euclaise/mathqa_programs huggingface dataset:
Problem: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 8 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 17 , e ) 50
Rationale: "his height was = 5 feet 8 inch = 8 + 60 = 68 inch . required % correction = 68 * ( 1.25 - 1 ) = 17 d"
Answer: d
Python program:
a = const_0_25 + const_0_25 
b = 25 + a 
c = b - 5
d = const_0_25 + const_0_25 
e = 25 + d 
f = e - 5
g = 100 + f 
h = c / g
i = h * 100
Problem: the tens digit of a two digit number is 4 times of its unit digit and the sum of the digits be 10 . then the first number is
Options: a ) 67 , b ) 73 , c ) 53 , d ) 82 , e ) 89
Rationale: let the number be 10 x + y according to the question x = 4 y x + y = 10 4 y + y = 10 or y = 2 and x = 8 so required number is = 10 * 8 + 2 = 82 answer : d
Answer: d
Python program:
a = 1 + 4 
b = 10 / a
c = 4 * b
d = c * 10
Problem: a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 180 - 50 ) m = 130 m . answer : c
Answer: c
Python program:
a = 3 / const_60
b = a * 1000
c = 180 - b
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 40 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 333 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 40 ) = 21 + 312 = > 333 hence answer will be ( a ) 333"
Answer: a
Python program:
a = 0 * 65
b = a * 12
Problem: in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is
Options: a ) 50 liters , b ) 55 liters , c ) 60 liters , d ) 70 liters , e ) 75 liters
Rationale: "quantity of milk = 60 x 2 litres = 40 litres . 3 quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = 40 . 20 + x now , 40 = 1 20 + x 2 20 + x = 80 x = 60 . quantity of water to be added = 60 liters . c"
Answer: c
Python program:
a = 2 + 1 
b = 60 / a
c = 60 - b
d = c * 2
e = 2 + 1 
f = 60 / e
g = d - f
Problem: a 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 280 / 9 = 500 / 9 x = 220 ans is 220 m answer : b"
Answer: b
Python program:
a = 120 + 80 
b = a * const_0_2778
c = 9 * b
d = c - 280
Problem: find the average of all the numbers between 11 and 34 which are divisible by 5 ?
Options: a ) 10 , b ) 20 , c ) 22 , d ) 30 , e ) 15
Rationale: "average = ( 15 + 20 + 25 + 30 ) 4 = 90 / 4 = 22 answer is c"
Answer: c
Python program:
a = 11 + 4 
b = 34 - 4
c = a + b 
d = c / 2
Problem: x and y can do a piece of work in 20 days and 12 days respectively . x started the work alone and then after 4 days y joined him till the completion of work . how long did the work last ?
Options: a ) 8 days , b ) 10 days , c ) 12 days , d ) 13 days , e ) 14 days
Rationale: "let the total units of work to be completed be 60 . units of work completed by x in a single day = 60 / 20 = 3 units . units of work completed by y in a single day = 60 / 12 = 5 units . thus , 8 units of work can be done by them in a single day working together . x works for 4 days alone = 12 units of work . remaining work = ( 60 - 12 ) = 48 units . now , x and y works together to complete the remaining work = 48 / 8 = 6 days hence , total days taken to complete the work = ( 6 + 4 ) = 10 days . answer : b"
Answer: b
Python program:
a = 4 / 20
b = 1 - a
c = 20 * b
d = 12 * c
e = 20 + 12 
f = d / e
g = 4 + f
Problem: if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 1 * 1 / 4 = 1 / 4 answer : a"
Answer: a
Python program:
a = 2 / 8
Problem: find the curved surface area , if the radius of a cone is 7 m and slant height is 14 m ?
Options: a ) 308 , b ) 369 , c ) 434 , d ) 476 , e ) 513
Rationale: "cone curved surface area = ï € rl 22 / 7 ã — 7 ã — 14 = 22 ã — 14 = 308 m ( power 2 ) answer is a ."
Answer: a
Python program:
a = 7 * 14
b = math.pi * a
Problem: if | x | = 9 x - 16 , then x = ?
