euclaise/mathqa_programs huggingface dataset:
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 3 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 3 and m + 2 = 2 * ( n + k ) + 3 . by 1 st equation we have m - 2 n = 3 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 3 = 2 k + 1 - - - > k = 1 . the answer is , therefore , ( b ) ."
Answer: b
Python program:
a = 3 + 2 
b = a - 3
c = b / 2
Problem: when positive integer x is divided by positive integer y , the remainder is 5 . if x / y = 96.2 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.2 and remainder is 5 so . 2 x y = 5 hence y = 25 ans d"
Answer: d
Python program:
a = math.floor(96, 2)
b = 96 - 2
c = 5 / b
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 3.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5040 , c ) 2889 , d ) 2870 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 3.5 = 5040 . answer : b"
Answer: b
Python program:
a = 8 * const_60
b = 3 * 5
c = 8 * const_60
d = 6 * const_60
e = c / d
f = e - 1
g = b / f
Problem: what is the greater of the two numbers whose product is 2048 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) a ) 90 , b ) b ) 32 , c ) c ) 64 , d ) d ) 70 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2048 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2048 / s = 64 . answer : c"
Answer: c
Python program:
a = 2 ** 4
b = a * 2
c = 2048 / b
Problem: a can finish a work in 6 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 2 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 6 b ' s 1 day work = 1 / 3 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 6 + 1 / 3 ) = 1 / 2 so in one day 1 / 2 work will be done answer : a"
Answer: a
Python program:
a = 1 / 6
b = 1 / 6
c = b * 2
d = a + c
Problem: a car averages 35 miles per hour for the first 4 hours of a trip and averages 53 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 50 miles per hour , how many hours long is the trip ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let t be the total time of the trip . 35 * 4 + 53 ( t - 4 ) = 50 t 3 t = 212 - 140 t = 24 the answer is e ."
Answer: e
Python program:
a = 50 * 4
b = 35 * 4
c = a - b
d = 53 - 50
e = c / d
f = e + 4
Problem: 8 men , working 9 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 * 9 * 24 = 1728 12 × 16 × ( x ) = 1728 x = 9 the answer is d ."
Answer: d
Python program:
a = 8 * 9
b = a * 24
c = 12 * 16
d = b / c
Problem: the speed of a boat in still water is 24 kmph . what is the speed of the stream if the boat can cover 64 km downstream or 32 km upstream in the same time ?
Options: a ) 8 kmph , b ) 6 kmph , c ) 7 kmph , d ) 5 kmph , e ) 4 kmph
Rationale: "x = the speed of the stream ( 24 + x ) / ( 24 - x ) = 2 / 1 24 + x = 48 - 2 x 3 x = 24 x = 8 km / hour if the speed of the stream is 8 km / hour , then the ' downstream ' speed of the boat is 24 + 8 = 32 km / hour and the ' upstream ' speed of the boat is 24 - 8 = 16 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 32 = 64 km downstream and 2 x 16 = 32 km / hour upstream . answer : a"
Answer: a
Python program:
a = 1 + 2 
b = 24 / a
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number m is
Options: a ) 74 , b ) m = 75 , c ) m = 175 , d ) m = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Python program:
a = 34 * 2
b = 34 * 2
c = 8 * 5
d = b - c
e = 5 - 1
f = d / e
g = a + f
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 15 % food additives ; 19 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 72 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 15 % food additives ; 19 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 15 + 19 + 8 ) = 20 % basic astrophysics . 10 % of 360 ° is 72 ° . answer : e ."
