euclaise/mathqa_programs huggingface dataset:
Problem: a certain social security recipient will receive an annual benefit of $ 12000 provided he has annual earnings of $ 9360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9360 . what amount of total annual earnings would result in a 65 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,960 , e ) $ 27,360
Rationale: for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.65 * 12000 = 12000 - 7800 x = 4200 earning becomes 9360 + 3 x = 9360 + 3 * 4200 = 21960 ans : d
Answer: d
Python program:
a = 3 * 10
b = 65 - a
c = b / 100
d = c * 12000
e = 3 * d
f = e + 9360 
g = 3 * 10
h = 65 - g
i = h / 100
j = i * 12000
k = 3 * j
l = k + 9360 
m = f / l
n = m * 3600
o = n / 10
Problem: jane and ashley take 13 1 / 3 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an 8 day leave from work . this led to jane ' s working for 4 extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 10 days , b ) 15 days , c ) 16 days , d ) 17 days , e ) 20 days
Rationale: let us assume that the work is laying 40 bricks . jane = 3 bricks per day ashley = 1 brick per day together = 4 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 12 remaining bricks = 40 - 20 = 20 so together , they would take 20 / 4 = 5 total no . of days = 8 + 4 + 5 = 17 answer is d
Answer: d
Python program:
a = 1 / 3
b = 4 * a
c = 1/(b)
d = c * 40
e = d - 13
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 82 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 32
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 82 thus m = 656 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 656 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 32 ans : e"
Answer: e
Python program:
a = 90 * 8
b = 82 * 8
c = a - b
d = 92 - 90
e = c / d
Problem: if the length of the longest chord of a certain circle is 24 , what is the radius of that certain circle ?
Options: a ) 12 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 24 = 2 * 12 so radius of the circle = 12 correct answer - a"
Answer: a
Python program:
a = 24 / 2
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 4 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 ) 5768 , b ) 5760 , c ) 5762 , d ) 5766 , e ) 5712
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 answer : b"
Answer: b
Python program:
a = 8 * const_60
b = 4 * a
c = 8 * const_60
d = 6 * const_60
e = c / d
f = e - 1
g = b / f
Problem: the class mean score on a test was 60 , and the standard deviation was 10 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 30 , b ) 31 , c ) 45 , d ) 90 , e ) 20
Rationale: 1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 70 to 50 , where 70 is within sd above the mean and 50 within 1 sd below the mean 2 sd = 10 twice = 20 from the the mean , which is 80 to 40 , where 80 is within 2 sd above the mean and 20 is within 2 sd below the mean . answer = e
Answer: e
Python program:
a = 2 * 10
Problem: if an object travels at eight feet per second , how many feet does it travel in one hour ?
Options: a ) 34880 , b ) 3778 , c ) 12788 , d ) 18000 , e ) 28800
Rationale: "explanation : if an object travels at 5 feet per second it covers 5 x 60 feet in one minute , and 5 x 60 x 60 feet in one hour . answer = 28800 answer : e ) 28800"
Answer: e
Python program:
a = 3 * const_60
b = a * const_60
Problem: the ratio of buses to cars on river road is 1 to 10 . if there are 90 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 50 , b ) 40 , c ) 100 , d ) 30 , e ) 20
Rationale: "b / c = 1 / 10 c - b = 90 . . . . . . . . . > b = c - 90 ( c - 90 ) / c = 1 / 10 testing answers . clearly eliminate abde put c = 100 . . . . . . . . . > ( 100 - 90 ) / 100 = 10 / 100 = 1 / 10 answer : c"
Answer: c
Python program:
a = 10 - 1
b = 90 / a
c = b * 10
Problem: a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 57.5 % . what % discount did the merchant offer ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.575 p x = 1.575 / 1.75 = 0.9 which is a discount of 10 % . the answer is a ."
Answer: a
Python program:
a = 75 / 100
b = 1 + a 
c = b - 1
d = 57 / 5
e = c - d
f = 75 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: a certain roller coaster has 5 cars , and a passenger is equally likely to ride in any 1 of the 5 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 5 times , what is the probability that the passenger will ride in each of the 5 cars ?
