euclaise/mathqa_programs huggingface dataset:
Problem: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 360 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 9000 , d ) 2766 , e ) 1811
Rationale: "p = 360 ( 100 / 5 ) ^ 2 = > p = 9000 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a + 1 
c = b ** 2
d = 20 / 100
e = d * 2
f = e + 1 
g = c - f
h = 360 / g
Problem: the average of 6 integers is 63 , and none of these integers is greater than 100 . if the average of 3 of the integers is 65 , what is the least possible value of one of the other two integers ?
Options: a ) 45 , b ) 62 , c ) 75 , d ) 83 , e ) 90
Rationale: when it comes to averages , we know thataverage value = ( sum of n values ) / n we can rewrite this into a useful formula : sum of n values = ( average value ) ( n ) the average of five integers is 63 so , the sum of all 5 integers = ( 63 ) ( 6 ) = 378 the average of three of the integers is 65 so , the sum of the 3 integers = ( 65 ) ( 3 ) = 195 so , the sum of the 2 remaining integers = 378 - 195 = 183 if the sum of the 2 remaining integers = 183 , and we want to minimize one value , we must maximize the other value . 100 is the maximum value so let 1 integer = 100 , which means the other must equal 83 answer : d
Answer: d
Python program:
a = 6 * 63
b = 3 * 65
c = a - b
d = c - 100
Problem: in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . what is the duration of the flight ?
Options: a ) 3 hours , b ) 2.4 hours , c ) 1.4 hours , d ) 1 hour , e ) none of these
Rationale: "explanation : let the duration of the flight be x hours . then 600 / x − 600 / x + 1 / 2 = 200 600 / x − 1200 / 2 x + 1 = 200 x ( 2 x + 1 ) = 3 2 x 2 + x − 3 = 0 = > ( 2 x + 3 ) ( x − 1 ) = 0 neglecting the negative value for x we get x = 1 option d"
Answer: d
Python program:
a = 200 * 30
b = a / 10
c = 600 / b
Problem: what is the tens digit of 7 ^ 1415 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1415 = 4 * 353 + 3 the ten ' s digit will be 4 . answer e"
Answer: e
Python program:
a = 4 + 1 
b = 7 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: the ratio of 2 numbers is 3 : 4 and their h . c . f . is 4 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 48 , d ) 36 , e ) 60
Rationale: "let the numbers be 3 x and 4 x their h . c . f . = 4 so the numbers are 3 * 4 , 4 * 4 = 12,16 l . c . m . = 48 answer is c"
Answer: c
Python program:
a = 4 ** 3
b = 2 ** 3
c = 3 ** 2
d = b + c 
e = a + d 
f = 4 / e
g = math.sqrt(f)
Problem: a 140 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 35 , b ) 20 , c ) 47 , d ) 36 , e ) 40
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 140 = 40 answer : e"
Answer: e
Python program:
a = 2 / 5
b = a + 1 
c = 140 / b
d = 140 - c
Problem: the sum of 3 consecutive numbers is definitely :
Options: a ) positive , b ) divisible by 2 . , c ) divisible by 3 , d ) divisible by 4 . , e ) divisible by 5
Rationale: "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : c"
Answer: c
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: a tree is 12 m tall and casts an an 8 m long shadow . at the same time , a flag pole caste a 100 m long shadow . how long is the flag pole ?
