euclaise/mathqa_programs huggingface dataset:
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 84 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 84 km time taken = distance / speed = 84 / 28 = 3 hours answer : option a"
Answer: a
Python program:
a = 24 + 4 
b = 84 / a
Problem: if 75 % of a boys answered the first question on a certain test correctly , 55 % answered the second question on the test correctly , and 20 % answered neither of the questions correctly , what % answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 50 % , d ) 60 % , e ) 65 %
Rationale: { total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 55 % - { both } + 20 % - - > { both } = 50 % . answer : c
Answer: c
Python program:
a = 75 + 55 
b = a + 20 
c = b - 100
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 50 years . find out the age of the youngest child ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 4
Rationale: let the age of the youngest child = x then , the ages of 5 children can be written as x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 ⇒ 5 x + 30 = 50 ⇒ 5 x = 20 ⇒ x = 205 = 4 answer is e .
Answer: e
Python program:
a = 50 / 5
b = a - 3
c = b - 3
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 6 x km .
Options: a ) 40 kmph , b ) 45 kmph , c ) 48 kmph , d ) 50 kmph , e ) 55 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 6 x / ( x / 8 ) = 48 kmph answer : c"
Answer: c
Python program:
a = 40 * 6
b = 40 / 40
c = 2 * 40
d = c / 20
e = b + d 
f = a / e
Problem: mary works in a restaurant a maximum of 45 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 410 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 25 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 25 ) = $ 250 . the total amount is $ 160 + $ 250 = $ 410 answer c 410 ."
Answer: c
Python program:
a = 45 * 8
b = 45 - 20
c = 25 / 100
d = 8 * c
e = b * d
f = a + e
Problem: a 20 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 250 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 20 , money invested = 100 × 20 / 8 = rs . 250 ie , market value of the stock = rs . 250 answer is c ."
Answer: c
Python program:
a = 100 / 8
b = a * 20
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 9 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 9 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 12 a . m . answer : d"
Answer: d
Python program:
a = 110 - 20
b = 25 + 20 
c = a / b
d = 8 + c
Problem: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 25 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 25 minutes , sam rides 5 km so sam will be 3 km ahead . it will take annie 60 minutes to catch sam . the answer is c ."
Answer: c
Python program:
a = 15 - 12
b = 40 / const_60
c = a * b
d = 12 / c
e = 15 - 12
f = 40 / const_60
g = e * f
h = d - g
i = 15 - 12
j = h / i
k = j * const_60
Problem: if 5 a = 3125 , then the value of 5 ( a - 3 ) is
Options: a ) 25 , b ) 50 , c ) 250 , d ) 300 , e ) none
Rationale: "sol . 5 a = 3125 = 5 a = 55 a = 5 . 5 ( 1 - 3 ) = 5 ( 5 - 3 ) = 5 ( 2 ) = 25 . answer a"
Answer: a
Python program:
a = 5 / 5
b = 5 / 3125
c = a * b
d = 3 * c
Problem: a train of length 250 m runs at a speed of 70 km / hr . what will be the time taken to cross any stationary object standing at the railway station ?
Options: a ) 20 sec , b ) 17.23 sec , c ) 12.86 sec , d ) 9.5 sec , e ) 8.5 sec
Rationale: explanation : length of train = 250 m , speed of train = 70 km / hr length of train is always considered as distance , and hence here distance = 250 m 1 ) first convert speed of km / hr into m / s speed of train = 70 x 5 = 19.44 m / s 18 2 ) we know that , speed = distance / time time taken to cross stationary object = 250 / 19.44 time taken to cross stationary object = 12.86 sec answer is c
Answer: c
Python program:
a = 70 / const_3_6
b = 250 / a
Problem: two pipes a and b can fill a tank in 4 and 5 hours respectively . if they are turned up alternately for one hour each , the time taken to fill the tank is ?
