euclaise/mathqa_programs huggingface dataset:
Problem: the maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 40 , c ) 80 , d ) 90 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1080 and 920 = 40 . answer b"
Answer: b
Python program:
a = math.gcd(1080, 920)
Problem: 76 ^ 77 / 7 remainder is ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: as , 4 ^ 3 / 3 = 64 / 3 remainder = 1 and also 4 / 3 = 1 and 5 ^ 3 / 3 remainder = 2 and also 5 / 3 = 2 so it does not matter on the power value so the answer will be 76 / 7 remainder = 6 answer : b
Answer: b
Python program:
a = 76 - 77
b = 7 + a
Problem: 30 ^ 10 / 240 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) ( 15 / 4 ) ^ 5 , c ) 3 ^ 6 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 240 ^ 5 = ? a . 6 ^ 5 b . ( 15 / 4 ) ^ 5 c . 3 ^ 6 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 240 ^ 5 = ( 30 ^ 10 ) / ( 8 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 8 ^ 5 ) = ( 2 ^ 5 ) ( 15 ^ 5 ) / ( 2 ^ 5 ) ( 4 ^ 5 ) = ( 15 / 4 ) ^ 5 . thus , b is the answer ."
Answer: b
Python program:
a = 30 ** 10
b = 30 ** 5
c = a / b
Problem: 20 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 380 , b ) 470 , c ) 560 , d ) 650 , e ) 740
Rationale: "2 * 20 c 2 = 2 * 190 = 380 the answer is a ."
Answer: a
Python program:
a = 20 - 1
b = 20 * a
Problem: working alone , a can complete a certain kind of job in 15 hours . a and d , working together at their respective rates , can complete one of these jobs in 10 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "let total time taken by d to complete the job = d total time taken by a to complete the job = 15 work done by a in an hour 1 / a = 1 / 15 working together a and d can complete the job in 10 hours 1 / a + 1 / d = 1 / 10 = > 1 / d = 1 / 10 - 1 / 15 = 1 / 10 - 1 / 15 = 1 / 30 = > d = 30 hours answer e"
Answer: e
Python program:
a = 1/(10)
b = 1/(15)
c = a - b
d = 1/(c)
Problem: a can do a job in 12 days and b can do it in 20 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 15 days , b ) 13 days , c ) 22 days , d ) 11 days , e ) 19 days
Rationale: "a 1 / 12 + 1 / 20 = 2 / 15 15 / 2 * 2 = 15 days"
Answer: a
Python program:
a = 1 / 12
b = 1 / 20
c = a + b
Problem: fresh grapes contain 80 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 40 kg of fresh grapes ?
Options: a ) 10 kg , b ) 12 kg , c ) 15 kg , d ) 16 kg , e ) 20 kg
Rationale: "from the question we know : 40 kg * 80 % = 32 kg of water in the fresh grapes 40 kg - 32 kg of water = 8 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 20 % of the weight of the dry graps is water and we know that 8 kg is non - water mass we can set up the following equation : x = 1 / 5 ( x ) + 8 kg 4 / 5 ( x ) = 8 kg x = 10 kg answer - a"
Answer: a
Python program:
a = 100 - 80
b = a * 40
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
Problem: java house charges $ 4.25 for a cup of coffee that costs a total of $ 3.85 to make . cup ' o ' joe charges $ 4.80 for a cup that costs $ 4.65 to make . if java house sells 55000 cups of coffee , how many must cup ' o ' joe sell to make at least as much in total gross profit as its competitor does ?
Options: a ) 7,858 , b ) 8,301 , c ) 14,667 , d ) 63,840 , e ) 146,667
Rationale: java : profit / cup = 4.25 - 3.85 = 0.4 : no of cups = 55,000 : gross profit = 55,000 * 0.4 = 22,000 joe : profit / cup = 0.15 : gross profit = 22,000 : no of cups = 22,000 / 0.15 = 220,000 / 1.5 ( only closes is 146,667 ) answer e
Answer: e
Python program:
a = 4 - 25
b = 55000 * a
c = 4 - 8
d = b / c
e = 10 * 1000
f = d / e
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 14 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 14 + 11 - - > { bike } = 49 - - > # those who have bike only is { bike } - { both } = 49 - 14 = 35 . answer : b ."