Options: a ) 150 m , b ) 200 m , c ) 125 m , d ) 115 m , e ) none
Rationale: answer ∵ 8 m shadow means original height = 12 m ∴ 1 m shadow means original height = 12 / 8 m ∴ 100 m shadow means original height = ( 12 / 8 ) x 100 m = ( 6 / 4 ) x 100 = 6 x 25 = 150 m correct option : a
Answer: a
Python program:
a = 12 / 8
b = 100 * a
Problem: in a division sum , the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
Options: a ) 53 , b ) 58 , c ) 51 , d ) 60 , e ) 62
Rationale: "diver = ( 4 * 3 ) + 2 = 14 4 * quotient = 14 quotient = 3.5 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 3.5 ) + 4 = 53 a"
Answer: a
Python program:
a = 4 * 3
b = a + 2 
c = 4 * 3
d = c + 2 
e = d / 3
f = b * e
g = f + 4
Problem: if x is equal to the sum of the integers from 20 to 30 , inclusive , and y is the number of even integers from 20 to 30 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 361 , d ) 461 , e ) 561
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 20 + ( 11 - 1 ) * 1 } = 11 * 25 = 275 = x number of even number = ( 30 - 20 ) / 2 + 1 = 6 = y x + y = 275 + 6 = 281 b"
Answer: b
Python program:
a = 20 + 30 
b = a / 2
c = 30 - 20
d = c + 1 
e = b * d
f = 30 - 20
g = f / 2
h = g + 1 
i = e + h
Problem: the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 36 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 36 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 36 x = 0.06 the answer is b ."
Answer: b
Python program:
a = math.sqrt(36)
Problem: there are 60 slots around a circle , numbered 1 to 60 . a man starts fromthe first slot and jumps to the 5 th slot . from there he jumps to the 9 th slot andso on . in which slot will he land in his 2200 th jump ?
Options: a ) 1
b ) 5
c ) 41
d ) 45
e ) 46
Rationale: every 15 th jump , he comes back to 1 st position so , 2200 / 15 = remainder 10 hence 10 th position is 41 st slot answer : c
Answer: c
Python program:
a = 2200 / 60
b = 2200 / 60
c = math.floor(b)
d = a - c
e = d * 60
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 6 hrs , e ) 5 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 6 ) = 1 / 6 the cistern will be filled in 6 / 1 hrs i . e . , 6 hrs . answer : d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 6
c = a - b
d = 1 / c
Problem: in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 3000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 23000 , b ) 22000 , c ) 20000 , d ) 25000 , e ) 30000
Rationale: "winner - looser 55 % - 45 % if 3000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 3,000 people compose 10 % of all voters , which means that the total number of votes is 30,000 . answer : e ."
Answer: e
Python program:
a = 10 / 100
b = 3000 / a
Problem: a departmental store has 9 managers and 18 associates . the 9 managers have an average salary of $ 1300 . the 18 associates have an average salary of $ 12000 . what is the average salary for the departmental store ?
Options: a ) $ 3556.25 , b ) $ 3988.89 , c ) $ 3836.56 , d ) $ 3745.56 , e ) $ 3428.56
Rationale: number of managers is 9 their average salary is $ 1300 number of associates is 18 their average salary is $ 12,000 total salary of managers is 9 * 1300 = $ 11700 total salary of associates is 18 * 12,000 = $ 96,000 total salary for the departmental store is 96,000 + 11700 = 107700 average salary for the departmental store is 107700 / 9 + 18 = 3988.89 answer is b
Answer: b
Python program:
a = 9 * 1300
b = 18 * 12000
c = a + b 
d = 9 + 18 
e = c / d
f = e / 2
g = f / 1000
h = math.floor(g)
i = h * 1000
j = 10 + 1 
k = i - j
Problem: how many different positive integers are factors of 256 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 16 , e ) 18
Rationale: "16 × 16 = 4 ^ 2 × 4 ^ 2 so total factors = ( 3 + 1 ) ( 3 + 1 ) = 16 answer : d"
Answer: d
Python program:
a = 2 ** 2
b = a + 2
Problem: find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 ?
