euclaise/mathqa_programs huggingface dataset:
Problem: if 5 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 8 , b ) - 4 , c ) - 3 , d ) 1 , e ) 6
Rationale: "the phrase “ 5 is one solution of the equation ” means that one value of x is 5 . thus , we first must plug 5 for x into the given equation to determine the value of k . so we have 5 ^ 2 + ( 3 ) ( 5 ) + k = 10 25 + 15 + k = 10 40 + k = 10 k = - 30 next we plug - 30 into the given equation for k and then solve for x . x ^ 2 + 3 x – 30 = 10 x ^ 2 + 3 x – 40 = 0 ( x + 8 ) ( x - 5 ) = 0 x = - 8 or x = 5 thus , - 8 is the other solution . answer a ."
Answer: a
Python program:
a = 5 ** 2
b = 3 * 5
c = a + b 
d = 10 - c
e = d / 5
Problem: if 350 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 88 , b ) 82 , c ) 86 , d ) 87 , e ) 80
Rationale: "the question actually asks the highest power of 10 which divides 350 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 350 factorial will have 86 as - 350 / 5 = 70 70 / 5 = 14 14 / 5 = 2 so answer will be ( c ) 86"
Answer: c
Python program:
a = 4 + 1 
b = 350 / a
c = 4 + 1 
d = b / c
e = 4 + 1 
f = 350 / e
g = d + f
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 80 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50
Rationale: "200 men do the rest of the work in 100 - 80 = 20 days 100 men can do the rest of the work in 20 * 200 / 100 = 40 days required number of days = 40 - 80 = 40 days answer is a"
Answer: a
Python program:
a = 100 - 80
Problem: solve the quickfire maths brain teaser â ˆ š 4 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 20 %
Rationale: â ˆ š 4 % = > â ˆ š 4 / â ˆ š 100 = > 2 / 10 = > 20 / 100 = > 20 % e
Answer: e
Python program:
a = 1 + 4 
b = 100 / a
Problem: the area of sector of a circle whose radius is 12 metre and whose angle at the center is 42 ° is ?
Options: a ) 52.7 m 2 , b ) 57.8 m 2 , c ) 52.8 metre sq , d ) 72.8 m 2 , e ) 52.8 m 2
Rationale: 42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c
Answer: c
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 42 / g
i = f * h
Problem: in a race of 1000 meters , a can beat b by 100 meters , in a race of 800 meters , b can beat c by 100 meters . by how many meters will a beat c in a race of 600 meters ?
Options: a ) 125.5 meters , b ) 126.5 meters , c ) 127.5 meters , d ) 128.5 meters , e ) none of these
Rationale: explanation : when a runs 1000 meters , b runs 900 meters and when b runs 800 meters , c runs 700 meters . therefore , when b runs 900 meters , the distance that c runs = ( 900 x 700 ) / 800 = 6300 / 8 = 787.5 meters . so , in a race of 1000 meters , a beats c by ( 1000 - 787.5 ) = 212.5 meters to c . so , in a race of 600 meters , the number of meters by which a beats c = ( 600 x 212.5 ) / 1000 = 127.5 meters . answer : c
Answer: c
Python program:
a = 1000 - 100
b = 800 - 100
c = a * b
d = c / 800
e = 1000 - d
f = 600 * e
g = f / 1000
Problem: if a and b get profits of rs . 18,000 and rs . 15,000 respectively at the end of year then ratio of their investments are
Options: a ) 6 : 5 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: "ratio = 18000 / 15000 = 6 : 5 answer : a"
Answer: a
Python program:
a = 3 * 2
b = a * 100
c = b * 100
d = 3 * 2
e = d * 100
f = e * 100
g = 2 + 3 
h = g * 2
i = f / h
j = c / i
Problem: he ratio between the sale price and the cost price of an article is 5 : 3 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 5 : 2 , e ) 2 : 5
Rationale: let c . p . = rs . 3 x and s . p . = rs . 5 x . then , gain = rs . 2 x required ratio = 5 x : 2 x = 5 : 2 answer : d
Answer: d
Python program:
a = 3 / 5
b = 1 - a
c = 1/(b)
Problem: the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 72 + x ) / 7 = 11 = > x = 5 . hence , the seventh observation is 5 . answer : c"
Answer: c
Python program:
a = 12 - 1
b = 6 + 1 
c = a * b
d = 12 * 6
e = c - d
Problem: a certain bag contains 100 balls â € ” 50 white , 20 green , 10 yellow , 17 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 20 + 10 ) / 100 = 80 / 100 = 0.8 . answer is d"
Answer: d
Python program:
a = 17 + 3 
b = 100 - a
c = b / 100
Problem: simplify : 8888 + 888 + 88 + 8
Options: a ) 9872 , b ) 9782 , c ) 9827 , d ) 9287 , e ) none of them
Rationale: "8888 888 88 8 - - - - - - - 9872 answer is a ."