Answer: b
Python program:
a = 90 - 11
b = a + 14 
c = b - 44
d = c - 14
Problem: if the product of two numbers is 62216 and their h . c . f . is 22 , find their l . c . m .
Options: a ) 2828 , b ) 2850 , c ) 1365 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 62216 , because we know product of two numbers = product of hcf and lcm lcm = 62216 / 22 = 2828 option a"
Answer: a
Python program:
a = 62216 / 22
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 12 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 96 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,12 = 12 / 100 x = 80 * 12 / 100 x = 9.6 9.6 / 10 = 0.96 = 96 % , answer d"
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 12 * b
d = c / 10
e = d * 100
Problem: a train crosses a tunnel of 1200 m in 45 sec , same train crosses another platform of length 180 m in 15 sec . then find the length of the train ?
Options: a ) 350 m , b ) 400 m , c ) 272 m , d ) 330 m , e ) 267 m
Rationale: length of the train be ‘ x ’ ( x + 1200 ) / 45 = ( x + 180 ) / 15 x + 1200 = 3 x + 540 2 x = 660 x = 330 m answer : d
Answer: d
Python program:
a = 45 / 15
b = a * 180
c = 1200 - b
d = c / 2
Problem: if 8 men or 12 women can do a piece of work in 40 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 24 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 40 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 40 = 1 / 480 so , 20 women work = 20 / 480 = 1 / 24 ans : 24 days answer : e"
Answer: e
Python program:
a = 8 * 40
b = 6 / a
c = 12 * 40
d = 11 / c
e = b + d 
f = 1/(e)
Problem: if the sides of a triangle are 21 cm , 19 cm and 5 cm , what is its area ?
Options: a ) 42.25 cm 2 , b ) 57.5 cm 2 , c ) 42.5 cm 2 , d ) 47.5 cm 2 , e ) 52.5 cm 2
Rationale: "the triangle with sides 21 cm , 19 cm and 5 cm is right angled , where the hypotenuse is 21 cm . area of the triangle = 1 / 2 * 19 * 5 = 47.5 cm 2 answer : d"
Answer: d
Python program:
a = 19 * 5
b = a / 2
Problem: excluding stoppages , the speed of a bus is 90 km / hr and including stoppages , it is 84 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 18 min , b ) 4 min , c ) 8 min , d ) 6 min , e ) 5 min
Rationale: "due to stoppages , it covers 6 km less . time taken to cover 6 km = 6 / 90 * 60 = 4 min . answer : b"
Answer: b
Python program:
a = 90 - 84
b = a / 90
c = const_60 * b
Problem: two persons a and b can complete a piece of work in 18 days and 24 days respectively . if they work together , what part of the work will be completed in 2 days ?
Options: a ) 7 / 36 , b ) 9 / 35 , c ) 4 / 37 , d ) 8 / 35 , e ) 5 / 3
Rationale: "a ' s one day ' s work = 1 / 18 b ' s one day ' s work = 1 / 24 ( a + b ) ' s one day ' s work = 1 / 18 + 1 / 24 = 7 / 72 the part of the work completed in 3 days = 2 ( 7 / 72 ) = 7 / 36 . answer : a"
Answer: a
Python program:
a = 1 / 18
b = 1 / 24
c = a + b 
d = 2 * c
Problem: present birth rate is 32 per 1000 while death rate is 11 per 1000 . what will be the percentage increase in the rate of population ?
