euclaise/mathqa_programs huggingface dataset:
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 50 , c ) c . 48 , d ) d . 46 , e ) e . 23
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 11 seconds . thus x = 1 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 23 seconds . answer e"
Answer: e
Python program:
a = 1 + 4 
b = 6 + a 
c = 11 / b
d = 1 + 4 
e = 6 + d 
f = 12 + e 
g = c * f
Problem: - 24 x 29 + 36 = ?
Options: a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 660 , e ) none of them
Rationale: "given exp . = - 24 x ( 30 - 1 ) + 36 = - ( 24 x 30 ) + 24 + 36 = - 720 + 60 = - 660 answer is d"
Answer: d
Python program:
a = 1 - 2
b = 24 * 29
c = b - 36
d = a * c
Problem: an alloy weighing 20 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 70 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 20 * ( 70 / 100 ) = 14 ounces . now we add x ounces of pure gold to make it 90 % gold . so 14 + x = ( 24 + x ) * 70 / 100 = > x = 9 . answer is b ."
Answer: b
Python program:
a = 70 / 100
b = a * 20
c = 70 / 100
d = b / c
Problem: a can do a piece of work in 10 days . he works at it for 4 days and then b finishes it in 9 days . in how many days can a and b together finish the work ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 4 , e ) 1
Rationale: "4 / 10 + 9 / x = 1 = > x = 15 1 / 10 + 1 / 15 = 1 / 6 = > 6 days answer : a"
Answer: a
Python program:
a = 1 / 10
b = 9 * 2
c = 1 / b
d = a + c 
e = 1/(d)
Problem: if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 2 : 1 / 11 : 1 / 12 : 1 / 13 then find the total number of items the wholesaler distributes ?
Options: a ) 289 , b ) 1289 , c ) 1389 , d ) 1281 , e ) 128
Rationale: "here , a : b : c : d = 1 / 2 : 1 / 11 : 1 / 12 : 1 / 13 1 ) l . c . m of 2 : 11 : 12 : 13 is 1716 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 2 ) x 1716 = 858 b = ( 1 / 11 ) x 1716 = 156 c = ( 1 / 12 ) x 1716 = 143 d = ( 1 / 13 ) x 1716 = 132 3 ) total number of toys = ( 858 x + 156 x + 143 x + 132 x ) = 1289 x minimum number of pens ( x ) = 1 therefore , total number of items = 1289 items . correct option : b"
Answer: b
Python program:
a = 100 * 4
b = a + 100 
c = 12 * 4
d = 4 + 3 
e = c + d 
f = b + e
Problem: the sum of ages of 5 children born 3 years different each is 60 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 5 x = 30 x = 6 . x + 12 = 6 + 12 = 18 d"
Answer: d
Python program:
a = 3 + 4 
b = 3 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 60 
g = f / 5
Problem: given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p - 3 ?
Options: a ) 10 , b ) 8 , c ) 7 , d ) 3 , e ) 11
Rationale: "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p - 3 is 6 - 3 = 3 . answer : d ."
Answer: d
Python program:
a = 3 + 3 
b = a + 3
Problem: a 240 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 144 , c ) 278 , d ) 126 , e ) 112
Rationale: "s = 240 / 6 * 18 / 5 = 144 kmph answer : b"
Answer: b
Python program:
a = 240 / 6
b = a * const_3_6
Problem: a person travels equal distances with speeds of 2 km / hr , 6 km / hr , 6 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 660 mts , d ) 2 km , e ) 250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 6 ) + ( x / 6 ) = 11 / 60 x = 0.22 total distance = 3 * 0.22 = 0.66 km = 660 meters correct option is c"
Answer: c
Python program:
a = 11 / const_60
b = 1 / 2
c = 1 / 6
d = b + c 
e = 1 / 6
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.75 , b ) 2.25 , c ) 2.5 , d ) 2.75 , e ) 3.25
Rationale: let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3 km / hour x / 3 = 3 x = 9 km the average speed while climbing = distance / time = 9 / 4 = 2.25 km / h the answer is b .
Answer: b
Python program:
a = 4 + 2 
b = a * 3
c = b / 2
d = c / 4
Problem: mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate p in miles per hour for the entire trip ?
Options: a ) p = 26.7 , b ) p = 30.0 , c ) p = 40.0 , d ) p = 53.3 , e ) p = 60.0
Rationale: "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ."