Answer: a
Python program:
a = 8888 * 888
b = 88 * 8
c = a + b
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 15 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 23 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 15 % of 300 seeds germinated , so 0.15 x 300 = 45 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 45 + 70 = 115 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 115 / 500 ) x 100 % , or 23 % . answer : c ."
Answer: c
Python program:
a = 15 / 100
b = a * 300
c = 35 / 100
d = c * 200
e = b + d 
f = 300 + 200 
g = e / f
h = g * 100
Problem: a man sitting in a train which is travelling at 50 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed .
Options: a ) 62 kmph , b ) 58 kmph , c ) 52 kmph , d ) 50 kmph , e ) none of these
Rationale: "relative speed = ( 280 ⁄ 9 ) m / sec = ( 280 ⁄ 9 × 18 ⁄ 5 ) kmph = 112 kmph . ∴ speed of goods train = ( 112 – 50 ) kmph = 62 kmph . answer a"
Answer: a
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 50
Problem: a can do a work in 15 days and b in 20 days . if they work on it together then in how many days required to complete the work ?
Options: a ) 300 / 31 , b ) 300 / 35 , c ) 300 / 21 , d ) 300 / 15 , e ) 300 / 20
Rationale: person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( 300 / 35 ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work = 300 / 35 answer is b
Answer: b
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = 1/(c)
Problem: what is the average of 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 ?
Options: a ) 1345 , b ) 1334 , c ) 1313.33 , d ) 1350 , e ) 1325
Rationale: "add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 11820 11820 / 9 = 1313.33 c"
Answer: c
Python program:
a = 1200 + 1300 
b = a + 1400 
c = b + 1510 
d = c + 1520 
e = d + 1530 
f = e + 1200 
g = 3 + 4 
h = f / g
Problem: the speed of a car is 90 km in the first hour and 50 km in the second hour . what is the average speed of the car ?
Options: a ) 70 , b ) 75 , c ) 88 , d ) 54 , e ) 15
Rationale: "s = ( 90 + 50 ) / 2 = 70 kmph answer : a"
Answer: a
Python program:
a = 90 + 50 
b = a / 2
Problem: of the 200 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 45 percent of the employees prefer city y and 55 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 135
Rationale: "110 prefer x ( group 1 ) ; 90 prefer y ( group 2 ) . city y needs 150 people : letall 90 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 40 people : 110 - 60 = 40 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 90 + 40 = 130 . answer : d ."
Answer: d
Python program:
a = 45 * 2
b = a + 55
Problem: a starts business with rs . 3500 and after 9 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 21000 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 9 = 3 months . so there profit ratio = ( 3500 ã — 12 ) : ( 3 x ) = 2 : 3 â ‡ ’ x = 21000 answer : d"
Answer: d
Python program:
a = 3500 * 12
b = a * 3
c = 12 - 9
d = c * 2
e = b / d
Problem: a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 80 then it is marked down by 10 % = 80 - 8 = 72 . hence it is 72 % of the original price . hence answer is a"
Answer: a
Python program:
a = 80 / 100
b = a * 10
c = 80 - b
Problem: what is the sum of all the prime factors of 220 and 330 ?
Options: a ) 15 , b ) 21 , c ) 35 , d ) 41 , e ) 64
Rationale: "prime factorization of both the numbers is as follows 220 = 2 * 2 * 5 * 11 sum of the prime factors of 220 = 20 330 = 2 * 3 * 5 * 11 sum of prime factors of 330 = 21 addition of both = 20 + 21 = 41 answer d"
Answer: d
Python program:
a = 330 - 220
b = a - 2
c = b / 2
d = c + 220 
e = 330 - 220
f = e + 2 
g = f / 2
h = d * g
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 5 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "share of each child ( 5 no ) and ( total share of grand children together ) 1 no = 1 / ( 5 + 1 ) = 1 / 6 as the grand children again equally share the part given to them : share of each grand child = [ ( 1 / 6 ) / 6 ] = 1 / 36 = 2.8 % answer : e"
Answer: e
Python program:
a = 100 / 3
b = a / 6
c = b / 100
d = c * 100
Problem: how many numbers from 10 to 50 are exactly divisible by 3
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 19
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits b )"
Answer: b
Python program:
a = 50 / 3
b = math.floor(a)
c = b * 3
d = 10 / 3
e = math.floor(d)
f = e + 1 
g = f * 3
h = c - g
i = h / 3
j = i + 1
Problem: at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "explanation : let rate will be r % 1200 ( 1 + r / 100 ) 2 = 134832 / 100 ( 1 + r / 100 ) 2 = 134832 / 120000 ( 1 + r / 100 ) 2 = 11236 / 10000 ( 1 + r / 100 ) = 106 / 100 = > r = 6 % option d"
Answer: d
Python program:
a = 1348 * 32
b = 1200 / 100
c = a / b
d = math.sqrt(c)
e = 1200 * 100
f = 1200 / 100
g = e / f
h = math.sqrt(g)
i = d - h
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ?