Options: a ) 4 hrs 29 min , b ) 4 hrs 24 min , c ) 8 hrs 24 min , d ) 4 hrs 44 min , e ) 5 hrs 24 min
Rationale: 1 / 4 + 1 / 5 = 9 / 20 20 / 9 = 2 2 / 9 9 / 20 * 2 = 9 / 10 - - - - 4 hours wr = 1 - 9 / 10 = 1 / 10 1 h - - - - 1 / 4 ? - - - - - 1 / 10 2 / 5 * 60 = 24 = 4 hrs 24 min answer : b
Answer: b
Python program:
a = 4 * 100
b = 1 / 4
c = 1 / 5
d = b + c 
e = d * 2
f = 1 - e
g = f * 4
h = g * const_60
i = a + h
Problem: if a ( a - 6 ) = 27 and b ( b - 6 ) = 27 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 6 , d ) 46 , e ) 48
Rationale: "i . e . if a = - 3 then b = 9 or if a = 9 then b = - 3 but in each case a + b = - 3 + 9 = 6 answer : option c"
Answer: c
Python program:
a = 6 + 27 
b = 6 - 27
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: when n is divided by 5 the remainder is 3 . what is the remainder when ( n - 1 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: n = 5 x + 3 , for some integer x ( n - 1 ) ^ 2 = ( 5 x + 2 ) ^ 2 = 5 y + 4 , for some integer y when we divide this by 5 , the remainder is 4 . the answer is e .
Answer: e
Python program:
a = 5 + 3 
b = a - 1
c = b ** 2
d = 5 + 3 
e = d - 1
f = e ** 2
g = f / 5
h = math.floor(g)
i = h * 5
j = c - i
Problem: how many 1 / 12 s are there in 37 1 / 2 ?
Options: a ) 350 , b ) 450 , c ) 500 , d ) 650 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 12 ) = ( 75 / 2 x 12 / 1 ) = 450 . answer : b"
Answer: b
Python program:
a = 1 / 2
b = 37 + a 
c = 1 / 12
d = b / c
Problem: . the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) none of these
Rationale: explanation : let the commodity p costs 40 paise more than the commodity q after n years price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 ⇒ n = 2.5 / . 25 = 250 / 25 = 101.15 ¯ = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 . answer : option d
Answer: d
Python program:
a = 6 - 3
b = 40 + a 
c = 40 - 15
d = b / c
e = 2001 + d
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 7.00 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 d ."
Answer: d
Python program:
a = 7 - 0
b = a * 100
c = b / 2
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 39 ?
Options: a ) 3 , b ) 8 , c ) 12 , d ) 32 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 39 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 8 more to make it 39 m + 39 answer - b"
Answer: b
Python program:
a = 39 - reminder
Problem: a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 800 square feet , what is the total length of the fence , in feet ?
Options: a ) 40 , b ) 80 , c ) 100 , d ) 120 , e ) 200
Rationale: "two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 800 ie x ^ 2 = 400 ie x = 20 l = 40 w = 20 total length of fence = 2 * 20 + 40 = 80 my answer is b"
Answer: b
Python program:
a = 1 + 1 
b = a * 2
c = b + 1 
d = 2 * c
e = 1 + 1 
f = e * 2
g = f + 1 
h = 2 * g
i = 1 + 1 
j = i * 2
k = j + 1 
l = 2 * k
m = h + l 
n = d + m 
o = 1 + 1 
p = o * 2
q = p + 1 
r = 1 + 1 
s = r * 2
t = s + 1 
u = 2 * t
v = q + u 
w = 1 + 1 
x = w * 2
y = x + 1 
z = v + y 
A = 800 / z
B = n + A
Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 3 flips but not on the last 3 flips ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Rationale: "p ( hhhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = a ** 6
Problem: a merchant marks his goods up by 50 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 20 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %
Rationale: "let the price be 100 . the price becomes 150 after a 50 % markup . now a discount of 20 % on 150 . profit = 120 - 100 20 % answer a"
Answer: a
Python program:
a = 50 + 100 
b = 50 + 100 
c = b * 20
d = c / 100
e = a - d
f = e - 100
Problem: a number when divided by a divisor leaves a remainder of 27 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 40 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 27 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 40 as d is also integer and 40 is a prime number , the d should be 40 to satisfy the above equation . hence answer is ' d '"
Answer: d
Python program:
a = 27 + 11
Problem: the triplicate ratio of 1 : 6 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 216
Rationale: "1 ^ 3 : 6 ^ 3 = 1 : 216 answer : e"
Answer: e
Python program:
a = 1 ** 6
b = 6 ** 6
c = a / b