Options: a ) 1 , b ) 1 / 2 , c ) 2 , d ) 4 , e ) - 1 / 2
Rationale: substituted option c i . e x = 2 . inequality satisfied . this eliminates all options except answer is c
Answer: c
Python program:
a = 9 - 1
b = 16 / a
Problem: sonika deposited rs . 8000 which amounted to rs . 10200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 10680 , c ) 2999 , d ) 2774 , e ) 1212
Rationale: "( 8000 * 3 * 2 ) / 100 = 480 10200 - - - - - - - - 10680 answer : b"
Answer: b
Python program:
a = 2 / 100
b = 10200 - 8000
c = b / 3
d = c / 8000
e = a + d 
f = e * 8000
g = f * 3
h = g + 8000
Problem: the average monthly salary of 24 employees in an organisation is rs . 2400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4900 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 2500 * 25 - 2400 * 24 ) = rs . 4900 answer : c"
Answer: c
Python program:
a = 2400 + 100 
b = 24 + 1 
c = a * b
d = 2400 * 24
e = c - d
Problem: the s . i . on a certain sum of money for 6 years at 16 % per annum is half the c . i . on rs . 8000 for 2 years at 20 % per annum . the sum placed on s . i . is ?
Options: a ) 3000.33 , b ) 2802.33 , c ) 1833.33 , d ) 2990.33 , e ) 2982.33
Rationale: c . i . = [ 8000 * ( 1 + 20 / 100 ) 2 - 8000 ] = ( 8000 * 6 / 5 * 6 / 5 - 8000 ) = rs . 3520 . sum = ( 3520 * 100 ) / ( 6 * 16 ) = rs . 1833.33 answer : c
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 2
d = 8000 * c
e = d - 8000
f = e / 2
g = 16 / 100
h = 6 * g
i = f / h
Problem: a farmer wishes to start a 100 square metres rectangular vegetable garden . since he has only 30 m barbed wire , he fences three sides of the garden letting his house compound wall act as the fourth side fencing . the dimension of the garden is :
Options: a ) 15 m × 6.67 m
b ) 20 m × 5 m
c ) 30 m × 3.33 m
d ) 40 m × 2.5 m
e ) none of these
Rationale: we have : 2 b + l = 30 ⇒ l = 30 – 2 b . area = 100 m 2 ⇒ l × b = 100 ⇒ b ( 30 – 2 b ) = 100 ⇒ b 2 – 15 b + 50 = 0 ⇒ ( b – 10 ) ( b – 5 ) = 0 ⇒ b = 10 or b = 5 . when b = 10 , l = 10 and when b = 5 , l = 20 . since the garden is rectangular , so its dimension is 20 m × 5 m . answer b
Answer: b
Python program:
a = 30 / 3
b = 100 / a
Problem: if z is a multiple of 9402 , what is the remainder when z ^ 2 is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the sum of the digits is 9 + 4 + 2 = 15 . thus 3 is a factor of 9402 , so 3 is a factor of z . then 3 ^ 3 = 9 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 9 is 0 . the answer is a ."
Answer: a
Python program:
a = 9402 / 3
b = a ** 2
c = b / 9
d = 9 - 2
e = 1000 * d
f = e * 100
g = 9 - 2
h = 1000 * g
i = h * 10
j = f + i 
k = 2 * 100
l = j + k 
m = 100 - 2
n = l + m 
o = c - n
p = o * 9
Problem: a techno company has 14 machines of equal efficiency in its factory . the annual manufacturing costs are rs 42000 and establishment charges are rs 12000 . the annual output of the company is rs 70000 . the annual output and manufacturing costs are directly proportional to the number of machines . the shareholders get 12.5 profit , which is directly proportional to the annual output of the company . if 7.14 machines remain closed throughout the year , then the percentage decrease in the amount of profit of the shareholders would be :
Options: a ) 12 % , b ) 12.5 % , c ) 13.5 % , d ) 13 % , e ) 14 %
Rationale: explanation : the original profit is : - = > 70000 − 42000 − 12000 = 16000 . if 7.14 % of 14 i . e . one of the machines closed throughout the year , then the change in profit will be : - = > ( 13 / 14 ) × [ 70000 − 42000 ] . = > 14000 . thus , decrease in the profit % is : - = > ( 2000 / 16000 ) × 100 . = > 12.5 % . answer : b
Answer: b
Python program:
a = 12 / 5
b = 70000 - 42000
c = b - 12000
d = a * c
e = 14 - 1
f = e / 14
g = 70000 - 42000
h = f * g
i = h - 12000
j = 12 / 5
k = i * j
l = d - k
m = 12 / 5
n = 70000 - 42000
o = n - 12000
p = m * o
q = l / p
r = q * 100
Problem: p and q can complete a work in 80 days and 48 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?
