euclaise/mathqa_programs huggingface dataset:
Problem: a man can row upstream at 25 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 77 , c ) 30 , d ) 99 , e ) 12
Rationale: "us = 25 ds = 35 m = ( 35 + 25 ) / 2 = 30 answer : c"
Answer: c
Python program:
a = 25 + 35 
b = a / 2
Problem: the product of two positive integers is 1023 and their difference is 2 . what is the bigger number ?
Options: a ) 29 , b ) 31 , c ) 33 , d ) 35 , e ) 37
Rationale: "let ' s use trial and error to find the two numbers . 32 * 30 = 960 ( too low ) 33 * 31 = 1023 the answer is c ."
Answer: c
Python program:
a = 1023 / 2
b = 1023 / a
c = b * 4
d = c + 10 
e = d - 1
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36 seconds . the length of each train is :
Options: a ) 50 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 92 m
Rationale: "let the length of each train be x metres . then , distance covered = 2 x metres . relative speed = ( 46 - 36 ) km / hr = ( 10 x ( 5 / 18 ) m / sec = ( 25 / 9 ) m / sec ( 2 x / 36 ) = ( 25 / 9 ) 2 x = 100 x = 50 . a"
Answer: a
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 36
e = d / 2
Problem: if the area of a square with sides of length 12 centimeters is equal to the area of a rectangle with a width of 6 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 24 , e ) 18
Rationale: "let length of rectangle = l 12 ^ 2 = l * 4 = > l = 144 / 6 = 24 answer d"
Answer: d
Python program:
a = 12 ** 2
b = a / 6
Problem: the average of first 20 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 21
Rationale: "sum of 20 even numbers = 20 * 21 = 420 average = 420 / 20 = 21 answer : e"
Answer: e
Python program:
a = 20 + 1
Problem: the difference between the two numbers is 1 / 3 of the larger number . if the smaller one is 48 the larger one is
Options: a ) 72 , b ) 60 , c ) 32 , d ) 96 , e ) 65
Rationale: explanation : let the larger number be x . then , x - 48 = 1 / 3 x x - x / 3 = 48 = > 2 x / 3 = 48 = > x = 72 answer : option a
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 48 / b
Problem: at an examination in which full marks were 500 . a got 10 % less than b , b got 25 % more than c and c got 20 % less than d . if a got 360 marks , what percentage of full marks was obtained by d ?
Options: a ) 88 % , b ) 90 % , c ) 80 % , d ) 87 % , e ) 20 %
Rationale: a b c d 90 100 80 100 a d 90 - - - - - 100 360 - - - - - - ? = 400 500 - - - - - - 400 100 - - - - - - - ? = > 80 % answer : c
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 + 25 
d = c / 100
e = b * d
f = 100 - 20
g = f / 100
h = e * g
i = 360 / h
j = i / 500
k = j * 100
Problem: a local restaurant recently renovated its dining space , purchasing new tables and chairs to use in addition to the original tables and chairs . the new tables each seat 6 customers , while the original tables each seat 4 customers . altogether , the restaurant now has 40 tables and is capable of seating 212 customers . how many more new tables than original tables does the restaurant have ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 24 , e ) 28
Rationale: if all the tables seated 4 , the number of customers could be 4 * 40 = 160 . 212 - 160 = 52 , so 52 / 2 = 26 tables must be tables seating 6 people . the number of tables seating 4 people is 40 - 26 = 14 . the number of new tables is 26 - 14 = 12 more than the number of old tables . the answer is b .
Answer: b
Python program:
a = 6 * 40
b = a - 212
c = 6 - 4
d = b / c
e = 40 - d
f = 6 * 40
g = f - 212
h = 6 - 4
i = g / h
j = e - i
Problem: if the circumference of a circle increases from 4 pi to 8 pi , what change occurs in the area ?
Options: a ) area is quadrupled
b ) area is tripled
c ) area is doubles
d ) area become half
e ) none of these
Rationale: explanation : 2 π r 1 = 4 π = > r 1 = 22 π r 2 = 8 π > r 2 = 4 original area = 4 π ∗ 22 = 16 π new area = 4 π ∗ 42 = 64 π so the area quadruples . option a
Answer: a
Python program:
a = math.pi * 8
b = a ** 2
c = math.pi * 4
d = b / c
e = math.pi * 4
f = e ** 2
g = math.pi * 4
h = f / g
i = d / h
Problem: a monkey ascends a greased pole 20 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) 37 th
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 18 metres , he ascends in 36 minutes . â ˆ ´ he reaches the top in 37 th minute . answer e"
Answer: e
Python program:
a = 2 * 20
b = a - 1
Problem: the sector of a circle has radius of 21 cm and central angle 225 o . find its perimeter ?