Answer: e
Python program:
a = 14 + 24 
b = a + 15 
c = b + 19 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 36 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 36 = 6 k + 4 p = > k = 4 , p = 3 total red ' s in bag a will be 2 k = 8 e"
Answer: e
Python program:
a = 3 * 2
b = a + 4 
c = 36 / b
Problem: when asked what the time is , a person answered that the amount of time left is 1 / 2 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 4 pm , e ) 6 pm
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 1 / 2 x ⇒ x = 16 time is 4 pm answer : d"
Answer: d
Python program:
a = 1 * 12
b = 1 * 12
c = 1 / 2
d = c + 1 
e = b / d
f = a - e
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 500 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 500 km in = 500 / 50 * 1 = 10 hours answer is a"
Answer: a
Python program:
a = 500 / 50
Problem: in a renowned city , the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 345,600 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 8 persons are added ( 10 - 2 ) . every second 4 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 4 = 345600 option c"
Answer: c
Python program:
a = 10 - 2
b = a * 3600
c = b * 12
Problem: two employees m and n are paid a total of $ 616 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 270 , b ) $ 280 , c ) $ 290 , d ) $ 300 , e ) $ 310
Rationale: "1.2 n + n = 616 2.2 n = 616 n = 280 the answer is b ."
Answer: b
Python program:
a = 120 / 100
b = a + 1 
c = 616 / b
Problem: in town x , 64 percent of the population are employed , and 38 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 38 are employed males , hence 26 % are employed females . ( employed females ) / ( total employed people ) = 26 / 64 = 40 % answer : d ."
Answer: d
Python program:
a = 64 - 38
b = a / 64
c = b * 100
Problem: there were two candidates in an election . winner candidate received 55 % of votes and won the election by 100 votes . find the number of votes casted to the winning candidate ?
Options: a ) 550 , b ) 744 , c ) 255 , d ) 199 , e ) 231
Rationale: "w = 55 % l = 45 % 55 % - 45 % = 10 % 10 % - - - - - - - - 100 55 % - - - - - - - - ? = > 550 answer : a"
Answer: a
Python program:
a = 100 - 55
b = 55 - a
c = b / 100
d = 100 / c
e = d * 55
f = e / 100
Problem: 5 friends adi , brian , close , derek and eli appeared in two aptitude tests . in the first aptitude test , derek score 50 % less than the average score of the 5 people . in the second aptitude test , derek score 50 % more than what he scored on the first aptitude test . if the score of his friend in the second aptitude test were same as their score in the first test , by approximately what percentage was derek ' s score less than the average score of the 5 people in the second aptitude ?
Options: a ) 25 % , b ) 28 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: average score in first test be x so derby score = 0.5 x ( first test ) derby score = 1.5 ( 0.5 x ) ( second test ) = . 75 x so less than x by . 25 answer a 25 %
Answer: a
Python program:
a = 5 * 5
b = 50 * a
c = b / 50
Problem: an escalator moves towards the top level at the rate of 12 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 8 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 10 sec , b ) 8 sec , c ) 9 sec , d ) 7 sec , e ) 12 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 12 + 8 ) = 8 sec answer : b"
Answer: b
Python program:
a = 12 + 8 
b = 160 / a
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 41 then sum is
Options: a ) s . 5000 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 4100
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 41 4100 answer : e"
Answer: e
Python program:
a = 10 / 100
b = 10 / 100
c = a * b
d = 41 / c
Problem: a leak in the bottom of a tank can empty the full tank in 4 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 2160 , e ) none
Rationale: solution work done by the inlet in 1 hour = ( 1 / 4 - 1 / 12 ) = 1 / 6 . work done by the inlet in 1 min . = ( 1 / 6 × 1 / 60 ) = 0.002778 volume of 0.002778 part = 6 litres . therefore , volume of whole = ( . 002778 × 6 ) ‹ = › 2160 litres . answer d
Answer: d
Python program:
a = 12 * const_60
b = 6 * a
c = 12 * const_60
d = 4 * const_60
e = c / d
f = e - 1
g = b / f
Problem: a can run 224 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 15 metre , e ) 28 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 224 / 32 = 28 / 4 = 7 m / sdistance covered by b in 4 seconds = speed × time = 7 × 4 = 28 metre i . e . , a beat b by 28 metre answer is b"
Answer: b
Python program:
a = 224 / 32
b = a * 28
c = 224 - b
Problem: in the manufacture of a certain product , 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.32 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 8 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 8 / 100 ) * 100 % = ( 32 / 10000 ) * 100 % = ( 32 / 100 ) % = . 32 % answer b"
Answer: b
Python program:
a = 4 / 100
b = 8 * a
Problem: $ 700 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 280 , e ) $ 250
Rationale: a : ( b + c ) = 2 : 3 a ' s share = 700 * 2 / 5 = $ 280 answer is d
Answer: d
Python program:
a = 2 / 3
b = a + 1 
c = 700 / b
d = 2 / 3
e = c * d
Problem: the number of boxes in a warehouse can be divided evenly into 12 equal shipments by boat or 32 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 96 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 12 and 32 = 96 answer c"
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 3
d = c * 12
Problem: the salary of a worker is first increased by 20 % and afterwards reduced by 20 % . what is the net change in the worker ' s salary ?