Options: a ) 240 / 1576 , b ) 240 / 1542 , c ) 240 / 1547 , d ) 240 / 1528 , e ) 240 / 1529
Rationale: "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c"
Answer: c
Python program:
a = 5 / 34
b = 7 / 48
c = a / b
d = 2 / 13
e = c * d
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 70 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 36 % , e ) 50 %
Rationale: say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 70 % more ie . , 170 recliners hence her sales tields 170 * 80 = $ 13600 increase in sales = 13600 - 10000 = $ 3600 so % increase = 3600 * 100 / 10000 = 36 % d is the answer
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 70 / 100
d = 1 + c 
e = b * d
f = e * 100
g = f - 100
Problem: the least number , which when divided by 12 , 31 , 20 and 54 leaves in each case a remainder of 8 is :
Options: a ) 448 , b ) 488 , c ) 16748 , d ) 548 , e ) 560
Rationale: "required number = ( l . c . m . of 12 , 31 , 20 , 54 ) + 8 = 16740 + 8 = 16748 . answer : c"
Answer: c
Python program:
a = 54 * 10
Problem: timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey . if he made no stops during the trip and his average speed for the entire journey was 40 mph , for what fraction of the total time did he drive at 50 mph ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 3 / 4 , e ) 3 / 5
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire journey was 40 mph , then he drove at 50 mph for a longer duration of time . 10 30 10 - - 40 - - - - - - 50 this shows that you can divide the entire journey into 4 equal parts . thus , 3 / 4 part he drove at 50 mph and 1 / 4 part he drove at 10 mph . answer : d
Answer: d
Python program:
a = 40 - 10
b = 50 - 40
c = a / b
d = c / 4
Problem: a certain car uses 12 gallons of gasoline in traveling 420 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "420 / 10 = 42 the difference is 42 - 35 = 7 . answer d"
Answer: d
Python program:
a = 420 / 10
b = 420 / 12
c = a - b
Problem: in august , a cricket team that played 120 matches won 26 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 65 , d ) 80 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 31.2 + x by solving we get x = 65 answer : c"
Answer: c
Python program:
a = 52 / 100
b = a * 120
c = 26 / 100
d = c * 120
e = b - d
f = 52 / 100
g = 1 - f
h = e / g
Problem: the average weight of a , b and c is 65 kg . if the average weight of a and b be 60 kg and that of b and c be 70 kg , then the weight of a is :
Options: a ) 55 kg , b ) 65 kg , c ) 75 kg , d ) 45 kg , e ) 63 kg
Rationale: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 65 x 3 ) = 195 â € ¦ . ( i ) a + b = ( 60 x 2 ) = 120 â € ¦ . ( ii ) b + c = ( 70 x 2 ) = 140 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 260 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 65 . substituting b in ( ii ) a + 65 = 120 a = 55 a â € ™ s weight = 55 kg . answer a"
Answer: a
Python program:
a = 60 * 2
b = 70 * 2
c = a + b 
d = 65 * 3
e = c - d
Problem: a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 2 , e ) 1
Rationale: "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 = > 4 days answer a"
Answer: a
Python program:
a = 1/(28)
b = 1/(7)
c = 1/(14)
d = b + c 
e = a + d 
f = 1/(e)
Problem: if a ^ 2 + b ^ 2 = 15 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2
Options: a ) 10 , b ) 20 , c ) 60 , d ) 30 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 15 - 20 = - 5 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 15 + 20 = 35 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 35 - 5 = 30 d"
Answer: d
Python program:
a = math.sqrt(15)
b = a * 10
c = b + 3
Problem: a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 105 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 27 , c ) 25 , d ) 15 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 105 × 9 / 35 = 3 × 9 = 27 answer is b ."