Options: a ) 70 , b ) 105 , c ) 178 , d ) 177 , e ) 169
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 18 35 - - - ? = > 70 answer : a"
Answer: a
Python program:
a = 100 / 45
b = a * 18
c = 30 / 45
d = c * 18
e = b + d 
f = e + 18
Problem: andrew purchased 7 kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 908 , c ) 930 , d ) 1075 , e ) 1080
Rationale: "cost of 7 kg grapes = 68 × 7 = 476 . cost of 9 kg of mangoes = 48 × 9 = 432 . total cost he has to pay = 476 + 432 = 908 b"
Answer: b
Python program:
a = 7 * 68
b = 9 * 48
c = a + b
Problem: two numbers a and b are such that the sum of 5 % of a and 3 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 7 : 3 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 5 % of a + 3 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 3 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 3 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 9 b = 12 a + 16 b ⇒ 3 a = 7 b ⇒ ab = 7 / 3 ⇒ a : b = 7 : 3 answer : option c"
Answer: c
Python program:
a = 8 / 100
b = a * 3
c = b / 3
d = 3 / 100
e = c - d
f = 5 / 100
g = 6 / 100
h = g * 2
i = h / 3
j = f - i
k = e / j
Problem: radha bought a watch for rs . 144 and got a percentage of profit equal to the cost price of the watch . what is the cost price of the watch ?
Options: a ) rs . 72 , b ) rs . 78 , c ) rs . 80 , d ) rs . 90 , e ) rs . 92
Rationale: sp = 144 cp = x profit % = x c . p . = ( 100 / ( 100 + gain % ) ) * s . p . x = ( 100 / 100 + x ) * 144 x ^ 2 + 100 x = 14400 x ^ 2 + 180 x - 80 x - 14400 = 0 ( x + 180 ) ( x - 80 ) = 0 x = - 180 x = 80 answer : d
Answer: d
Python program:
a = 100 * 100
b = 100 * 144
c = b * 4
d = a + c 
e = math.sqrt(d)
f = e - 100
g = f / 2
h = g + 10
Problem: a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 3 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 36 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 3 = 1 / 3 ( b + 3 ) - - - - > 3 a - 9 = b + 3 scenario 2 b - 3 = 1 / 2 ( a + 3 ) - - - - - > 2 b - 6 = a + 3 from scenario 1 , b = 3 a - 12 substitute b with this information in stmt 2 2 ( 3 a - 12 ) - 9 = a + 3 - - - - - - > 6 a - 24 - 9 = a + 3 - - - - - - > 6 a - a = 33 + 3 - - - > 5 a = 36 a = 36 / 5 , answer choice a"
Answer: a
Python program:
a = 3 + 3 
b = a + 2 
c = 3 / 2
d = b * c
e = 1 / 2
f = 2 + e 
g = d / f
Problem: 27 is a perfect cube . when x is perfect cube which is added to the prime factor of 27 , the result is not a prime number . what is the square root of x ?
Options: a ) 2
b ) 4
c ) 6
d ) 8
e ) 10
Rationale: 27 is 3 * 3 * 3 2 * 2 = 4 , 3 + 4 = 7 4 * 4 = 16 , 3 + 16 = 17 6 * 6 = 36 , 3 + 36 = 39 8 * 8 = 64 , 3 + 64 = 67 10 * 10 = 100 , 3 + 100 = 103 here c is the only addition that is not a prime number . so the answer is c
Answer: c
Python program:
a = 2 * 2
b = 2 * a
c = 27 + b 
d = math.sqrt(c)
Problem: | x + 3 | – | 4 - x | = | 8 + x | how many k solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Python program:
a = 4 + 3 
b = a * 2
c = b / 8
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 55 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 55 has the form 4 k + 3 , so the units digit of 93 ^ 55 is 7 . the units digit of powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a
Python program:
a = reminder * (
b = reminder + (
Problem: a train traveling at 36 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 120 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 36 kmph * 12 seconds convert 36 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 36 kmph = 5 / 18 ∗ 36 = 10 m / sec therefore , length of the platform = 10 m / s * 12 sec = 120 meters . choice a"
Answer: a
Python program:
a = 36 * 1000
b = a / 3600
c = b * 30
d = 36 * 1000
e = d / 3600
f = e * 12
g = c - f
Problem: when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.05 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 280 , d ) 112 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.05 = 14 / j 0.05 * j = 14 j = 14 / 0.05 = 1400 / 5 = 280 so j = 280 , answer = c ."