Options: a ) 4 % decrease , b ) 8 % decrease , c ) 4 % increase , d ) 8 % increase , e ) no change
Rationale: "let x be the original salary . the final salary is 0.8 ( 1.2 x ) = 0.96 x the answer is a ."
Answer: a
Python program:
a = 20 + 100 
b = 20 + 100 
c = b * 20
d = c / 100
e = a - d
f = 100 - e
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 37 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 148 mins , b ) 140 mins , c ) 136 mins , d ) 132 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 37 = > 4 / x = 1 / 37 x = 37 ∗ 4 = 148 mins option a"
Answer: a
Python program:
a = 1 + 4 
b = a * 37
Problem: the average age of applicants for a new job is 31 , with a standard deviation of 5 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 11 , b ) 14 , c ) 15 , d ) 18 , e ) 30
Rationale: within one standard deviation of the average age means 31 + / - 7 26 - - 31 - - 36 number of dif . ages - 26 27 28 29 30 31 32 33 34 35 36 total = 11 a
Answer: a
Python program:
a = 5 * 2
b = a + 1
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 78 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2600 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 78 1 percent for 1 year = 26 = > 100 percent = 2600 answer : b"
Answer: b
Python program:
a = 78 / 3
b = a * 100
Problem: what is the dividend . divisor 16 , the quotient is 6 and the remainder is 2
Options: a ) 86 , b ) 87 , c ) 88 , d ) 89 , e ) 90
Rationale: "c = d * q + r c = 16 * 6 + 2 c = 86 + 2 c = 88"
Answer: c
Python program:
a = 16 * 6
b = a + 2
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 8 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 8 / 15 , e ) 1 / 15
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 8 = 280 remaining work is 300 - 280 = 20 remaining fraction of work is = 20 / 300 = 1 / 15 answer e"
Answer: e
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = c * 8
e = 1 - d
Problem: in a college the ratio of the numbers of boys to the girls is 5 : 7 . if there are 140 girls , the total number of students in the college is ?
Options: a ) 200 , b ) 240 , c ) 160 , d ) 250 , e ) 310
Rationale: "let the number of boys and girls be 5 x and 7 x then , 7 x = 140 x = 20 total number of students = 12 x = 12 * 20 = 240 answer is b"
Answer: b
Python program:
a = 5 / 7
b = a * 140
c = b + 140
Problem: 62467 × 9998 = ?