Answer: b
Python program:
a = 15 * 3
b = 10 * 7
c = 12 * 5
d = b + c 
e = 15 * 3
f = d + e 
g = a / f
h = 105 * g
Problem: mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 80 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 2 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 35 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 80 , t = t d = 80 t since they went the same distance : 50 t + 50 / 4 = 80 t 30 t = 50 / 4 = 50 / 120 * 60 = 25 min t = 25 min d
Answer: d
Python program:
a = 15 / const_60
b = 50 * a
c = 80 - 50
d = b / c
e = const_60 * d
Problem: in a recent head - to - head run - off election , 18,000 absentee ballets were cast . 3 / 7 of the absentee ballets were thrown out and 2 / 9 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
Rationale: "4 / 7 * 7 / 9 ( total absentee votes ) = 4 / 9 ( total votes ) = 4 / 9 * 18000 = 8000 answer is d"
Answer: d
Python program:
a = 2 * 4
b = a * 1000
c = 2 * 4
d = c * 1000
e = 3 / 7
f = d * e
g = b - f
h = 2 * 4
i = h * 1000
j = 2 * 4
k = j * 1000
l = 3 / 7
m = k * l
n = i - m
o = 2 / 9
p = n * o
q = g - p
r = q / 1000
s = r / 4
t = s * 2
Problem: how many multiples of 2 are there between 10 and 100 ( both are inclusive ) ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 46 , e ) 3
Rationale: the answer is ( 100 - 10 ) / 2 + 1 = 46 answer is d
Answer: d
Python program:
a = 100 - 10
b = a / 2
c = b + 1
Problem: if 25 % of a number exceeds 8 % of it by 11.9 , then find the number ?
Options: a ) 76 , b ) 70 , c ) 55 , d ) 65 , e ) 22
Rationale: "use the elimination method to find the correct option . of all the options only 70 fits 25 % of 70 = 17.5 8 % of 70 = 5.6 17.5 - 5.6 = 11.9 required number is 70 . answer : b"
Answer: b
Python program:
a = 25 - 8
b = a / 100
c = 11 / 9
d = c + 8
Problem: in a 20 litre mixture ratio of milk and water is 3 : 1 . how much milk should added so that mixture ratio become 4 : 1 ?
Options: a ) 3 , b ) 2 , c ) 8 , d ) 6 , e ) 5
Rationale: amount of milk = 20 × 3 / 4 = 15 litre and water = 5 litre let x litre milk to be added then 15 + x / 5 = 4 / 1 = 15 + x = 20 , x = 5 answer e
Answer: e
Python program:
a = 1 + 3 
b = 1 / a
c = 20 * b
d = c * 4
e = 3 / 4
f = 20 * e
g = d - f
Problem: the price of an item is discounted 5 percent on day 1 of a sale . on day 2 , the item is discounted another 5.00001 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 80 % , b ) 82.5 % , c ) 83 % , d ) 84 % , e ) 85.5 %
Rationale: "let initial price be 100 price in day 1 after 5 % discount = 95 price in day 2 after 5 % discount = 90.25 price in day 3 after 10 % discount = 81.23 so , price in day 3 as percentage of the sale price on day 1 will be = 81.23 / 95 * 100 = > 85.5 % answer will definitely be ( e )"
Answer: e
Python program:
a = 10 / 100
b = 1 / 5
c = 1 - b
d = a / c
e = d * 100
f = e + 2
Problem: a 14 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 4
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 14 = 4 answer : e"
Answer: e
Python program:
a = 2 / 5
b = a + 1 
c = 14 / b
d = 14 - c
Problem: what is the smallest positive perfect square that is divisible by 9 , 15 , and 25 ?
Options: a ) 100 , b ) 225 , c ) 900 , d ) 1,600 , e ) 4,900
Rationale: "the number needs to be divisible by 3 ^ 2 , 3 * 5 , and 5 ^ 2 . the smallest such perfect square is 3 ^ 2 * 5 ^ 2 = 225 the answer is b ."
Answer: b
Python program:
a = 3 ** 2
b = 9 * a
c = b * 15
d = c * 2
e = 15 * 25
f = d + e
Problem: a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 18.1 , c ) 17.5 , d ) 18.7 , e ) 19.1
Rationale: a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.50 + $ 15.6 = $ 18.1 . answer : b .
Answer: b
Python program:
a = 1 / 5
b = 8 / a
c = b - 1
d = c * 0
e = 2 + 5
Problem: water is poured into a tank so that the tank is being filled at the rate of 5 cubic feet per hour . if the empty rectangular tank is 10 feet long , 6 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ?