Options: a ) 0.21 % , b ) 21 % , c ) 0.021 % , d ) 2.1 % , e ) none of these
Rationale: birth rate = 32 / 1000 = 0.032 death rate = 11 / 1000 = 0.011 increase in population = 0.032 - 0.011 = 0.021 = 2.1 % answer : d
Answer: d
Python program:
a = 32 - 11
b = a / 1000
c = b * 100
Problem: on selling 11 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 45 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 120
Rationale: "( c . p . of 11 balls ) - ( s . p . of 11 balls ) = ( c . p . of 5 balls ) c . p . of 6 balls = s . p . of 11 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 6 = rs . 120 . answer : option e"
Answer: e
Python program:
a = 11 - 5
b = 720 / a
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 2 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) ( a ) 7 / 16 , b ) ( b ) 7 / 11 , c ) ( c ) 10 / 21 , d ) ( d ) 17 / 35 , e ) ( e ) 1 / 2
Rationale: "a simpler way i guess would be to think that in total 5 cups were sold . out of which 2 are small and 3 are large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 2 * 6 = 12 and 3 * 7 = 21 . total revenue was 12 + 21 = 33 and large cup sales as found above is 21 therefore answer is 21 / 33 i . e 7 / 11 b"
Answer: b
Python program:
a = 2 / 5
b = a * 10
c = 10 - b
d = 7 / 6
e = 2 / 5
f = e * 10
g = d * f
h = c * g
i = 2 / 5
j = i * 10
k = 2 / 5
l = k * 10
m = j * l
n = 2 / 5
o = n * 10
p = 10 - o
q = 7 / 6
r = 2 / 5
s = r * 10
t = q * s
u = p * t
v = m + u 
w = h / v
Problem: a boy is travelling from his home to school at 3 km / hr and reached 7 min late . next day he traveled at 6 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 1.2 km , b ) 1.3 km , c ) 1.4 km , d ) 1.5 km , e ) 1.6 km
Rationale: "let the distance be x t 1 = x / 3 hr t 2 = x / 6 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 3 - x / 6 = 1 / 4 x / 6 = 1 / 4 x = 1.5 km answer is d"
Answer: d
Python program:
a = 7 / const_60
b = 8 / const_60
c = a + b 
d = 1 / 6
e = c / d
Problem: a parking garage rents parking spaces for $ 15 per week or $ 30 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 420 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 15 = 780 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 30 = 360 $ 780 - 360 = 420 ans d"
Answer: d
Python program:
a = 3 + 2 
b = 15 * a
c = b + 2 
d = c * 15
e = 30 * 12
f = d - e
Problem: the price of commodity x increases by 40 cents every year , while the price of commodity y increases by 15 cents every year . in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 6.30 . in which year will the price of commodity x be 15 cents more than the price of commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 15 cents more than commodity y . $ 2.25 / 25 cents = 9 years the answer is 2001 + 9 years = 2010 . the answer is a ."
Answer: a
Python program:
a = 15 / 100
b = 6 - 30
c = a + b 
d = 40 / 100
e = 6 - 30
f = d - e
g = c / f
h = 2001 + g
Problem: steve traveled the first 2 hours of his journey at 60 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
Options: a ) 60 mph , b ) 72 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "distance traveled in 2 hours = 2 * 60 = 120 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 120 = 360 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 360 / 5 = 72 mph answer : b"
Answer: b
Python program:
a = 80 * 3
b = 60 * 2
c = a + b 
d = 3 + 2 
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g
Problem: a 12 % stock yielding 10 % is quoted at :
Options: a ) rs . 83.33 , b ) rs . 110 , c ) rs . 112 , d ) rs . 120 , e ) rs . 140
Rationale: income of rs 10 on investment of rs 100 income of rs 12 on investment of ? = ( 12 * 100 ) / 10 = 120 answer : d
Answer: d
Python program:
a = 100 / 10
b = a * 12
Problem: machine a takes 100 hours to complete a certain job and starts that job at 7 am . after two hour of working alone , machine a is joined by machine b and together they complete the job at 12 pm . how long would it have taken machine b to complete the jobif it had worked alone for the entire job ?
Options: a ) 100.11 , b ) 10.98 , c ) 18.07 , d ) 45.01 , e ) 35.09
Rationale: let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 2 hr ( so 2 units done ) then a and b finish total work in 15 hours . hence a and b finish 98 units in 15 hours . of these 1 x 15 = 15 units were done by a . hence b did 83 units in 15 hours . hence b ( working rate ) = 83 / 15 units / hr hence b takes 100 x 15 / 83 = 18.07 hours to complete the job . answer c .