Problem: for a race a distance of 224 meters can be covered by p in 14 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 232 m , b ) 288 m , c ) 324 m , d ) 231 m , e ) 236 m
Rationale: explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 14 = 16 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 18 seconds therefore , distance covered by p in that time = 16 m / s x 18 seconds = 288 metres answer : b
Answer: b
Python program:
a = 14 * speed
b = 224 - a
Problem: in an office , totally there are 2200 employees and 40 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 661 , b ) 600 , c ) 620 , d ) 616 , e ) none of these
Rationale: "number of male employees = 2200 * 40 / 100 = 880 required number of male employees who are less than 50 years old = 880 * ( 100 - 30 ) % = 880 * 75 / 100 = 616 . answer : d"
Answer: d
Python program:
a = 2200 * 40
b = a / 100
c = 100 - 30
d = c / 100
e = b * d
Problem: the sum of ages of 5 children born at theintervals of 3 years each is 50 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 9 , d ) 8 , e ) 10
Rationale: "the age of children x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 , x = 4 . correct answer ( a )"
Answer: a
Python program:
a = 50 / 5
b = a - 3
c = b - 3
Problem: if jake loses 35 pounds , he will weigh thrice as much as his sister . together they now weigh 275 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 35 = 3 s j = 3 s + 35 ( equation 1 ) next , we are told that “ together they now weigh 275 pounds . ” we can also put this into an equation . j + s = 275 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 3 s + 35 = 275 - s 4 s = 240 s = 60 j + 60 = 275 j = 215 answer : e
Answer: e
Python program:
a = 2 * 275
b = a + 35 
c = b / 3
Problem: pipe a fills a tank of capacity 900 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 42 minutes , b ) 14 minutes , c ) 54 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 900 = 50 * n = > n = 18 here n = number of cycles . total time = 18 * 3 = 54 as in one cycle there are 3 minutes . thus 54 minutes answer : c"
Answer: c
Python program:
a = 40 + 30 
b = a - 20
c = 900 / b
d = c * 3
Problem: how many even number in the range between 6 to 100 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 32 , 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 , 6 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 48 . for 6 , 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 16 . hence , only divisible by 2 but not 3 = 48 - 16 = 32 . hence , answer c"
Answer: c
Python program:
a = 100 - 6
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: 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days z do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time z = 3 days to finish the task imo a"
Answer: a
Python program:
a = 6 * 8
b = 3 * 6
c = a - b
d = 6 + 4 
e = c / d
Problem: of the diplomats who attended a summit conference : 20 spoke latin , 32 did not speak russian and 20 % of the diplomats spoke neither latin nor russian . if 10 % of the diplomats spoke both latin and russian , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
Python program:
a = 32 - 20
b = 20 / 100
c = 10 / 100
d = b - c
e = a / d
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 3 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 3 / 4 , e ) 3 / 5
Rationale: "let boy be represented by b and girl by g . the possible outcomes of two children of same sex and one of opposite sex can be : bbg or gbb or bgb or ggb or bgg or gbg ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 = 6 / 8 = 3 / 4 answer : ( d )"
Answer: d
Python program:
a = 2 / 3
Problem: a man buys 12 lts of liquid which contains 20 % of the liquid and the rest is water . he then mixes it with 10 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 75.45 , b ) 76.45 , c ) 77.45 , d ) 74.45 , e ) 73.45
Rationale: "20 % in 12 lts is 2.4 . so water = 12 - 2.4 = 9.6 lts . 30 % of 10 lts = 3 . so water in 2 nd mixture = 10 - 3 = 7 lts . now total quantity = 12 + 10 = 22 lts . total water in it will be 9.6 + 7 = 16.6 lts . % of water = ( 100 * 16.6 ) / 22 = 75.45 answer : a"
Answer: a
Python program:
a = 12 - 20
b = 12 * a
c = 12 - 30
d = 10 * c
e = b + d 
f = 12 + 10 
g = e / f
Problem: a and b can do a work in 20 days , b and c can do it in 30 days ; a , b and c together can finish it in 40 days . a and c together will do it in ?