Options: a ) 35 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 8 days = 8 ã — ( 1 / 80 ) = 1 / 10 remaining work = 1 â € “ 1 / 10 = 9 / 10 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 9 / 10 ) / ( 1 / 30 ) = 27 total days = 8 + 27 = 35 answer : option a"
Answer: a
Python program:
a = 8 / 80
b = 1 - a
c = 1/(80)
d = 1/(48)
e = c + d 
f = b / e
g = 8 + f
Problem: a and b together can complete work in 6 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 3 , b ) 8 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : ( a + b ) one day work = 1 / 6 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 6 - 1 / 6 = 1 / 6 b alone can complete the work in 6 days so half of the work in 3 days answer : option a
Answer: a
Python program:
a = 3 / 6
b = 6 * a
Problem: how many even number in the range between 25 to 100 inclusive are not divisible by 3
Options: a ) 27 , b ) 30 , c ) 31 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 26 , 28,30 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 38 . for 6 , 36 , 42 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 11 . hence , only divisible by 2 but not 3 = 38 - 11 = 27 . hence , answer a"
Answer: a
Python program:
a = 100 - 25
b = a - 2
c = b / 2
d = 100 - 2
e = 3 * 4
f = d - e
g = f - 3
h = g - 3
i = h / 3
j = i / 2
k = c - j
Problem: sum of two numbers is 30 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 30 2 x – 3 y = 5 x = 19 y = 11 c )"
Answer: c
Python program:
a = 5 / 2
b = 30 - a
c = b / 2
d = 30 - c
Problem: the sum of three consecutive multiples of 3 is 72 . what is the larget number ?
Options: a ) 26 , b ) 27 , c ) 46 , d ) 57 , e ) none
Rationale: "sol . let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 ⇔ 9 x = 63 ⇔ x = 7 . ∴ largest number = 3 x + 6 = 27 . answer b"
Answer: b
Python program:
a = 3 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 3 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 3 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 3 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: 9 log 9 ( 6 ) = ?
Options: a ) 1 , b ) 6 , c ) 3 , d ) 4 , e ) 5
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 6 ) = 6 correct answer b"
Answer: b
Python program:
a = 9 * 9
b = math.log(a)
c = math.log(10)
d = b / c
Problem: two mixtures of a and b have a and b in the ratio 3 : 2 and 3 : 4 . in what proportion should these two mixtures be mixed to get a new mixture in which the ration of a to b is 5 : 4 ?
Options: a ) 6 : 1 , b ) 5 : 4 , c ) 20 : 7 , d ) 10 : 9 , e ) 14 : 11
Rationale: i got c but with a different , yet slightly longer approach , which i constantly use for proportion problems such as this one . usually , this approach is very efficient when used with slightly difficult questions , but this problem is quite hard so i had to slightly tweak it . i will show you how i usually use the approach and later show you how to use it with this specific problem . example . 1 liter of solution a contains 45 % alcohol , while 1 liter of solution b contains 20 % alcohol . in what ratio must the two solutions be used to get a solution with 30 % alcohol solution : 1 . 45 / 100 * [ a / ( a + b ) ] + 20 / 100 * [ b / ( a + b ) ] = 30 / 100 2 . multiply 100 to both sides to arrive at 45 a / ( a + b ) + 20 b / ( a + b ) = 30 3 . multiply ( a + b ) to both sides to arrive at 45 a + 20 b = 30 a + 30 b 4 . distribute to arrive at 15 a = 10 b 5 . thus the ratio is a / b = 10 / 15 = 2 / 3 now using this same approach , we tackle gopu 106 ’ s question . it is important to first think of x in the mixture as the alcohol in the problem above ; hence , a mixture of x and y in the ratio of 3 : 2 translates to x is 3 / 5 of the solution . applying this concept to all three equations , we write : 1 . 3 / 5 * [ a / ( a + b ) ] + 3 / 7 * [ b / ( a + b ) ] = 5 / 9 2 . now here is the tweak that must be made to continue with this approach . you must find the common denominator for all three numbers and organize the fractions accordingly . by finding the common denominator of 5 , 79 ( or 315 ) we re - write the equations as follows 3 . 189 / 315 * [ a / ( a + b ) ] + 135 / 315 * [ b / ( a + b ) ] = 175 / 315 4 . multiply 315 to both sides to arrive at 189 a / ( a + b ) + 135 b / ( a + b ) = 175 5 . multiply ( a + b ) to both sides to arrive at 189 a + 135 b = 175 a + 175 b 6 . distribute to arrive at 14 a = 40 b 7 . thus the ratio is a / b = 40 / 14 = 20 / 7 or answer c
Answer: c
Python program:
a = 5 + 4 
b = 5 / a
c = 3 + 4 
d = 3 / c
e = b - d
f = 3 / 5
g = 5 + 4 
h = 5 / g
i = f - h
j = e / i
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 60 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 80 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 60 % is one st . dev , then on either side of m we have 60 / 2 = 30 % . so , 30 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 30 = 80 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 80 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it a"
Answer: a
Python program:
a = 100 - 60
b = a / 2
c = 100 - b
Problem: 8 kilograms of rice costing rs . 16 per kg is mixed with 4 kilograms of rice costing rs . 22 per kg . what is the average price of the mixture ?