Answer: c
Python program:
a = 640 / 2
b = a / 80
c = b * 2
d = 640 / 2
e = d / 80
f = c + e 
g = 640 / 2
h = g / 80
i = f + h 
j = 640 / i
Problem: a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 1 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 62 , c ) 49 , d ) 53 , e ) 86
Rationale: "4 x + 1 = 5 y + 1 . . . . . . . . . . . ie : 4 x - 5 y = 2 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x = fraction ( not possible ) if y = 4 thus x = 5 n = 21 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 41 21 + 41 = 62 . . . . . b"
Answer: b
Python program:
a = 5 * 2
b = a + 1 
c = 2 * 1
d = 5 * c
e = d + 1 
f = b + e
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 12 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.9 %
Rationale: "12 = 1.1 * x x = 10.90 % answer e )"
Answer: e
Python program:
a = 12 * 100
b = 12 + 100 
c = a / b
Problem: if a - b = 6 and a ^ 2 + b ^ 2 = 100 , find the value of ab
Options: a ) 10 , b ) 32 , c ) 15 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 100 - 36 = 64 = > ab = 32 answer : b"
Answer: b
Python program:
a = math.sqrt(100)
b = a - 6
c = b / 2
d = 6 + c 
e = math.sqrt(100)
f = e - 6
g = f / 2
h = d * g
i = h * 2
Problem: the average amount with a group of 7 numbers is rs . 20 . if the newly joined member has rs . 56 with him , what was the average amount with the group before his joining the group ?
Options: a ) s . 13 , b ) s . 12 , c ) s . 15 , d ) s . 22 , e ) s . 14
Rationale: total members in the group = 7 average amount = rs . 20 total amount with them = 7 * 20 = rs . 140 one number has rs . 56 . so , the amount with remaining 6 people = 140 - 56 = rs . 84 the average amount with them = 84 / 6 = rs . 14 . answer : e
Answer: e
Python program:
a = 20 * 7
b = a - 56
c = 7 - 1
d = b / c
Problem: find the missing figures : ? % of 50 = 2.125
Options: a ) 8.55 , b ) 6.55 , c ) 8.75 , d ) 7.75 , e ) 4.25
Rationale: ( i ) let x % of 50 = 2.125 . then , ( x / 100 ) * 50 = 2.125 x = ( 2.125 * 2 ) = 4.25 answer is e .
Answer: e
Python program:
a = 2 * 125
b = a / 50
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 8 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 200 , d ) 112.5 , e ) 212.5
Rationale: explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 8 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 8 × 2 / 100 = 800 his overall gain in 2 years = rs . 800 - rs . 400 = rs . 400 his overall gain in 1 year = 400 / 2 = rs . 200 answer : option c
Answer: c
Python program:
a = 5000 * 8
b = a * 2
c = b / 100
d = 5000 * 4
e = d * 2
f = e / 100
g = c - f
h = g / 2
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 114 ounces , what is the volume , in cubic inches , of 63 ounces of this substance ?
Options: a ) 27 , b ) 26 , c ) 42 , d ) 64 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 114 ) * 63 = 26 cubic inches answer b"
Answer: b
Python program:
a = 48 / 114
b = a * 63
Problem: a circular mat with radius 10 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?
Options: a ) 5 / 12
b ) 2 / 5
c ) 0.5451
d ) 3 / 4
e ) 5 / 6
Rationale: c . it is a circle inscribed in a square . square side = 24 - - - > square ( table ) area = 24 ^ 2 circle diameter = 20 - - - > circle area = pir ^ 2 = 100 pi ( where pi = ~ 3.14 ) covered fraction = 100 * 3.14 / 24 * 24 = ~ 314 / 24 * 24 = 0.5451 c
Answer: c
Python program:
a = circle_area / (
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 1500 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 13,500 , d ) $ 15,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1500 triples to $ 4500 , in 28 years , it will again triple to $ 4500 * 3 = $ 13,500 answer c"
Answer: c
Python program:
a = 112 / 8
b = 28 / a
c = 3 ** b
d = 1500 * c
Problem: the sum of ages of 5 children born 3 years different each is 75 yrs . what is the age of the elder child ?
Options: a ) 7 , b ) 9 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 75 5 x = 45 x = 9 . x + 12 = 9 + 12 = 21 e"
Answer: e
Python program:
a = 3 + 4 
b = 3 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 75 
g = f / 5
Problem: in how many ways can a teacher write an answer key for a mini - quiz that contains 3 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 88 , b ) 90 , c ) 96 , d ) 98 , e ) 102
Rationale: 2 multiples - choice questions can be answered in = 4 x 4 = 16 ways 3 true - false questions can be answered in = 2 x 2 x 2 = 8 ways but out of the 8 ways , 2 ways [ ( true - true - true ) ( false - false - false ) ] will contain same answers thus 3 true - false questions can be answered in = 2 x 2 x 2 = 6 ways total ways to answer the quiz = 16 x 6 = 96 answer c
Answer: c
Python program:
a = 2 * 2
b = 2 * a
c = b - 2
d = 4 * 4
e = c * d
Problem: a 50 - liter solution of alcohol and water is 5 percent alcohol . if 1.5 liters of alcohol and 8.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 5.5 % , b ) 6 % , c ) 6 1 / 3 % , d ) 6 2 / 3 % , e ) 7 %
Rationale: "50 l * . 05 = 2.5 l of alc , 50 l - 2.5 l = 47.5 l of water 2.5 + 1.5 = 4 l of alcohol in new solution 47.5 l + 8.5 l = 56 l of water 4 l / 56 l = 1 / 14 this is ~ 7 % answer : e"
Answer: e
Python program:
a = 5 / 100
b = 50 * a
c = b + 1 
d = 1 + 5 
e = 50 + d 
f = c / e
g = f * 100
Problem: there are 3 departments having students 72 , 5824 . in an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only ( no mixing of departments ) . find the minimum number of rooms required ?
