euclaise/mathqa_programs huggingface dataset:
Problem: if the product of 8 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "the product of 8 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 7 correct option : e"
Answer: e
Python program:
a = 8 - 1
Problem: shopkeeper rise price by 35 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 5.275 % , b ) 4.275 % , c ) 3.275 % , d ) 6.275 % , e ) 7.275 %
Rationale: "let d initial price be 100 35 % rise now price = 135 / 100 * 100 = 135 10 % discount then price = 135 * 90 / 100 = 121.5 15 % discount then price = 121.5 * 85 / 100 = 103.275 so gain = 103.275 - 100 = 3.275 gain % = gain * 100 / cp = = > 3.275 * 100 / 100 = 3.275 % answer : c"
Answer: c
Python program:
a = 100 + 35 
b = 100 - 10
c = b / 100
d = a * c
e = 100 - 15
f = e / 100
g = d * f
h = g - 100
Problem: in what ratio must tea at rs . 65 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 6 per kg ?
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none
Rationale: "required ratio = 500 : 500 = 1 : 1 answer a"
Answer: a
Python program:
a = 70 - 6
b = 6 - 65
c = a / b
Problem: a briefcase has a number - lock system containing a combination of 3 digits ( each digit can be of numbers 0 to 8 ) . if the correct combination is unknown , how much maximum time would be required to open the bag if each “ trial ” of combination takes 3 seconds ?
Options: a ) 36.45 minutes , b ) 36.47 minutes , c ) 36.41 minutes , d ) 36.42 minutes , e ) 36.65 minutes
Rationale: explanation : maximum number of trials required = 9 * 9 * 9 = 729 . since for each combination trial , 3 seconds are required to open the briefcase is given as 3 * 729 = 2187 seconds = 36.45 minutes . answer : a
Answer: a
Python program:
a = 8 + 1 
b = 8 + 1 
c = a * b
d = 8 + 1 
e = c * d
f = e * 3
g = f / const_60
Problem: a driver just filled the car ' s gas tank with 27 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4
Rationale: let x be the number of liters of ethanol added to the gas tank . 0.05 ( 27 ) + x = 0.1 ( 27 + x ) 0.9 x = 2.7 - 1.35 = 1.35 x = 1.5 liters the answer is b .
Answer: b
Python program:
a = 27 * 5
b = 100 - 10
c = a / b
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 18 years investment will become $ 8,000 * 2 = $ 16,000 and in another 18 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c ."
Answer: c
Python program:
a = 8000 * 2
b = a * 2
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 460 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 40 / 23
Rationale: "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 460 km time taken by freddy = 4 hours average speed of freddy = 460 / 4 = 115 km / hour ratio of average speed of eddy to freddy = 200 / 115 = 40 / 23 answer e"
Answer: e
Python program:
a = 600 / 3
b = 460 / 4
c = a / b
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 42 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 24
Rationale: "12 * 42 = 504 504 % 21 = 24 answer : e"
Answer: e
Python program:
a = 12 * 42
b = a / 21
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 7,4 ) , and ( 7,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 2 / 7 , d ) 4 / 9 , e ) 7 / 10
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 28 . p ( x + y < 4 ) = 8 / 28 = 2 / 7 the answer is c ."
Answer: c
Python program:
a = 4 * 4
b = a / 2
c = 1 + 4 
d = 4 * c
e = b / d
Problem: the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 750 , b ) 650 , c ) 625 , d ) 115 , e ) 400
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 160 ) = rs . 625 . answer : b"
Answer: b
Python program:
a = 60 / 100
b = 1 + a 
c = 1000 / b
Problem: one - third of 1206 is what percent of 200 ?
Options: a ) 3 , b ) 201 , c ) 300 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 200 . ∵ 1206 / 3 = ( n x 200 ) / 100 ∴ n = ( 402 x 100 ) / 200 = 201 correct option : b"
Answer: b
Python program:
a = 1206 / 3
b = a / 200
c = 100 * b
Problem: machine p and machine q are each used to manufacture 660 sprockets . it takes machine p 10 hours longer to produce 660 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 6
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 660 / x = 660 / 1.1 x + 10 1.1 ( 660 ) = 660 + 11 x 11 x = 66 x = 6 the answer is e ."
Answer: e
Python program:
a = 10 / 100
b = a + 1 
c = 660 / b
d = 660 - c
e = d / 10
Problem: a train 280 m long is running at a speed of 54 km / hr . in what time will it pass a bridge 200 m long ?
