = ( 1 / 16 ) part filled b in 1 hr = ( 1 / 24 ) part filled by ( a + b ) together in 1 hr = ( 1 / 16 ) + ( 1 / 24 ) = 5 / 48 so , the tank will be full in 48 / 5 hrs time taken to fill exact quarter tank = ( 48 / 5 ) * ( 5 / 4 ) = 12 hrs answer : b
Answer: b
Python program:
a = 1 / 16
b = 1 / 24
c = a + b 
d = 1/(c)
e = d / 4
f = e * 5
Problem: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 504 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 2778 , d ) 4200 , e ) 2791
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 504 = > 36 x / 100 - 24 x / 100 = 504 = > 12 x / 100 = 840 = > x = 4200 . answer : d"
Answer: d
Python program:
a = 18 - 12
b = a * 2
c = b / 100
d = 504 / c
Problem: the average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 99 , d ) 38 , e ) 27
Rationale: "total age increased = ( 8 * 2 ) years = 16 years . sum of ages of two new men = ( 21 + 23 + 16 ) years = 60 years average age of two new men = ( 60 / 2 ) years = 30 years . answer : b"
Answer: b
Python program:
a = 21 + 23 
b = a / 2
c = 1 * 8
d = b + c
Problem: a boy traveled from the village to the post - office at the rate of 12.5 kmph and walked back at the rate of 2 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village .
Options: a ) 5 km , b ) 7 km , c ) 9 km , d ) 10 km , e ) 12 km
Rationale: explanation : solution : average speed = 2 xy / ( x + y ) km / hr = ( 2 * 12.5 * 2 ) / ( 12.5 + 2 ) km / hr = 50 / 14.5 km / hr . total distance = ( 50 / 14.5 * 29 / 5 ) km . = 20 km . required distance = 20 / 2 = 10 km . answer : d
Answer: d
Python program:
a = 48 / const_60
b = 5 + a 
c = 12 * 5
d = c * 2
e = 12 + 5 
f = d / e
g = b * f
h = g / 2
Problem: the sum of the numbers is 177 . if the ratio between the first and the second be 5 : 3 and that between the second and third be 4 : 9 , then find the second number ?
Options: a ) 12 , b ) 20 , c ) 45 , d ) 60 , e ) 52
Rationale: "given ratios 5 : 3 4 : 9 20 : 12 : 27 the second number = 177 / ( 20 + 12 + 27 ) * 15 = 45 answer is c"
Answer: c
Python program:
a = math.lcm(3, 4)
b = 177 * a
c = 9 * 3
d = 4 * 5
e = 4 * 3
f = d + e 
g = c + f 
h = b / g
Problem: a green lizard can travel from the green cave to the blue cave in 108 minutes ; the blue lizard can travel from the blue cave to the green cave in 25 % less time . if the green lizard started to travel 7.5 minutes before the blue lizard , how many minutes after the blue lizard , will the green lizard pass the middle line ?
Options: a ) 2 . , b ) 3.5 . , c ) 4 . , d ) 5.5 . , e ) 6 .
Rationale: time take by the green lizard to cover the distance between the caves = 108 mins time take by the green lizard to cover half the distance = 108 / 2 = 54 mins time take by the blue lizard to cover the distance between the caves = 108 x 3 / 4 = 81 mins time take by the blue lizard to cover half the distance = 81 / 2 = 40.5 mins now the green lizard had been travelling for 7.5 mins when the blue lizard started . therefore when the blue lizard starts to move the green lizard will have to cover 54 - 7.5 = 46.5 mins worth of distance at its current speed . difference in time when they both reach the mid point = 46.5 - 40.5 = 6 mins . e is the correct answer .
Answer: e
Python program:
a = 108 / 2
b = a - 7
c = 3 / 4
d = 108 * c
e = d / 2
f = b - e
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 16 , and 18 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 144 / 17 , e ) 11 / 4
Rationale: "p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 16 + 1 / 18 = 17 / 144 therefore they take 144 / 17 ratio = 144 / 17 = d"
Answer: d
Python program:
a = 1 / 16
b = 1 / 18
c = a + b 
d = 1 / c
e = 12 / d
Problem: the first year , two cows produced 8100 litres of milk . the second year their production increased by 15 % and 10 % respectively , and the total amount of milk increased to 9100 litres a year . how many litres were milked from each cow each year ?
Options: a ) 3472 , b ) 8222 , c ) 4370 , d ) 26777 , e ) 8222
Rationale: let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 − x ) ( 8100 − x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % 15 % or 10 % 10 % . so 8100 + 15100 ⋅ x + 10100 ⋅ ( 8100 − x ) = 91008100 + 15100 ⋅ x + 10100 ⋅ ( 8100 − x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 − x ) = 91008100 + 320 x + 110 ( 8100 − x ) = 9100 120 x = 190120 x = 190 x = 3800 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , respectively . answer : c
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b * 8100
d = 9100 - c
e = 15 / 100
f = 1 + e 
g = 10 / 100
h = 1 + g 
i = f - h
j = d / i
k = 8100 - j
Problem: sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 2.5 per pound , and german chocolate cost $ 1.5 per pound . if the total the she spent on chocolate was $ 15 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "if there were all the expensive ones 2.5 . . . . there would be 15 / 2.5 or 6 of them but since 1.5 $ ones are also there , answer has to be > 6 . . . . if all were 1.5 $ ones , there will be 15 / 1.5 or 10 . . . so only 8 is left ans b . ."
Answer: b
Python program:
a = 2 + 5 
b = a / 2
c = 15 / b
Problem: an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 2 ) will be divisible by 3 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: n ( n + 2 ) to be divisible by 3 either n or n + 2 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 1 , or 3 . thus , the overall probability is 2 / 3 . answer : d .
Answer: d
Python program:
a = 99 / 3
b = a / 99
c = b * 2
Problem: find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 15 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 15 = 1485 answer : d"
Answer: d
Python program:
a = 3 / 2
b = volume_cylinder * (
Problem: a car started running at a speed of 28 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 37 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 37 km the total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in ap whose first term is 28 and last term is 46 = 10 / 2 [ 28 + 46 ] = 370 km ."
Answer: a
Python program:
a = 2 * 10
b = 28 + a 
c = b + 28 
d = c / 2