Options: a ) 20 , b ) 18 , c ) 16 , d ) 19 , e ) 17
Rationale: p 1 = rs . 16 per kg , p 2 = rs . 22 per kg , q 1 = 8 kg , q 2 = 4 kg now , p = ( p 1 q 1 + p 2 q 2 ) / ( q 1 + q 2 ) average price of the mixture = 8 * 16 + 4 * 22 / 12 = 128 + 88 / 12 = 216 / 12 = 18 answer : b
Answer: b
Python program:
a = 22 * 4
b = 8 * 16
c = a + b 
d = 8 + 4 
e = c / d
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 70 metres ?
Options: a ) 22 seconds , b ) 65 seconds , c ) 78 seconds , d ) 12 seconds , e ) 14 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 70 / 5 = 14 seconds . answer : e"
Answer: e
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 70 / b
Problem: if the numbers 1 to 99 are written on 99 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 99 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 73 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 99 . answer : c"
Answer: c
Python program:
a = 1 / 99
Problem: a trader purchased two colour televisions for a total of rs . 35000 . he sold one colour television at 30 % profit and the other 40 % profit . find the difference in the cost prices of the two televisions if he made an overall profit of 32 % ?
Options: a ) 21000 , b ) 21009 , c ) 21029 , d ) 21298 , e ) 21098
Rationale: let the cost prices of the colour television sold at 30 % profit and 40 % profit be rs . x and rs . ( 35000 - x ) respectively . total selling price of televisions = x + 30 / 100 x + ( 35000 - x ) + 40 / 100 ( 35000 - x ) = > 130 / 100 x + 140 / 100 ( 35000 - x ) = 35000 + 32 / 100 ( 35000 ) x = 28000 35000 - x = 7000 difference in the cost prices of televisions = rs . 21000 answer : a
Answer: a
Python program:
a = 100 + 32 
b = a / 100
c = b * 35000
d = 100 + 30 
e = d / 100
f = e * 35000
g = c - f
h = 100 + 40 
i = h / 100
j = 100 + 30 
k = j / 100
l = i - k
m = g / l
n = 35000 - m
o = 100 + 32 
p = o / 100
q = p * 35000
r = 100 + 30 
s = r / 100
t = s * 35000
u = q - t
v = 100 + 40 
w = v / 100
x = 100 + 30 
y = x / 100
z = w - y
A = u / z
B = n - A
Problem: an article is bought for rs . 775 and sold for rs . 900 , find the gain percent ?
Options: a ) 11.1 % , b ) 12.1 % , c ) 13.1 % , d ) 15.1 % , e ) 16.1 %
Rationale: "775 - - - - 125 100 - - - - ? = > 16.1 % answer : e"
Answer: e
Python program:
a = 900 * 100
b = a / 775
c = 100 - b
Problem: 9 ! / ( 9 - 3 ) ! = ?
Options: a ) 336 , b ) 346 , c ) 356 , d ) 366 , e ) 504
Rationale: 9 ! / ( 9 - 3 ) ! = 9 ! / 6 ! = 9 * 8 * 7 = 504 . hence , the correct answer is e .