Options: a ) 624545037 , b ) 627745452 , c ) 624545077 , d ) 624545066 , e ) 625454211
Rationale: "d 624545066 62467 × 9998 = 62467 × ( 10000 - 2 ) = 62467 × 10000 - 62467 × 2 = 624670000 - 124934 = 624545066"
Answer: d
Python program:
a = 62467 / 9998
b = a * 100
Problem: a boat takes 38 hours for travelling downstream from point a to point b and coming back to point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 240 km , b ) 120 km , c ) 360 km , d ) 180 km , e ) none of these
Rationale: "explanation : velocity of the stream = 4 kmph speed of the boat in still water is 14 kmph speed downstream = ( 14 + 4 ) = 18 kmph speed upstream = ( 14 - 4 ) = 10 kmph let the distance between a and b be x km time taken to travel downstream from a to b + time taken to travel upstream from b to c ( mid of a and b ) = 38 hours ⇒ x / 18 + ( x / 2 ) 10 = 38 ⇒ x / 18 + x / 20 = 38 ⇒ 19 x / 180 = 38 ⇒ x / 180 = 2 ⇒ x = 360 i . e . , the distance between a and b = 360 km . answer : option c"
Answer: c
Python program:
a = 14 + 4 
b = 1 / a
c = 14 - 4
d = c * 2
e = 1 / d
f = b + e 
g = 38 / f
Problem: a boatman goes 3 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour 7 min , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 3 / 1 = 3 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 3 + 6 ) = 4.5 kmhr time taken in stationary = 5 / 4.5 = 1 hrs 7 min answer : b"
Answer: b
Python program:
a = 1 / 10
b = a * const_60
c = 3 / 3
d = b + c 
e = d / 2
f = 5 / e
Problem: 30 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 32 , c ) 45 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 30 ã — 13.5 = 405 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 405 â  „ 9 = 45 answer c"
Answer: c
Python program:
a = 13 * 5
b = a / 9
Problem: a man two flats for $ 675958 each . on one he gains 14 % while on the other he loses 14 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.96 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 14 / 10 ) ^ 2 = 49 / 25 = 1.96 % answer is a"
Answer: a
Python program:
a = 100 + 14 
b = 100 / a
c = b * 675958
d = 100 - 14
e = 100 / d
f = e * 675958
g = c + f 
h = 675958 + 675958 
i = g - h
j = 100 + 14 
k = 100 / j
l = k * 675958
m = 100 - 14
n = 100 / m
o = n * 675958
p = l + o 
q = i / p
r = q * 100
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 20 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 18 sec , c ) 12 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 80 + 20 = 100 * 5 / 18 = 250 / 9 t = 500 * 9 / 250 = 18 sec answer : option b"
Answer: b
Python program:
a = 80 * const_0_2778
b = 250 / a
Problem: how many pairs ( r , r + 1 ) have one or more prime factors common , where r is an integer and 2 ≤ r ≤ 9 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: r and r + 1 are consecutive integers . two consecutive integers are co - prime , which means that they do n ' t share any common factor but 1 . for example 20 and 21 are consecutive integers , thus only common factor they share is 1 . answer : a .
Answer: a
Python program:
a = 1 - 1
Problem: walking at 4 / 5 of his usual speed a man is 10 mins too late . find his usual time .
Options: a ) 81 mins , b ) 64 mins , c ) 52 mins , d ) 40 mins , e ) none
Rationale: "speed = s , time = t , 4 / 5 s * ( t + 10 ) = st t = 40 answer : d"
Answer: d
Python program:
a = 10 * 4
b = a / 5
c = b * 5
d = c * 2
e = d / const_60
Problem: tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 7 weeks have been $ 406 , $ 413 , $ 420 , $ 436 , $ 395 , $ 410 , $ 360 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average weekly income to $ 400 over the 9 - week period ?
Options: a ) $ 360 , b ) $ 380 , c ) $ 430 , d ) $ 290 , e ) $ 520
Rationale: official solution : ( b ) first , we need to add up the wages over the past 7 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 + $ 410 + $ 360 = $ 2840 . to average $ 400 over 9 weeks , the salesman would need to earn : $ 400 × 9 = $ 3600 . subtract $ 2840 from $ 3600 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 9 weeks : $ 3600 – $ 2840 = $ 760 . dividing $ 760 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 760 / 2 = $ 380 . the correct answer is choice ( b ) .
Answer: b
Python program:
a = 400 * 9
b = 406 + 413 
c = b + 420 
d = c + 436 
e = d + 395 
f = e + 410 
g = f + 360 
h = a - g
i = h / 2
Problem: a furniture manufacturer has two machines , but only one can be used at a time . machine q is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine q can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
Options: a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7
Rationale: machine q finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of q = 5 shifts / day rate of b = 4 shifts / day rate of ( q + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d
Answer: d
Python program:
a = 12 * 2
b = 1 / a
c = 15 * 2
d = 1 / c
e = b + d 
f = 12 * 2
g = 1 / f
h = g / 2
i = 15 * 2
j = 1 / i
k = j / 2
l = h + k 
m = e + l 
n = 1 / m