Options: a ) 32 sec , b ) 42 sec , c ) 45 sec , d ) 18 sec , e ) 49 sec
Rationale: "total length = 280 + 200 = 480 speed = 54 km / h = ( 54 * 5 ) / 18 = 15 / 1 m / s time = ( 480 * 1 ) / 15 = 32 sec . answer : a"
Answer: a
Python program:
a = 54 - 200
b = a * const_0_2778
c = 280 / b
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 10,500 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 3000 , c ) 3600 , d ) 4200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 10500 = > 7 x = 10500 = > x = 1500 total number of motorcycles = 2 x = 2 * 1500 = 3000 answer b"
Answer: b
Python program:
a = 3 * 3
b = a * 1000
c = b + 100 
d = c / 7
e = d * 2
Problem: what is the sum of the 1 st 6 prime numbers greater than 10 ?
Options: a ) 112 , b ) 111 , c ) 212 , d ) 115 , e ) 113
Rationale: required numbers are = ( 11 + 13 + 17 + 19 + 23 + 29 ) = 112 note : 1 is not a prime number answer a
Answer: a
Python program:
a = 1 + 10 
b = 1 + 10 
c = b + 2 
d = a + c 
e = 1 + 10 
f = e + 2 
g = f + 4 
h = d + g 
i = 1 + 10 
j = i + 2 
k = j + 4 
l = k + 2 
m = h + l 
n = 1 + 10 
o = n + 2 
p = o + 4 
q = p + 2 
r = q + 4 
s = m + r 
t = 1 + 10 
u = t + 2 
v = u + 4 
w = v + 2 
x = w + 4 
y = x + 6 
z = s + y
Problem: $ 8,000 is deposited in a savings account that pays 12 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 8288.55 , b ) $ 8985.10 , c ) $ 8988.80 , d ) $ 8977.14 , e ) $ 8964.95
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 12 / 2 = 6 % now , ca = 8000 ( 1 + 6 / 100 ) ^ 2 = $ 8988.80 hence answer is c"
Answer: c
Python program:
a = 100 * 100
Problem: a , b and c can do a piece of work in 9 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ?
Options: a ) 4.12 days , b ) 4.52 days , c ) 3.52 days , d ) 2.52 days , e ) 4.92 days
Rationale: 1 / 9 + 1 / 14 + 1 / 28 = 55 / 252 = > 252 / 55 days = > 4.52 days answer : b
Answer: b
Python program:
a = 1/(28)
b = 1/(9)
c = 1/(14)
d = b + c 
e = a + d 
f = 1/(e)
Problem: in a division sum , the divisor is 12 times the quotient and 6 times the remainder . if the remainder is 24 , what is the divident ?
Options: a ) 1738 , b ) 1752 , c ) 1846 , d ) 1648 , e ) none
Rationale: "solution : dividend = [ divisor * quotient ] + remainder - - - - > ( 1 ) . given divisor = 6 * 24 = 144 . 12 * quotient = 144 = > quotient = 144 / 12 = 12 . substitute these values in the ( 1 ) then we get 1752 as dividend . answer b"
Answer: b
Python program:
a = 6 * 24
b = 6 * 24
c = b / 12
d = a * c
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 775 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 194 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 775 . as per question we need to take 1 / 4 of 775 to be considered for top 10 movies = 193.75 approximate the value we 194 . imo option b is the correct answer . . ."
Answer: b
Python program:
a = 775 / 4
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean a . if 68 % of the distribution lies one standard deviation d of the mean , what percent of the distribution is less than a + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ a + d 34 % ________________________________________________ a 34 % ________________________________________________ a - d 16 % since 68 % lies one standard deviation from mean a , = > 50 % of 68 % lies on either side as it is symmetric about a . thus 16 % lie below a - d and 16 % lie above a + d now below a + d = 16 + 34 + 34 = 84 % hence d"
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 8 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 16 , e ) 1 / 4
Rationale: "say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 8 - - > f = 16 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 16 ) = 3 / 16 . answer : d ."
Answer: d
Python program:
a = 3 * 3
b = 3 * 8
c = 2 * b
d = a / c
Problem: share rs . 4320 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1440
Rationale: "amount received by sanjay . 4 / 12 x 4320 = 1440 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1440 . e"
Answer: e
Python program:
a = 4320 / 2
b = 4320 / 6
c = a - b
Problem: a man rows his boat 78 km downstream and 56 km upstream , taking 4 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 5 , c ) 7 , d ) 8 , e ) 3
Rationale: "speed downstream = d / t = 78 / ( 4 ) = 20 kmph speed upstream = d / t = 56 / ( 4 ) = 14 kmph the speed of the stream = ( 20 - 14 ) / 2 = 3 kmph answer : e"
Answer: e
Python program:
a = 78 / 4
b = 56 / 4
c = a - b
d = c / 2
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1040 , b ) 1045 , c ) 1055 , d ) 1060 , e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 . c )"
Answer: c
Python program:
a = 8 * 70
b = 9 * 55
c = a + b
Problem: a car traveling at a certain constant speed takes 10 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 40 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 35 , b ) 35.5 , c ) 36 , d ) 36.5 , e ) 37
Rationale: "40 * t = 1 km = > t = 1 / 40 km / h v * ( t + 10 / 3600 ) = 1 v ( 1 / 40 + 10 / 3600 ) = 1 v ( 100 / 3600 ) = 1 v = 36 km / h the answer is c ."