Options: a ) 0 , b ) 24 / 625 , c ) 2 / 9 , d ) 1 / 3 , e ) 1
Rationale: "if he is to ride 5 times and since he can choose any of the 5 cars each time , total number of ways is = 5 * 5 * 5 * 5 * 5 = 3125 now the number of ways if he is to choose a different car each time is = 5 * 4 * 3 * 2 * 1 = 120 so the probability is = 120 / 3125 = 24 / 625 answer : b"
Answer: b
Python program:
a = math.factorial(5)
b = 1 / 5
c = b ** 5
d = a * c
Problem: jane and ashley take 10 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 10.2 days , b ) 15.2 days , c ) 16.2 days , d ) 18 days , e ) 20 days
Rationale: let us assume that the work is laying 40 bricks . jane = 4 bricks per day ashley = 1 brick per day together = 5 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 16 remaining bricks = 40 - 24 = 16 so together , they would take 16 / 5 = 3.2 total no . of days = 8 + 4 + 3.2 = 15.2 answer is b
Answer: b
Python program:
a = 1 / 10
b = 4 * a
c = 1 - b
d = 4 + 4 
e = 1 / 40
f = d * e
g = c - f
h = 1 / 10
i = 1 / 40
j = h + i 
k = g / j
l = 4 + 4 
m = k + l 
n = m + 4
Problem: if john covers a certain distance in 1 hr . 24 min . by covering two third of the distance at 4 kmph and the rest at 5 kmph , then find the total distance .
Options: a ) 9 km , b ) 2 km , c ) 1 km , d ) 6 km , e ) 7 km
Rationale: "explanation : let the total distance be y km . then , ( 2 / 3 ) y / 4 + ( 1 / 3 ) y / 5 = 7 / 5 y / 6 + y / 15 = 7 / 5 7 y = 42 y = 6 km answer : d"
Answer: d
Python program:
a = 2 / 3
b = 24 / const_60
c = 1 + b 
d = a * c
e = 4 * d
f = 2 / 3
g = 1 - f
h = 24 / const_60
i = 1 + h 
j = g * i
k = j * 5
l = e + k
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 10 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 28 , b ) 224 , c ) 320 , d ) 512 , e ) 1,600
Rationale: "you need to integers which squared are equal 10 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 stop . the integers ca n ' t be greater than 3 or we will score above 10 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 the only pair that matches is 3 ^ 2 + 1 ^ 2 = 10 . so 3 ^ 3 + 1 ^ 3 = 28 . answer a . )"
Answer: a
Python program:
a = math.gcd(10, 4)
Problem: in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 90 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ?
Options: a ) 12 % , b ) 16 % , c ) 20 % , d ) 24 % , e ) 40 %
Rationale: "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.9 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.9 x = 1.1 x the number of students in advanced trigonometry is 0.4 x the percentage in advanced trigonometry is 0.4 x / 2.5 x = 16 % the answer is b ."
Answer: b
Python program:
a = 50 * 2
b = a + 50 
c = 50 * 2
d = b + c 
e = 4 / 5
f = d * e
g = f - 90
h = 50 * 2
i = h + 50 
j = 50 * 2
k = i + j 
l = g / k
m = 50 * 2
n = l * m
Problem: a certain club has 10 members , including jarry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that jarry will be either the member chose to be secretary or the member chose to be treasurer ?
Options: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5
Rationale: in order to become a secretary the person can not be chosen as a president . this can be done in 9 / 10 ways . then to become a secretary this person ' s probability is 1 / 9 probability to become a secretary = ( 9 / 10 * 1 / 9 ) = 1 / 10 similar concept for treasurer . probability of not president = 9 / 10 , probability of not secretary = 8 / 9 , probability of treasurer 1 / 8 probability to become a treasurer = ( 9 / 10 * 8 / 9 * 1 / 8 ) = 1 / 10 since , the problem is saying jarry secretary or treasurer it is addition : 1 / 10 + 1 / 10 = 1 / 5 = e
Answer: e
Python program:
a = 1 / 10
b = 9 / 10
c = 8 / 9
d = b * c
e = 8 - 1
f = e / 8
g = d * f
h = a + g 
i = 1 - h
Problem: two dice are thrown simultaneously . what is the probability of getting two numbers whose product is not an even ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: total number of cases = 6 * 6 = 36 favourable cases = [ ( 1,3 ) , ( 1,5 ) , ( 1,1 ) , ( 3,1 ) , ( 3,3 ) , ( 3,5 ) , ( 5,1 ) , ( 5,3 ) , ( 5,5 ) ] = 9 so probability = 9 / 36 = 1 / 4 answer is b
Answer: b
Python program:
a = 3 + 3 
b = 3 / a
c = 3 + 3 
d = 3 / c
e = b * d
Problem: the difference between a number and its two - fifth is 510 . what is 40 % of that number ?
Options: a ) 342 , b ) 340 , c ) 344 , d ) 346 , e ) 348
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 40 % of 850 = 340 . answer : b"
Answer: b
Python program:
a = 4 + 1 
b = 510 * a
c = 1 + 2 
d = b / c
Problem: a and b can do a piece of work in 9 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 11.25 days , b ) 19.5 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days
Rationale: "c = 1 / 5 – 1 / 9 = 4 / 45 = > 11.25 days answer : a"
Answer: a
Python program:
a = 5 / 9
b = 5 - a
c = 1/(b)
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 123 , what is the least possible value of n ?