Answer: c
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 134 - 5
e = 14 / d
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 8 ?
Options: a ) 61,600 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 8 seeing the options after dividing an finding the reminder of 2 my answer was a"
Answer: a
Python program:
a = 1000 - 3
b = 3 * 3
c = b * 10
d = 3 * 3
e = c + d 
f = e + 3 
g = a - f
h = g / 8
i = h + 1 
j = i / 2
k = 1000 - 3
l = 3 * 3
m = l * 10
n = 3 * 3
o = m + n 
p = o + 3 
q = k + p 
r = j * q
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 35 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 . 53 , c ) c . 55 , d ) d . 68 , e ) e . 60
Rationale: "35 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 = ( 35 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 87.5 that is approximately 88 thus , more men needed to finish the task = 88 - 35 = 53 hence answer is b"
Answer: b
Python program:
a = 15 - 2
b = 35 * a
c = b * 100
d = 300 - 100
e = 2 * 5
f = c / e
g = f - 35
Problem: what least number should be subtracted from 1,439 so that the remainder when divided by 5 , 11 , and 13 will leave in each case the same remainder 3 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the lcm of 5 , 11 , and 13 is 715 . the next multiple is 2 * 715 = 1,430 . 1,430 + { remainder } = 1,430 + 3 = 1,433 , which is 6 less than 1,439 . answer : e ."
Answer: e
Python program:
a = 5 * 11
b = a * 13
c = b * 2
d = c + 3 
e = 1 - 439
Problem: a and b invests rs . 5000 and rs . 6000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 2 : 3 , b ) 82 : 31 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 5000 * 4 ) + ( 2500 * 8 ) : ( 6000 * 6 ) + ( 4000 * 6 ) 40000 : 60000 2 : 3 answer : a"
Answer: a
Python program:
a = 5000 * 4
b = 6000 / 3
c = 2 * 4
d = b * c
e = a + d 
f = 2 * 3
g = 6000 * f
h = 6000 / 3
i = 6000 - h
j = 2 * 3
k = i * j
l = g + k 
m = e / l
Problem: how long will a boy take to run round a square field of side 20 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 24 sec , e ) 39 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 20 * 4 = 80 m time taken = 80 * 3 / 10 = 24 sec answer is d"
Answer: d
Python program:
a = 20 * 4
b = 1000 / 3600
c = 12 * b
d = a / c
Problem: ( 4300731 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1765113 , d ) 1675123 , e ) none of them
Rationale: "let 4300731 - x = 2535618 then x = 4300731 - 2535618 = 1765113 answer is c"
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 4300731 * b
Problem: what two - digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 4 = 10 x + y = x ^ 2 y ^ 2 - 11 thus 2 xy + 4 = x ^ 2 + y ^ 2 - 11 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 26 or 98 thus the answer is c"
Answer: c
Python program:
a = 11 - 4
b = a + 1 
c = 10 * b
d = c + 4
Problem: if a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius , then surface area of each ball ( in sq . cm ) is ?
Options: a ) 100 π
b ) 101 / π
c ) 99 π / 12
d ) 54 / 13 π
e ) 22 / 10 π
Rationale: explanation : 4 / 3 π x 10 x 10 x 10 = 8 x 4 / 3 π rxrxr r = 5 4 π x 5 x 5 = 100 π answer is a
Answer: a
Python program:
a = 4 / 3
b = 10 ** 3
c = a * b
d = c * math.pi
e = d / 8
f = e * 3
g = 4 * math.pi
h = f / g
i = 1/(3)
j = h ** i
k = j ** 2
l = k * 4
m = l * math.pi
Problem: what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1115 , 1120 , and 1 , 1252140 , 2345 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54
Rationale: add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e
Answer: e
Python program:
a = 12 + 13 
b = a + 14 
c = b + 510 
d = c + 520 
e = d + 530 
f = e + 1115 
g = f + 1120 
h = 1115 + 10 
i = g + h 
j = 100 * 2
k = j + 4 
l = k + 1 
m = 2345 - l
n = i + m 
o = n + 2345 
p = 10 + 1 
q = o / p
Problem: the price of a certain painting increased by 20 % during the first year and decreased by 25 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 90 % , c ) 120 % , d ) 85 % , e ) 95 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.25 = 120 * 0.75 = 90 hence required answer = ( 90 / 100 ) * 100 % = 90 % answer is b ."
Answer: b
Python program:
a = 20 - 25
b = 25 * 20
c = b / 100
d = a - c
e = d + 100
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 13 years and that of the other 9 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15
Rationale: explanation : age of the 15 th student = [ 15 * 15 - ( 13 * 5 + 16 * 9 ) ] = 16 years . answer : b
Answer: b
Python program:
a = 15 * 15
b = 5 * 13
c = 9 * 16
d = b + c 
e = a - d