Answer: c
Python program:
a = 1 / 40
b = 3600 * a
c = b + 10 
d = c / 3600
e = 1 / d
Problem: a camera lens filter kit containing 5 filters sells for $ 87.50 . if the filters are purchased individually , 2 of them are priced at $ 16.45 each , 2 at $ 14.05 each , 1 at $ 19.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 7 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) 11 %
Rationale: "cost of kit = $ 87.50 if filters are purchased individually - $ 16.45 * 2 + $ 14.05 * 2 + $ 19.50 = $ 80.50 amount saved = $ 87.50 - $ 80.50 = $ 7 required % age = ( $ 7 / $ 87.50 ) * 100 = 8 % so , the correct answer is b ."
Answer: b
Python program:
a = 2 * 16
b = 2 * 14
c = a + b 
d = 19 + 50 
e = 87 - 50
f = e * 100
g = f / 87
Problem: a man swims downstream 30 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 3 , b ) 8 , c ) 9 , d ) 4 , e ) 2
Rationale: 30 - - - 3 ds = 10 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 10 + 6 ) / 2 = 8 answer : b
Answer: b
Python program:
a = 18 / 3
b = 30 / 3
c = a + b 
d = c / 2
Problem: if a speaks the truth 75 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.45 , d ) 0.482 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 75 / 100 = 0.75 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.75 × 0.6 = 0.45 answer : c"
Answer: c
Python program:
a = 4 * 5
b = a * 5
c = 75 / b
d = 4 * 5
e = d * 5
f = 60 / e
g = c * f
Problem: what is the dividend . divisor 16 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 149 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 16 * 9 + 5 d = 144 + 5 d = 149 answer c"
Answer: c
Python program:
a = 16 * 9
b = a + 5
Problem: what is the positive difference between the sum of the squares of the first 3 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 24 , e ) 27
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 = 14 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 14 is 27 . so the answer is ( e ) ."
Answer: e
Python program:
a = 2 ** 2
b = 1 + a 
c = 3 ** 2
d = b + c 
e = 4 ** 2
f = d + e 
g = 4 + 1 
h = g ** 2
i = f + h 
j = 3 ** 2
k = i + j 
l = 4 + 3 
m = l + 3 
n = 2 + 3 
o = 4 + 1 
p = n + o 
q = 4 + 3 
r = p + q 
s = 2 + 3 
t = s + 3 
u = r + t 
v = m + u 
w = k - v
Problem: the charge for a single room at hotel p is 40 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) e . 150 %
Rationale: "p = 0.6 r = 0.9 g r = 0.9 g / 0.6 = 1.5 * g thus r is 50 % greater than g . the answer is d ."
Answer: d
Python program:
a = 100 - 40
b = 100 - 10
c = a / b
d = c * 100
e = 100 - d
f = 100 - 40
g = 100 - 10
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6800 ?
Options: a ) 4966 , b ) 6791 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6800 x 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 answer : b"
Answer: b
Python program:
a = 6835 + 9927 
b = a + 6855 
c = b + 7230 
d = c + 6562 
e = d / 5
f = e - 6800
g = f * 5
Problem: in a group of cheerleaders , the group made of 10 males and 16 females . every cheerleader gets to choose between a coke or malt . the number of those that choose malt is double the number that chose coke , if all the 6 males choose malt , how many females chose malt ?
Options: a ) 30 , b ) 5 , c ) 8 , d ) 20 , e ) 10
Rationale: number of cheerleaders = 27 number of male = 10 number of female = 17 coke = 9 maly = 17 female who chose malt = 17 - 9 = 8 answer = c
Answer: c
Python program:
a = 10 + 16 
b = 2 + 1 
c = a / b
d = math.floor(c)
e = 16 - d
Problem: if a certain number is divided by 5 , the quotient , dividend , and divisor , added together , will amount to 65 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 50
Rationale: "let x = the number sought . then x / 5 + x + 5 = 65 . x = 50 . e"
Answer: e
Python program:
a = 65 - 5
b = a * 5
c = 5 + 1 
d = b / c
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 105 , then what is the value of k ?
Options: a ) 209 , b ) 212 , c ) 215 , d ) 218 , e ) 221
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 105 ) / 5 + 32 = 221 the answer is e ."