Options: a ) 37 , b ) 123 , c ) 41 , d ) 52 , e ) 87
Rationale: 123 is 3 * 41 , so n needs to be at least 41 , so the answer is c .
Answer: c
Python program:
a = 123 / 2
Problem: the elevator in an 11 - story office building travels at the rate of one floor per 1 / 4 minute , which allows time for picking up and discharging passengers . at the main floor and at the top floor , the operator stops for 1 minute . how many complete trips will an operator make during a 4 - hour period ?
Options: a ) 88 , b ) 56 , c ) 42 , d ) 34 , e ) 64
Rationale: complete trip = 10 floors up and 10 floors down = 20 floors = 20 * 1 / 4 = 5 minutes plus 2 minutes = 7 minutes . 4 hour = 240 minutes . in 240 minutes operator can make 240 / 7 = 34 trips . answer : d .
Answer: d
Python program:
a = 4 * const_60
b = 11 - 1
c = 11 - 1
d = b + c 
e = 1/(4)
f = d * e
g = f + 1 
h = g + 1 
i = a / h
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 30 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 4.8 miles , d ) 8 miles , e ) 6.9 miles
Rationale: "answer : e ) 6.9 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 30 / ( 5 + 30 ) = 6.9 m / hr the distance between schoolhome should be half of that . ie . 6.9 miles answer e"
Answer: e
Python program:
a = 1 / 5
b = 1 / 30
c = a + b 
d = 1 / c
e = d * const_1_6
Problem: find the product of the localvalue and absolutevalue of 7 in 20768 ?
Options: a ) 9200 , b ) 1100 , c ) 4900 , d ) 3200 , e ) 1600
Rationale: "local value of 7 = 7 x 100 = 700 place value of 7 = 7 there fore = 7 x 700 = 4900 c"
Answer: c
Python program:
a = 7 * 1000
b = a * 7
Problem: a certain no . when divided by 35 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b"
Answer: b
Python program:
a = 35 - 25
b = a - 4
c = b - 2
Problem: you have a flashlight that takes 2 working batteries . you have 8 batteries but only 4 of them work . what is the fewest number of pairs you need to test to guarantee you can get the flashlight on ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 4
Rationale: if you break the batteries into 3 groups : two groups of 3 and one group of 2 . by doing this you guarantee that one of the groups has 2 working batteries . both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination . so , 3 + 3 + 1 = 7 tries at most to find two working batteries .
Answer: c
Python program:
a = 2 + 1 
b = a * 2
c = b + 1
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ?
Options: a ) 22 , b ) 26 , c ) 25 , d ) 28 , e ) 12
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c"
Answer: c
Python program:
a = 90 * 5
b = 5 * 40
c = a - b
d = 90 - 80
e = c / d
Problem: in a certain alphabet , 16 letters contain a dot and a straight line . 30 letters contain a straight line but do not contain a dot . if that alphabet has 50 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 16 + 30 = 46 ; next , we find the total # of letters without line : 50 - 46 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 . answer : a"
Answer: a
Python program:
a = 16 + 30 
b = 50 - a
Problem: evaluate : 13 + sqrt ( - 4 + 5 ã — 3 ã · 3 ) = ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "according to order of operations , inner brackets first where 5 x 3 ã · 3 is first calculated since it has a multiplication and a division . 5 ã — 3 ã · 3 = 15 ã · 3 = 5 hence 13 + sqrt ( - 4 + 5 ã — 3 ã · 3 ) = 13 + sqrt ( - 4 + 5 ) = 13 + sqrt ( 1 ) = 13 + 1 = 14 correct answer c ) 14"
Answer: c
Python program:
a = 5 * 4
b = a / 3
c = b - 4
d = math.sqrt(c)
e = 13 + d
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 1125 in 5 years ?
Options: a ) 2 , b ) 10 , c ) 4 , d ) 5 , e ) 6
Rationale: "375 = ( 750 * 5 * r ) / 100 r = 10 % . answer : b"
Answer: b
Python program:
a = 1125 - 750
b = a / 750
c = b / 5
d = c * 100
Problem: if two positive numbers are in the ratio 1 / 6 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 20 %
Rationale: "given ratio = 1 / 6 : 1 / 5 = 5 : 6 let first number be 5 x and the second number be 9 x . the second number is more than first number by 1 x . required percentage = x / 5 x * 100 = 20 % . answer : e"
Answer: e
Python program:
a = 1 / 5
b = a * 100
Problem: given two cylindrical containers - - a and b . cylinder a has a diameter of 12 meters and a height of 10 meters . cylinder b has a radius of 2 meters and a height of 4 meters . if cylinder a is filled to capacity with water , how many cylinder b will be filled to capacity with the content of cylinder a ?