Answer: e
Python program:
a = math.factorial(9)
b = 9 - 3
c = math.factorial(b)
d = a / c
Problem: if 213 × 16 = 3408 , then 1.6 × 21.3 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 1.6 × 21.3 = ( 16 / 10 x 213 / 10 ) = ( 16 x 213 / 100 ) = 3408 / 100 = 34.08 . answer c"
Answer: c
Python program:
a = 1 * 6
Problem: if the simple interest on a sum of money for 5 years at 18 % per annum is rs . 900 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 1287.76 , b ) rs . 1284.76 , c ) rs . 1587.76 , d ) rs . 1266.76 , e ) rs . 1283.76
Rationale: "sum = ( 900 * 100 ) / ( 5 * 18 ) = rs . 1 , 000.00 c . i . on rs . rs . 1 , 000.00 for 5 years at 18 % = rs . 2 , 287.76 . = rs . 2 , 287.76 - 1 , 000.00 = rs . 1287.76 answer : a"
Answer: a
Python program:
a = 18 / 100
b = a * 5
c = 900 / b
d = c * 18
e = d / 100
f = 18 / 100
g = f * 5
h = 900 / g
i = e + h 
j = 18 / 100
k = j * 5
l = 900 / k
m = l * 18
n = m / 100
o = 18 / 100
p = o * 5
q = 900 / p
r = n + q 
s = r * 18
t = s / 100
u = i + t 
v = 18 / 100
w = v * 5
x = 900 / w
y = u - x
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 150 . the amount of the bill is
Options: a ) 1200 , b ) 1764 , c ) 1400 , d ) 1354 , e ) none of these
Rationale: explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 150 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 150 or x = 1250 . p . w . = rs . 1250 sum due = p . w . + t . d . = rs . ( 1250 150 ) = rs . 1400 answer : c
Answer: c
Python program:
a = 4 * 3
b = 9 / a
c = b * 16
d = c / 100
e = 150 / d
f = e + 150
Problem: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.81 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.81 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.81 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.81 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"
Answer: b
Python program:
a = 1 + 75 
b = a + 1 
c = b + 2 
d = c + 1 
e = d + 2 
f = e + 1 
g = f / 7
h = min(g)
Problem: a freight elevator can carry a maximum load of 1100 pounds . sean , who weighs 200 pounds , is in the elevator with two packages weighing 150 pounds and 280 pounds . if he needs to fit 3 more packages in the elevator that weigh as much as possible without exceeding the elevator limit , what is the difference between their average and the average of the two packages already in the elevator ?
Options: a ) 59 , b ) 85 , c ) 190 , d ) 215 , e ) 210
Rationale: the average of existing 2 package is 150 + 280 / 2 = 430 / 2 = 215 remaining allowed weight = 1100 - 200 - 430 = 470 . allowed per package = 470 / 3 = 156 so difference in average of existing and allowable = 215 - 156 = 59 hence a
Answer: a
Python program:
a = 150 + 280 
b = a / 2
c = 1100 - 200
d = 150 + 280 
e = c - d
f = e / 3
g = b - f
Problem: power windows : 60 % anti - lock brakes : 25 % cd player : 75 % the table above shows the number of vehicles at bill ' s car dealership that have certain features . no vehicle has all 3 features , but 10 % have power windows and anti - lock brakes , 15 % have anti - lock brakes and a cd player , and 22 % have power windows and a cd player . what percent of the vehicles at bill ' s car dealership have a cd player but no power windows or anti - lock brakes ?
Options: a ) 25 , b ) 18 , c ) 11 , d ) 38 , e ) 0
Rationale: answer : d were looking for the number of cars with a cd player but no other features . we know that 40 % of the cars have a cd player , 15 % have a cd player and anti - lock brakes , while 22 % have a cd player and power windows . since no car has all three features , those account for all of the possibilities except for what were looking for . if a car has a cd player , it must either have anti - lock brakes , power windows , or no other features . since the total of cars with a cd player is 75 % , we can set up the following equation : 75 = 15 + 22 + x x = 38 , choiced .
Answer: d
Python program:
a = 75 - 15
b = a - 22
Problem: a train 360 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 30 sec , c ) 26 sec , d ) 27 sec , e ) 34 sec
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 50 = 30 sec answer : b"
Answer: b
Python program:
a = 60 - 140
b = a * const_0_2778
c = 360 / b
Problem: the value of ( log 9 27 + log 8 32 ) is :
Options: a ) 7 / 2 , b ) 19 / 6 , c ) 5 / 3 , d ) 7 , e ) 8
Rationale: let log 9 27 = x . then , 9 x = 27 = > ( 32 ) x = 33 = > 2 x = 3 = > x = 3 / 2 let log 8 32 = y . then 8 y = 32 = > ( 23 ) y = 25 = > 3 y = 5 = > y = 5 / 3 answer : c
Answer: c
Python program:
a = math.log(32)
b = math.log(8)
c = a / b