Options: a ) 73 , b ) 74 , c ) 75 , d ) 76 , e ) 77
Rationale: we need to take gcd which is 2 thus all the rooms will have 2 students of the same dept 1 ) 72 / 2 = 36 2 ) 58 / 2 = 29 3 ) 24 / 2 = 12 total no . of min rooms reqd = 36 + 12 + 29 = 77 answer : e
Answer: e
Python program:
a = 72 / 2
b = a + 12 
c = 72 / 2
d = c + 12 
e = d + 10 
f = e / 2
g = b + f
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 120 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 121.5 , b ) 122 , c ) 122.5 , d ) 113 , e ) 112.5
Rationale: "e 120 * t = 1 km = > t = 1 / 120 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 120 + 2 / 3600 ) = 1 = > v = 112.5 km / h"
Answer: e
Python program:
a = 1 / 120
b = 3600 * a
c = b + 2 
d = c / 3600
e = 1 / d
Problem: an article is bought for rs . 765 and sold for rs . 1000 , find the gain percent ?
Options: a ) 30.6 % , b ) 30.5 % , c ) 30.7 % , d ) 30.8 % , e ) 30.9 %
Rationale: "765 - - - - 235 100 - - - - ? = > 30.7 % answer : c"
Answer: c
Python program:
a = 1000 * 100
b = a / 765
c = 100 - b
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 70 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 40 % , c ) 35 % , d ) 77.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 70 percent is reduced which means the new price is merely 30 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 10 ) p = 9 / 40 p is the new price after both deduction which is 22.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 77.5 % of p . so answer is d = 77.5 %"
Answer: d
Python program:
a = 100 - 70
b = a / 100
c = 100 - 25
d = b * c
e = 100 - d
Problem: the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 35 % profit ?
Options: a ) 2080 , b ) 2778 , c ) 2299 , d ) 2778 , e ) 2771
Rationale: let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 130 % of rs . 1600 = 130 / 100 * 1600 = rs . 2080 . answer : a
Answer: a
Python program:
a = 100 + 35 
b = a / 100
c = 1920 + 1280 
d = c / 2
e = b * d
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2700 , d ) 10800 , e ) none
Rationale: "let the number of required bottles be x machine 6 : 10 time 1 : 4 = : : 270 : x therefore 6 x 1 x x = 10 x 4 x 270 = > x = ( 10 x 4 x 270 ) / ( 6 ) = > x = 1800 answer : option b"
Answer: b
Python program:
a = 270 / 6
b = a * 4
c = b * 10
Problem: thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 40 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 40 = 70 members have not passed the test , thus 0.7 * total = 70 - - > total = 100 . answer : c ."
Answer: c
Python program:
a = 40 + 30 
b = 100 - 30
c = b / 100
d = a / c
Problem: what is the smallest number which when diminished by 8 , is divisible by 9 , 6 , 12 and 18 ?
Options: a ) 50 , b ) 45 , c ) 44 , d ) 60 , e ) 65
Rationale: "explanation : required number = lcm of ( 9 , 6 , 12 and 18 ) + 8 = 36 + 8 = 44 answer : option c"
Answer: c
Python program:
a = math.lcm(9, 6)
b = math.lcm(12, 18)
c = math.lcm(a, b)
d = c + 8
Problem: the ratio of two quantities is 1 to 2 . if each of the quantities is increased by 15 , what is the ratio of these 2 new quantities ?
Options: a ) 5 : 6 , b ) 25 : 27 , c ) 15 : 16 , d ) 20 : 21 , e ) it can not be determined from the information given
Rationale: "the ratio can not be straight way added any quantity . . . 1 : 2 means 1 x : 2 x . . . so when you add a quantity , it becomes 1 x + 15 : 2 x + 15 . . so value of x is must . . ans e"
Answer: e
Python program:
a = 1 + 15 
b = 2 + 15 
c = a / b
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets rain cloud , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 5 , e ) 1 / 4
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : c
Answer: c
Python program:
a = math.lcm(2, 3)
b = a / 2
c = b - 2
Problem: two tracks are parallel . the first track has 6 checkpoints and the second one has 10 checkpoints . in how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle ?