Options: a ) 91.5 , b ) 92 , c ) 93 , d ) 94 , e ) 124.5
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 225 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 124.5 cm answer : option e"
Answer: e
Python program:
a = 21 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 21
Problem: the product of the squares of two positive integers is 400 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0
b ) 1
c ) 2
d ) 3
e ) 4
Rationale: first break down 200 into 20 * 20 and further into the prime factors 2 * 2 * 5 * 2 * 2 * 5 . now we are looking for all the possible pairs ( 2 numbers ) of squares whose product results in 400 . 1 st : 2 ^ 2 * 10 ^ 2 ( i . e . the first two 2 ' s and two times 2 * 5 = 10 ) 2 nd : 4 ^ 2 * 5 ^ 2 ( i . e . two times 2 * 2 = 4 = 4 ^ 2 and 5 ^ 2 ) . 3 rd : 1 ^ 2 * 20 ^ 2 ( i . e . two times 2 * 2 * 5 and 1 ^ 2 = 1 ) answer d .
Answer: d
Python program:
a = 2 + 3 
b = a - 2
Problem: george baked a total of 175 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "3 / 5 of the 175 pizzas cooked on saturday = 105 pizzas 3 / 5 of the remaining pizzas on sunday = 42 pizzas we ' re left with ( 175 - 105 - 42 ) = 28 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 8 7 6 4 3 = 28 w = 6 d"
Answer: d
Python program:
a = 3 / 7
b = 175 * a
c = 175 - b
d = 3 / 7
e = 175 * d
f = 175 - e
g = 3 / 7
h = f * g
i = c - h
j = i - 3
k = 3 / 7
l = 175 * k
m = 175 - l
n = 3 / 7
o = 175 * n
p = 175 - o
q = 3 / 7
r = p * q
s = m - r
t = s - 3
u = j / t
Problem: n and m are each 3 - digit integers . each of the numbers 2 , 3,4 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 39 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 387 and 426 ( difference is 39 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 684 and 723 ( difference is 39 ) a
Answer: a
Python program:
a = 8 - 2
b = a * 10
c = 100 - b
d = c - 1
Problem: gary ’ s gas station serves an average of 12 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
Options: a ) 1,072 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
Rationale: "6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 12 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 12 + 10 ) = 16 * 67 = 1072 answer : a"
Answer: a
Python program:
a = 6 + 10 
b = 12 + 10 
c = 4 + 1 
d = 9 * c
e = b + d 
f = a * e
g = f / 1000
h = math.floor(g)
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 35 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 121.5 , e ) 108
Rationale: assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 35 % = 90 * 1.35 = 121.5 thus ratio = 121.5 / 100 = 1.215 ( in % terms = 121.5 % ) . thus d is the correct answer .
Answer: d
Python program:
a = 100 + 20 
b = a / 100
c = 100 * b
d = 100 - 25
e = d / 100
f = c * e
g = 100 + 35 
h = g / 100
i = f * h
Problem: you enter a weight loss challenge game and manage to lose 15 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13.3 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 15 % ) * ( 100 % + 2 % ) = 0.85 * 1.02 = 13.3 % the weigh in records your weight loss at 13.3 % ! the answer is a"
Answer: a
Python program:
a = 15 / 100
b = 1 - a
c = 2 / 100
d = 1 + c 
e = b * d
f = 1 - e
g = f * 100
Problem: if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 89 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 34 , e ) 42
Rationale: "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 89 a = 34 the answer is d ."
Answer: d
Python program:
a = 89 * 2
b = 16 - 8
c = a - b
d = 2 + 3 
e = c / d
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 92 . if $ 2000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000
Rationale: 0.1 x = 0.08 ( 2000 - x ) + 92 0.18 x = 252 x = 1400 then the amount invested at 8 % is $ 2000 - $ 1400 = $ 600 the answer is a .
Answer: a
Python program:
a = 10 / 100
b = a * 2000
c = b - 92
d = 8 / 100
e = 10 / 100
f = d + e 
g = c / f
Problem: four 6 faced dice are thrown together . the probability that all the four show the same number on them is ?
Options: a ) 1 / 248 , b ) 1 / 216 , c ) 1 / 144 , d ) 1 / 200 , e ) 1 / 242
Rationale: "it all 4 numbers have to be same basically we want quadruplets . 1111 , 2222 , 3333 , 4444 , 5555 and 6666 . those are six in number . further the four dice can fall in 6 * 6 * 6 * 6 = 1296 ways . hence the probability is 6 / 1296 = 1 / 216 answer : b"
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: the tax on a commodity is diminished by 10 % and its consumption increased by 25 % . the effect on revenue is ?