Options: a ) 23
b ) 22
c ) 21
d ) 25
e ) 24
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h cylinder a volume = 1130.97 cylinder b volume = 50.27 therefore the number of cylinders b that can be filled to capacity = 1130.97 / 50.27 = 22.5 answer is b only 22 cylinders b can be filled to capacity .
Answer: b
Python program:
a = 12 / 2
b = volume_cylinder / (
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 6000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,000
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 6000 ) solving for x , we get the shares as 16000 . ans : ( option e )"
Answer: e
Python program:
a = 5 + 6
Problem: a man bought 40 shares of rs . 60 at 5 discount , the rate of dividend being 12 % the rate of interest obtained is
Options: a ) 13.09 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 5 = rs . 55 number of shares = 40 dividend = 12 % dividend per share = 60 × 12 × 100 = rs . 7 1 / 5 total dividend = ( 40 × 7 1 / 5 ) ie , he got a dividend of ( 40 × 7 1 / 5 ) for an investment of rs . ( 40 × 55 ) interest obtained = 40 × 7 1 / 5 × 100 / 40 × 55 = 13.09 % answer : option a"
Answer: a
Python program:
a = 40 * 60
b = 12 / 100
c = a * b
d = 60 - 5
e = 40 * d
f = c / e
Problem: what is the sum of 60 consecutive integers from - 30 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 29 , c ) - 30 , d ) 30 , e ) 60
Rationale: from - 39 to - 1 - - > 30 nos . zero - - > 1 number from + 1 to + 29 - - > 29 nos . when we add up nos . from - 30 to + 29 sum will be - 30 for total 60 numbers . c is the answer .
Answer: c
Python program:
a = 30 + 1
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 18 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 5 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: answer : a 18 ° divided by 360 ° equals 0.05 , therefore the sector is equal to 5 % of the total
Answer: a
Python program:
a = 3600 / 10
b = 18 / a
c = b * 100
Problem: find two numbers whose sum is 26 and whose product is 165 .
Options: a ) 11 and 12 , b ) 11 and 13 , c ) 11 and 15 , d ) 11 and 16 , e ) 11 and 19
Rationale: let the two numbers be a and b and use the sum and product to write two equations with two unknowns a + b = 26 and a b = 165 solve the first equation for b b = 26 - a substitute b in the equation a b = 165 by 26 - a a ( 26 - a ) = 165 write the above equation in standard form - a 2 + 26 a - 165 = 0 solve the above equation for a a = 11 and a = 15 . use b = 26 - a to find b when a = 11 , b = 15 and when a = 15 , b = 11 . the two numbers are 11 and 15 . answer c
Answer: c
Python program:
a = 10 + 1 
b = a + 4 
c = b * 165
d = 10 + 1 
e = d * 165
f = c - e
g = f * 2
h = g - 165
Problem: a river 7 m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 54996.5 , b ) 32296.5 , c ) 34996.5 , d ) 34996.5 , e ) 31255.5
Rationale: "rate of water flow - 4 kmph - - 4000 / 60 - - 66.66 m / min depth of river - - 7 m width of river - - 75 m vol of water per min - - 66.66 * 7 * 75 - - - 34996.5 answer c"
Answer: c
Python program:
a = 7 * 75
b = 4 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: what is the largest 4 digit number exactly divisible by 24 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9984
Rationale: "largest 4 digit number = 9999 9999 ÷ 24 = 416 , remainder = 15 hence largest 4 digit number exactly divisible by 24 = 9999 - 15 = 9984 answer : e"
Answer: e
Python program:
a = 10 ** 4
b = a / 24
c = math.floor(b)
d = c * 24
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 110 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 220
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 110 total = 110 + 110 = 220 answer ( e )"
Answer: e
Python program:
a = 60 / 100
b = 110 * a
c = 55 / 100
d = 110 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
Problem: if k ^ 3 is divisible by 540 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "540 = 2 ^ 2 * 3 ^ 3 * 5 therefore k must include at least 2 * 3 * 5 = 30 . the answer is b ."
Answer: b
Python program:
a = 540 / 2
b = a / 2
Problem: the average weight of 8 persons increases by 1.5 kg when a person weighting 65 kg is replaced by a new person . what could be the weight of the new person ?
Options: a ) 67 kg , b ) 77 kg , c ) 87 kg , d ) 97 kg , e ) none of these
Rationale: "explanation : let the average weight of 8 persons be ‘ x ’ years and the age of the new person be ‘ y ’ years so , ( 8 x – 65 + y ) / 8 = x + 1.5 so , y = 77 kgs 65 + 8 x 1.5 = 77 kgs answer b"
Answer: b
Python program:
a = 8 * 1
b = 65 + a