Options: a ) 120
b ) 150
c ) 200
d ) 270
e ) 420
Rationale: to make a triangle , you need 2 checkpoints from one track and 1 from the other . you can not have all 3 from the same track since then the points will be in a line ( assuming straight line of track ) you select 2 checkpoints from the first track and one from the second or two from the second track and one from the first . 6 c 2 * 10 c 1 + 10 c 2 * 6 c 1 = 150 + 270 = 420 answer ( e )
Answer: e
Python program:
a = math.factorial(10)
b = 10 - 2
c = math.factorial(b)
d = a / c
e = math.factorial(2)
f = d / e
g = math.factorial(6)
h = 6 - 1
i = math.factorial(h)
j = g / i
k = f * j
l = math.factorial(10)
m = 10 - 1
n = math.factorial(m)
o = l / n
p = math.factorial(6)
q = p / 2
r = 6 - 2
s = math.factorial(r)
t = q / s
u = o * t
v = k + u
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 55 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 55 , d ) d . 68 , e ) e . 83
Rationale: "55 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 55 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 137.5 that is approximately 138 thus , more men needed to finish the task = 138 - 55 = 83 hence answer is e"
Answer: e
Python program:
a = 15 - 2
b = 55 * a
c = b * 100
d = 300 - 100
e = 2 * 5
f = c / e
g = f - 55
Problem: bob invested $ 2000 in fund a and $ 1000 in fund b . over the next two years , the money in fund a earned a total interest of 12 percent for the two years combined and the money in fund b earned 30 percent annual interest compounded annually . two years after bob made these investments . bob ' s investment in fund a was worth how much more than his investment in fund b ?
Options: a ) $ 500 , b ) $ 550 , c ) $ 600 , d ) $ 650 , e ) $ 700
Rationale: bob earned 2000 * ( 1 + 0.12 ) in total by fund a and earned 1000 * ( 1 + 0.3 ) ^ 2 in total by fund b . so 2000 * ( 1.12 ) - 1000 * ( 1.69 ) = 550 . the answer is , therefore , ( b ) .
Answer: b
Python program:
a = 12 / 100
b = 1 + a 
c = 2000 * b
d = 30 / 100
e = 1 + d 
f = e ** 2
g = 1000 * f
h = c - g
Problem: the ratio between the sale price and the cost price of an article is 6 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 1 : 5 , c ) 3 : 6 , d ) 2 : 0 , e ) 2 : 1
Rationale: let c . p . = rs . 5 x and s . p . = rs . 6 x . then , gain = rs . x required ratio = x : 5 x = 1 : 5 answer : b
Answer: b
Python program:
a = 6 - 5
b = a / 5
Problem: how many digits 2 ^ 1000 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 99 , e ) 310
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 1000 = ( 1.024 ) ^ 100 * 10 ^ 300 therefore 310 digits would be my best guess e"
Answer: e
Python program:
a = math.log(2)
b = math.log(10)
c = a / b
d = c * 1000
e = 1 + d 
f = math.floor(e)
Problem: a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose their own dress ?
Options: a ) 22 , b ) 87 , c ) 29 , d ) 26 , e ) 191
Rationale: answer : b
Answer: b
Python program:
a = math.comb(2, 1)
b = math.factorial(3)
c = a / b
Problem: if the population of a certain country increases at the rate of two person every 60 seconds , by how many persons does the population increase in 100 minutes ?
Options: a ) 120 , b ) 150 , c ) 240 , d ) 220 , e ) 200
Rationale: "answer = 2 * 100 = 200 answer = e"
Answer: e
Python program:
a = const_60 / 60
b = a * 100
Problem: a salt manufacturing company produced a total of 2500 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 100 , b ) 105 , c ) 109 , d ) 120 , e ) 90
Rationale: "total production of salt by the company in that year = 2500 + 2600 + 2700 + . . . . + 3600 = 36600 . average monthly production of salt for that year = 36600 / 365 â ‰ ˆ 100 answer : a"
Answer: a
Python program:
a = 2500 * 2
b = 12 - 1
c = b * 100
d = a + c 
e = d * 12
f = e / 2
g = 3 * 100
h = 2 * 3
i = h * 10
j = g + i 
k = 2 + 3 
l = j + k 
m = f / l
Problem: 1200 men have provisions for 18 days . if 450 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 12.5 , d ) 12.2 , e ) 13.1
Rationale: "1200 * 18 = 1650 * x x = 13.1 answer : e"
Answer: e
Python program:
a = 18 * 1200
b = 1200 + 450 
c = a / b