Options: a ) 12 % decrease , b ) 18 % decrease , c ) 19 % decrease , d ) 13 % decrease , e ) 12.5 % increase
Rationale: "100 * 100 = 10000 90 * 125 = 11250 - - - - - - - - - - - 10000 - - - - - - - - - - - 1250 100 - - - - - - - - - - - ? = > 12.5 % decrease answer : e"
Answer: e
Python program:
a = 25 / 100
b = 1 + a 
c = 10 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: a man ’ s wages were decreased by 50 % . again , the reduced wages were increased by 50 % . he has a loss of ?
Options: a ) 35 % , b ) 25 % , c ) 20 % , d ) 30 % , e ) none of these
Rationale: here , x = - 50 and y = 50 therefore , the net % change in value = ( x + y + xy / 100 ) % = [ - 50 + 50 + ( - 50 x 50 ) / 100 ] % or - 25 % since the sign is negative , there is loss of 25 % answer : b
Answer: b
Python program:
a = 100 + 50 
b = a / 100
c = b * 50
d = 100 - c
Problem: a cubical block of metal weighs 7 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 56 , e ) 12
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 7 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 7 pounds = 56 pounds so answer is d and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 7 * 8 = 56 so answer is d"
Answer: d
Python program:
a = 2 * 4
b = 7 * a
Problem: two cubes of their volumes in the ratio 8 : 125 . the ratio of their surface area is :
Options: a ) 1.5 : 5
b ) 2 : 5
c ) 3 : 5
d ) 1 : 5
e ) 4 : 5
Rationale: the ratio of their surface area is 8 : 125 2 : 5 answer is b .
Answer: b
Python program:
a = 8 ** const_0_33
b = 125 ** const_0_33
c = a / b
Problem: find the compound ratio of ( 4 : 3 ) , ( 1 : 3 ) and ( 2 : 3 ) is
Options: a ) 16 : 27 , b ) 12 : 13 , c ) 13 : 14 , d ) 14 : 15 , e ) 31 : 27
Rationale: required ratio = 4 / 3 * 1 / 3 * 2 / 3 = 16 / 27 = 16 : 27 answer is a
Answer: a
Python program:
a = 4 / 3
b = 4 / 3
c = 1 / 3
d = b * c
e = a * d
Problem: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 19 seconds . what is the length of the platform in meters ?
Options: a ) 220 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 19 * 20 = 380 = length of train length of platform = 600 - 380 = 220 answer : a"
Answer: a
Python program:
a = 72 * 1000
b = a / 3600
c = b * 30
d = 72 * 1000
e = d / 3600
f = e * 19
g = c - f
Problem: a batsman scored 140 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 50 % , b ) 40 % , c ) 60 % , d ) 57 % , e ) 80 %
Rationale: "number of runs made by running = 140 - ( 3 x 4 + 8 x 6 ) = 140 - ( 60 ) = 80 now , we need to calculate 80 is what percent of 140 . = > 80 / 140 x 100 = 57 % answer : d"
Answer: d
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 140 - c
e = d / 140
f = e * 100
Problem: an escalator moves towards the top level at the rate of 11 ft . sec and its length is 140 feet . if a person walks on the moving escalator at the rate of 3 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 5 sec
Rationale: explanation : time taken to cover the entire length = tot . dist / resultant speed = 140 / ( 11 + 3 ) = 10 sec answer : b
Answer: b
Python program:
a = 11 + 3 
b = 140 / a
Problem: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 25 true ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 2 , e ) 9
Rationale: answer d ( a + b ) ( a - b ) = 25 5 cases for ( a + b ) , ( a - b ) 25 , 1 5 , 5 answer d
Answer: d
Python program:
a = math.log(25)
b = 4 + 1 
c = math.log(b)
d = a / c
Problem: set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 8 , while all other numbers remain the same , what is the new average of set s ?
Options: a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 7.0 , e ) 6.9
Rationale: old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 8 then total increased to 62 + 8 = 70 new avg - 70 / 10 = 7.0 . hence answer is d .
Answer: d
Python program:
a = 10 * 6
b = a + 8 
c = b / 10
Problem: 14 men can complete a piece of work in 32 days . in how many days can 16 men complete that piece of work ?
Options: a ) 23 , b ) 27 3 / 4 , c ) 20 1 / 2 , d ) 27 1 / 2 , e ) 11
Rationale: "14 * 32 = 16 * x = > x = 27 1 / 2 days answer : d"
Answer: d
Python program:
a = 32 * 14
b = a / 16
Problem: a work crew of 7 men takes 10 days to complete one - half of a job . if 8 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 3 1 / 3 , d ) 4 , e ) 4 2 / 3
Rationale: suppose 1 man can do work in x days . . so 7 men will do in . . 7 / x = 1 / 10 * 1 / 2 as half job is done x = 140 now 8 more are added then 15 / 140 = 1 / 2 * 1 / d for remaining half job d = 4 2 / 3 number of days e
Answer: e
Python program:
a = 7 * 10
b = 7 + 8 
c = a / b
d = 10 + c
Problem: a train running at the speed of 90 km / hr crosses a pole in 6 seconds . what is the length of the train ?