Answer: c
Python program:
a = 1/(100)
b = a * 2
c = 1 - b
d = 12 * 2
e = d - 7
f = e - 2
g = c / f
h = 1/(100)
i = g - h
j = 1/(i)
Problem: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,070 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 8 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: "79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,070 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,070 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is b ."
Answer: b
Python program:
a = 79 * 48
b = const_0_25 * 1000
c = b * 100
d = 3 + 4 
e = d * 10
f = c + e 
g = f + 3 
h = a * g
Problem: to fill a tank , 20 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to one - fifth of its present ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 20 x . new capacity of bucket = 1 / 5 x therefore , required number of buckets = ( 20 x ) / ( 1 x / 5 ) = ( 20 x ) x 5 / 1 x = 100 / 1 = 100 answer is a ."
Answer: a
Python program:
a = 4 + 1 
b = 20 * a
c = b / 2
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) rs . 14,000 , b ) rs . 12,000 , c ) rs . 30,000 , d ) rs . 40,000 , e ) rs . 45,000
Rationale: "explanation : [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer is b"
Answer: b
Python program:
a = 5 * 4
b = a - 12
Problem: shopkeeper rise price by 32 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 0.98 % , b ) 4.98 % , c ) 3.95 % , d ) 6.98 % , e ) 7.98 %
Rationale: "let d initial price be 100 32 % rise now price = 132 / 100 * 100 = 132 10 % discount then price = 132 * 90 / 100 = 118.8 15 % discount then price = 118.8 * 85 / 100 = 100.98 so gain = 100.98 - 100 = 0.98 gain % = gain * 100 / cp = = > 0.98 * 100 / 100 = 0.98 % answer : a"
Answer: a
Python program:
a = 100 + 32 
b = 100 - 10
c = b / 100
d = a * c
e = 100 - 15
f = e / 100
g = d * f
h = g - 100
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 20000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 4000 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 20000 = > x = 4000 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 4000 answer : b"
Answer: b
Python program:
a = 4 / 5
b = a * 20000
c = 20000 - b
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 17 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 38 % , e ) 8.5 %
Rationale: "instead of using complex calculations and remembering formulae , why dont u directly get to weighted average . 3 parts of 10 % + 1 part of x ( unknown ) % = 4 parts of 17 % = > x % = 68 % - 30 % = 38 % ans d it is ."
Answer: d
Python program:
a = 17 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 10 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
Problem: 8 x 1.6 - 3 x 1.4 / 1.3 = ?
Options: a ) 21.5 , b ) 22 , c ) 15.8 , d ) 12.8 , e ) 25
Rationale: "given expression = ( 12.8 - 4.2 ) / 0.4 = 8.6 / 0.4 = 8.6 / 0.4 = 21.5 answer is a ."
Answer: a
Python program:
a = 8 * 1
b = 3 * 1
c = a - b
d = c / 1
Problem: a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 3.5 t seconds , then what is the length of the platform ?
Options: a ) 0.5 l , b ) 1.5 l , c ) 2.5 l , d ) 3.5 l , e ) 4.5 l
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 3.5 t ( l + p ) / ( l / t ) = 3.5 t p = 2.5 l the answer is c ."
Answer: c
Python program:
a = 3 - 5
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1045 , c ) c ) 1055 , d ) d ) 1190 , e ) e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 70 × 9 = 630 . total cost he has to pay = 560 + 630 = 1190 . d )"
Answer: d
Python program:
a = 8 * 70
b = 9 * 70
c = a + b
Problem: a cycle is bought for rs . 840 and sold for rs . 1220 , find the gain percent ?