Options: a ) 40
b ) 45
c ) 50
d ) 55
e ) 60
Rationale: the volume the tank is : length * width * depth = 10 * 6 * 5 = 300 cubic feet . 300 cubic feet / 5 cubic feet per hour = 60 hours . it will take 60 hours to fill the tank . the answer is e .
Answer: e
Python program:
a = volume_rectangular_prism / (
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 69 km downstream .
Options: a ) 3.6 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 13 km / hr speed of the stream = 6 km / hr speed downstream = ( 13 + 6 ) = 19 km / hr time taken to travel 69 km downstream = 69 â  „ 19 = 17 â  „ 4 = 3.6 hours answer is a"
Answer: a
Python program:
a = 13 + 6 
b = 69 / a
Problem: a string of 50 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.05 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.05 , b ) ( 0.05 ) ^ 50 , c ) 1 - ( 0.96 ) ^ 50 , d ) 1 - ( 0.95 ) ^ 50 , e ) ( 0.95 ) ^ 50
Rationale: the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 50 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.05 = 0.95 the the probability that none of the 50 light bulbs fails is 0.95 ^ 50 . hence , the probability that at least one light bulb fails is 1 - 0.95 ^ 50 . answer : d . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 50 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.05 = 5 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) .
Answer: d
Python program:
a = 1 - 0
b = a ** 50
c = 1 - b
Problem: a sum was put at simple interest at a certain rate for 7 years had it been put at 2 % higher rate , it would have fetched 140 more . find the sum .
Options: a ) 500 , b ) 750 , c ) 1000 , d ) 1250 , e ) 1500
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 140 = p × 7 x 2 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 140 × 100 / 7 × 2 = 1000 answer c"
Answer: c
Python program:
a = 2 / 100
b = a * 7
c = 140 / b
Problem: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 8 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 8 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 8 3 x - 2 ( 8 - x ) = 25 3 x - 16 + 2 x = 25 5 x = 41 x = 8.2 or between 8 and 9 . 9 ans c )"
Answer: c
Python program:
a = 8 - 2
b = 2 * a
c = 3 * 2
d = b - c
e = d + 31 
f = 3 + 2 
g = e / f
Problem: a positive number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 7 / 3 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "sq rt ( 7 x / 3 ) = x = > 7 x / 3 = x ^ 2 = > x = 7 / 3 ans - a"
Answer: a
Python program:
a = 7 / 3
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 23 , b ) 19 , c ) 42 , d ) 20 , e ) 21
Rationale: "let the total number of workers be x . then , 8000 x = ( 18000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 84000 = x = 42 . answer : c"
Answer: c
Python program:
a = 18000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: a company charges a fixed rental of rs . 350 per month . it allows 200 calls free per month . each call is charge at rs . 1.4 when the number of calls exceed 200 per month and it charges rs . 1.6 when the number of calls exceeds 400 per month and so on . a customer made 150 calls in february and 250 calls in march . by how much percent each call is cheaper in march than each call in february .
Options: a ) 28 % , b ) 25 % , c ) 18.5 % , d ) 16 % , e ) none of these
Rationale: solution : charge per call in february = 350 / 150 = 7 / 3 = 2.33 charge per call in march = [ 350 + ( 50 * 1.4 ) ] / 250 = 420 / 250 = 42 / 25 = 1.68 % cheaper call rate in march = [ ( 2.33 - 1.68 ) / 2.33 ] * 100 = 28 % . answer : option a
Answer: a
Python program:
a = 350 / 150
b = 250 - 200
c = b * 1
d = c + 350 
e = d / 250
f = a - e
g = 350 / 150
h = f / g
i = h * 100
Problem: 3 * 12 + 3 * 13 + 3 * 16 + 11 = ?
Options: a ) 122 , b ) 126 , c ) 134 , d ) 148 , e ) 151
Rationale: 3 * 12 + 3 * 13 + 3 * 16 + 11 = 36 + 39 + 48 + 11 = 134 the answer is c .
Answer: c
Python program:
a = 3 * 12
b = 3 * 13
c = a + b 
d = 3 * 16
e = c + d 
f = e + 11