Answer: e
Python program:
a = 105 * 9
b = a / 5
c = b + 32
Problem: a camera lens filter kit containing 5 filters sells for $ 57.50 . if the filters are purchased individually , 2 of them are priced at $ 10.45 each , 2 at $ 12.05 each , 1 at $ 17.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 7 % , b ) 8 % , c ) 8.5 % , d ) 10 % , e ) 11 %
Rationale: "cost of kit = $ 57.50 if filters are purchased individually - $ 10.45 * 2 + $ 12.05 * 2 + $ 17.50 = $ 62.50 amount saved = $ 62.50 - $ 57.50 = $ 5 required % age = ( $ 5 / $ 62.50 ) * 100 = 8 % so , the correct answer is b ."
Answer: b
Python program:
a = 2 * 10
b = 2 * 12
c = a + b 
d = 17 + 50 
e = 57 - 50
f = e * 100
g = f / 57
Problem: there were two candidates in an election . winner candidate received 75 % of votes and won the election by 500 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 750 , d ) 199 , e ) 231
Rationale: "w = 75 % l = 25 % 75 % - 25 % = 50 % 50 % - - - - - - - - 500 75 % - - - - - - - - ? = > 750 answer : c"
Answer: c
Python program:
a = 100 - 75
b = 75 - a
c = b / 100
d = 500 / c
e = d * 75
f = e / 100
Problem: if 170 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 47 , b ) 46 , c ) 41 , d ) 48 , e ) 45
Rationale: "the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 170 factorial will have 41 as - 170 / 5 = 34 34 / 5 = 6 6 / 5 = 1 so answer will be ( c ) 41"
Answer: c
Python program:
a = 4 + 1 
b = 170 / a
c = 4 + 1 
d = b / c
e = 4 + 1 
f = 170 / e
g = d + f
Problem: the ratio of spinsters to cats is 2 to 7 . if there are 35 more cats than spinsters , how many spinsters are there ?
Options: a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42
Rationale: let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 35 x = 7 and the number of spinsters is 2 ( 7 ) = 14 . the answer is a .
Answer: a
Python program:
a = 7 - 2
b = 35 / a
c = b * 2
Problem: chris mixed 3 pounds of raisins with 3 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 3 3 lbs of nuts = $ 9 total value of mixture = 9 + 3 = 12 fraction of the value of raisin = 3 / 12 = 1 / 4 ans : c"
Answer: c
Python program:
a = 3 * 3
b = a + 3 
c = 3 / b
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 9 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 72 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,09 = 9 / 100 x = 80 * 9 / 100 x = 7.2 7.2 / 10 = 0.72 = 72 % , answer b"
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 9 * b
d = c / 10
e = d * 100
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 4 m x 2 m x 25 cm ?
Options: a ) 5600 , b ) 6000 , c ) 1185 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 400 x 200 x 25 ) / ( 25 x 11.25 x 6 ) = 1185 . answer : option c"
Answer: c
Python program:
a = 4 * 100
b = 2 * 100
c = a * b
d = c * 25
e = 25 * 11
f = e * 6
g = d / f
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220
Rationale: orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b
Answer: b
Python program:
a = 8 * 370
b = 3320 - a
c = 12 - 8
d = b / c
e = 370 - d
f = 8 * 370
g = 3320 - f
h = 12 - 8
i = g / h
j = e - i
Problem: what is the sum of natural numbers between 40 and 100
Options: a ) 4800 , b ) 4270 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 40 and 100 numbers = 61 = > 100 - 40 = 60 + 1 = 61 sn = 61 / 2 ã — 140 = 61 ã — 70 = 4270 answer : b"
Answer: b
Python program:
a = 100 + 1
Problem: if 4 consecutive letters are selected at random from the english alphabet , then the probability that one of the letters is a vowel is ?
Options: a ) 13 / 23 , b ) 16 / 23 , c ) 11 / 23 , d ) 17 / 23 , e ) 18 / 23
Rationale: total no . of ways of selecting 4 consecutive letters = > 23 [ like abcd , bcde , efgh , . . etc ] no . of ways of having one is a vowel = > abcd , bcde , cdef , defg , efgh , fghi , ghij , hijk , ijkl , lmno , mnop , nopq , opqr , rstu , stuv , tuvw , uvwx . . . = 17 p ( one of letter is vowel ) = 17 / 23 answer : d
Answer: d
Python program:
a = const_26 - 3
b = 6 / a
c = 1 - b
Problem: a man is 36 years older than his son . in three years , his age will be thrice the age of his son . the present age of this son is
Options: a ) 28 years , b ) 22 years , c ) 18 years , d ) 16 years , e ) 15 years
Rationale: "let ' s son age is x , then father age is x + 36 . = > 3 ( x + 3 ) = ( x + 36 + 3 ) = > 3 x + 9 = x + 39 = > 2 x = 30 years = 15 years answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 36 - b
d = 2 - 1
e = c / d