Options: a ) 70 % , b ) 45 % , c ) 48 % , d ) 30 % , e ) 40 %
Rationale: "explanation : 840 - - - - 380 100 - - - - ? = > 45 % answer : b"
Answer: b
Python program:
a = 1220 - 840
b = a / 840
c = b * 100
Problem: for all numbers a and b , the operationis defined by ab = ( a + 2 ) ( b – 3 ) . if 3 x = – 25 , then x =
Options: a ) – 15 , b ) – 2 , c ) - 3 , d ) 6 , e ) 15
Rationale: ( 3 + 2 ) ( x - 3 ) = - 25 . . x - 3 = - 5 . . x = - 2 b
Answer: b
Python program:
a = 2 + 3 
b = 25 / a
c = 3 - b
Problem: the ratio of length to width of a rectangular showroom window is 3.3 to 2 . if the width of the window is 8 feet , what is the approximate length of the display in feet ?
Options: a ) 7
b ) 11
c ) 13
d ) 16
e ) 26
Rationale: explanation : letting l be the length of the window , the proportion for the ratio of the length to the width can be expressed in the following equation : 3.3 / 2 = l / 8 26.4 = 2 l 13.2 = l answer : option c
Answer: c
Python program:
a = 8 / 2
b = 3 * 3
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 170 , what is the least possible value of n ?
Options: a ) 14 , b ) 13 , c ) 15 , d ) 17 , e ) 16
Rationale: 17 , since n needs to be the largest of the prime factors . therefore , the answer is d .
Answer: d
Python program:
a = 170 / 2
Problem: in a jar there are balls in different colors : blue , red , green and yellow . the probability of drawing a blue ball is 1 / 8 . the probability of drawing a red ball is 2 / 5 . the probability of drawing a green ball is 7 / 10 . if a jar can not contain more than 50 balls , how many yellow balls are in the jar ?
Options: a ) 12 , b ) 15 , c ) 23 , d ) 7 , e ) 5
Rationale: answer of 1 st just add the given probabilities p ( blue ) + p ( red ) + p ( green ) i . e 1 / 8 + 2 / 5 + 3 / 10 = 5 + 16 + 12 / 40 now we know p ( blue ) + p ( red ) + p ( green ) + p ( yellow ) = 1 33 / 40 + p ( yellow ) = 1 p ( yellow ) = 33 / 40 i . e why yellow balls are 7 . d
Answer: d
Python program:
a = math.lcm(8, 5)
b = math.lcm(a, 10)
c = b / 8
d = math.lcm(8, 5)
e = math.lcm(d, 10)
f = e / 5
g = f * 2
h = c + g 
i = math.lcm(8, 5)
j = math.lcm(i, 10)
k = j / 10
l = k * 7
m = h + l 
n = 50 - m
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 3.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is e
Answer: e
Python program:
a = 4 - 2
b = a * 100
c = b / 2
Problem: of the 90 people in a room , 2 / 5 are women . if 2 / 3 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 26 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "women = 2 / 5 * 90 = 36 married = 2 / 3 * 90 = 60 unmarried = 30 max ( un - married women ) = 30 b"
Answer: b
Python program:
a = 2 / 5
b = 90 * a
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1 . 5 kmph . a man rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is
Options: a ) 16 hours , b ) 18 hours , c ) 20 hours , d ) 24 hours , e ) 28 hours
Rationale: "upstream = 9 kmph - 1.5 kmph = 7.5 kmph downstream = 9 kmph + 1.5 kmph = 10.5 kmph total time taken = 105 / 7.5 + 105 / 10.5 = 24 hrs answer : d"
Answer: d
Python program:
a = 9 + 1 
b = 5 / a
c = 9 - 1
d = 5 / c
e = b + d
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 83 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8300 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 83 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 83 = > total appeared candidates in state b = 83 x 100 = 8300 = > total appeared candidates in state a = total appeared candidates in state b = 8300"
Answer: b
Python program:
a = 7 - 6
b = a / 100
c = 83 / b
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is :
Options: a ) 16 hours , b ) 18 hours , c ) 20 hours , d ) 24 hours , e ) 26 hours
Rationale: "speed of upstream = 9 - 1.5 = 7.5 kmph speed of down stream = 9 + 1.5 = 10.5 kmph total time = ( 105 / 7.5 ) + ( 105 / 10.5 ) = 24 hrs answer : d"
Answer: d
Python program:
a = 9 + 1 
b = 105 / a
c = 9 - 1
d = 105 / c
e = b + d