Options: a ) 25 days , b ) 30 days , c ) 20 days , d ) 15 days , e ) 10 days
Rationale: a + b + c 1 day work = 1 / 40 a + b 1 day work = 1 / 20 b + c 1 day work = 1 / 30 a + c 1 day work = 2 * 1 / 40 - 1 / 20 + 1 / 30 = 1 / 30 a and c together will do the work in 30 days . answer is b
Answer: b
Python program:
a = 1 / 30
b = 1 / 20
c = 1 / 40
d = b - c
e = a - d
f = 1 / 20
g = 1 / 40
h = f - g
i = e + h 
j = 1/(i)
Problem: the least perfect square , which is divisible by each of 21 , 36 and 66 is :
Options: a ) 213444 , b ) 214344 , c ) 214434 , d ) 231444 , e ) 233444
Rationale: "explanation : l . c . m . of 21 , 36 , 66 = 2772 . now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 22 x 32 x 72 x 112 = 213444 answer is a"
Answer: a
Python program:
a = 3 + 4 
b = a ** 2
c = 36 / 3
d = c / 2
e = d ** 2
f = b * e
g = 2 ** 2
h = f * g
i = 3 ** 2
j = h * i
Problem: find the greatest number that will divide 54 , 87 and 172 so as to leave the same remainder in each case
Options: a ) 13 , b ) 3 , c ) 15 , d ) 1 , e ) 2
Rationale: explanation : required number = ( 87 - 54 ) , ( 172 - 87 ) , ( 172 - 54 ) = h . c . f of 33,85 and 118 is 1 answer : option d
Answer: d
Python program:
a = 172 - 87
b = a - 54
c = 87 - 54
d = math.gcd(b, c)
e = 172 - 87
f = math.gcd(d, e)
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 9 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 13 / 18 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 9 x = 8 / 9 x so if gold card balance is transferred then the rest unspent will be 8 / 9 x - x / 6 = 13 / 18 x so the ans is d"
Answer: d
Python program:
a = 1/(3)
b = 1/(2)
c = a * b
d = 1/(9)
e = c + d 
f = 1 - e
Problem: the number which exceeds 12 % of it by 52.8 is :
Options: a ) 60 , b ) 77 , c ) 269 , d ) 26 , e ) 91
Rationale: "explanation : let the number be x . then , x – 12 % of x = 52.8 x – ( 12 / 100 ) x = 52.8 x ( 1 – 12 / 100 ) = 52.8 ( 88 / 100 ) x = 52.8 x = ( 100 x 52.8 ) / 88 = 60 answer : a"
Answer: a
Python program:
a = 52 * 8
b = 100 - 12
c = a / b
Problem: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 360 6 ounces servings of orange juice ?
Options: a ) a ) 45 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its a . total juice rquired = 360 * 6 = 2160 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 2160 / 48 = 45 . answer a"
Answer: a
Python program:
a = 360 * 6
b = a / 12
c = b / 4
Problem: solution for 2.01 + . 3 + . 34
Options: a ) 2.91 , b ) 2.65 , c ) 2.938 , d ) 2.986 , e ) 2.999
Rationale: "2.01 + . 3 + . 34 = 0 0 = 0 - 2.01 - 0.3 - 0.34 0 = - 2.65 answer : b"
Answer: b
Python program:
a = 3 / 1000
b = 2 + 1 
c = 34 / 1000
d = b + c
Problem: two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 6 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "let x be the total time it takes for the cistern to fill . 6 / 12 + x / 15 = 1 x / 15 = 1 / 2 x = 7.5 after the first pipe is turned off , it takes 1.5 more minutes to fill the cistern . the answer is b ."
Answer: b
Python program:
a = 1 / 12
b = 1 / 15
c = a + b 
d = c * 6
e = 1 - d
f = e * 15
Problem: in the xy - coordinate system , what is the slope of the line that goes through the point ( 1 , 1 ) and is equidistant from the two points p = ( 3 , 7 ) and q = ( 9 , 11 ) ?
Options: a ) 0.5 , b ) 0.625 , c ) 0.75 , d ) 0.875 , e ) 1.0
Rationale: "first , get the middle coordinate between ( 3,7 ) and ( 9,11 ) . . . x = 3 + ( 9 - 3 ) / 2 = 6 y = 7 + ( 11 - 7 ) / 2 = 9 second , get the slope of ( 9,6 ) and ( 1,1 ) . m = 6 - 1 / 9 - 1 = 5 / 8 = 0.625 answer : b"
Answer: b
Python program:
a = 1 + 2 
b = a / 2
c = 1 + 1 
d = c / 7
e = b / d