Options: a ) 255 , b ) 205 , c ) 502 , d ) 225 , e ) 235
Rationale: "speed = ( 90 * 5 / 18 ) m / sec = ( 25 ) m / sec length of the train = ( speed x time ) = ( 25 * 9 ) m = 225 m . answer : d"
Answer: d
Python program:
a = 90 * 1000
b = a / 3600
c = b * 6
Problem: the angle of elevation of a ladder leaning against a wall is 60 ° and the foot of the ladder is 4.6 m away from the wall . the length of the ladder is
Options: a ) 2.3 m , b ) 4.6 m , c ) 7.8 m , d ) 9.2 m , e ) none
Rationale: solution let ab be the wall and bc be the ladder . then , < abc = 60 ° ac = 4.6 m . ; ac / bc = cos 60 ° = 1 / 2 ‹ = › bc = 2 × ac = ( 2 × 4.6 ) m = 9.2 m answer d
Answer: d
Python program:
a = 4 * 6
Problem: in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many t eggs does the plant process per day ?
Options: a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000
Rationale: "straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there t = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c ."
Answer: c
Python program:
a = 99 - 96
b = 12 / a
c = b * 100
Problem: the sale price sarees listed for rs . 510 after successive discount is 12 % and 15 % is ?
Options: a ) 298 , b ) 237 , c ) 342 , d ) 381 , e ) 291
Rationale: 510 * ( 88 / 100 ) * ( 85 / 100 ) = 381 answer : d
Answer: d
Python program:
a = 510 * 12
b = a / 100
c = 510 - b
d = 510 * 12
e = d / 100
f = 510 - e
g = f * 15
h = g / 100
i = c - h
Problem: the present population of a town is 3456 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2400 , b ) 2100 , c ) 3500 , d ) 3600 , e ) 2050
Rationale: "p = 3456 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 3456 / ( 1 + 20 / 100 ) ^ 2 = 3456 / ( 6 / 5 ) ^ 2 = 2400 ( approximately ) answer is a"
Answer: a
Python program:
a = 3456 * 20
b = a / 100
c = 3456 + b
Problem: the distance from city a to city b is 150 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 90 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42.85 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the time it takes cara to drive to city b is 150 / 30 = 5 hours . dan needs to take less than 3.5 hours for the trip . dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour . the answer is a ."
Answer: a
Python program:
a = 150 / 30
b = 90 / 90
c = a - b
d = 150 / c
Problem: the interest on a certain deposit at 4.5 % p . a . is rs . 202.50 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a . ?
Options: a ) rs . 20.25 , b ) rs . 22.50 , c ) rs . 25 , d ) rs . 42.75 , e ) none
Rationale: "solution s . i . = rs . 202.50 , r = 4.5 % , t = 1 year . principal = rs . ( 100 x 202.50 / 4.5 x 1 ) = rs . 4500 . now , p = rs . 4500 , r = 5 % , t = 1 year . s . i . = rs . ( 4500 x 5 x 1 / 1000 = rs . 225 . ∴ difference in interest = rs . ( 225 - 202.50 ) = rs . 22.50 . answer b"
Answer: b
Python program:
a = 4 / 5
b = 202 / 50
c = b * 5
d = c / 100
e = d - 202
Problem: if a ( a - 4 ) = 12 and b ( b - 4 ) = 12 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 5 , c ) 4 , d ) 46 , e ) 48
Rationale: i . e . if a = 6 then b = - 2 or if a = - 2 then b = 6 but in each case a + b = - 2 + 6 = 4 answer : option c
Answer: c
Python program:
a = 4 + 12 
b = 4 - 12
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: what percent of 60 is 120 ?
Options: a ) 200 , b ) 75 , c ) 60 , d ) 33 1 ⁄ 3 , e ) 25
Rationale: "% of 60 is 120 ? = 120 / 60 = 21 = 200 % thus a is the correct answer ."
Answer: a
Python program:
a = 60 / 120
b = a * 100
Problem: the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 6.30 . in which year will the price of commodity x be 65 cents more than the price of commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 65 cents more than commodity y . $ 2.75 / 25 cents = 11 years the answer is 2001 + 11 years = 2012 . the answer is c ."
Answer: c
Python program:
a = 65 / 100
b = 6 - 30
c = a + b 
d = 45 / 100
e = 6 - 30
f = d - e
g = c / f
h = 2001 + g
Problem: the number of timeshare condos available at sunset beach is 3 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 400 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 100 , e ) 240
Rationale: "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 3 / 5 x = 400 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 3 / 5 x = 2 / 5 x = 2 / 5 ( 250 ) = 100 the correct answer is d"
Answer: d
Python program:
a = 400 * 3
b = a / 5
c = 3 * 5
d = b + c