euclaise/mathqa_programs huggingface dataset:
Problem: ( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + 0.086 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.86 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: given expression = ( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + ( 0.86 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.86 - 0.1 ) = 0.76 answer is e
Answer: e
Python program:
a = 0 ** 86
b = 0 ** 1
c = a - b
d = 0 ** 86
e = d + 0 
f = 0 ** 1
g = e + f 
h = c / g
Problem: find the ratio in which wheat of inferior quality ( rs . 14 / kg ) be mixed with wheat of superior quality ( rs . 28 / kg ) so that the shopkeeper gains rs . 2 by selling the resulting mixture at rs . 20 / kg .
Options: a ) 5 : 2 , b ) 5 : 9 , c ) 5 : 3 , d ) 5 : 1 , e ) 5 : 8
Rationale: explanation : let the resulting mixture be 1 kg , and x kg be the amount of wheat of inferior quality . therefore , ( 1 - x ) kg is the amount of wheat of superior quality . as the shopkeeper gains rs . 2 , the cost of the mixture is rs . 18 14 * x + 28 * ( 1 - x ) = 18 14 x - 28 x + 28 = 18 14 x = 10 x = 5 / 7 ( 1 – x ) = 2 / 7 x : ( 1 - x ) = 5 / 7 : 2 / 7 = 5 : 2 answer : a
Answer: a
Python program:
a = 20 / 2
b = a / 2
c = b / 2
Problem: george baked a total of 75 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 5 , b ) 4 , c ) 2 , d ) 6 , e ) 7
Rationale: "3 / 5 of the 75 pizzas cooked on saturday = 45 pizzas 3 / 5 of the remaining pizzas on sunday = 18 pizzas we ' re left with ( 75 - 45 - 18 ) = 12 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 5 4 2 1 0 = 12 w = 2 c"
Answer: c
Python program:
a = 3 / 7
b = 75 * a
c = 75 - b
d = 3 / 7
e = 75 * d
f = 75 - e
g = 3 / 7
h = f * g
i = c - h
j = i - 3
k = 3 / 7
l = 75 * k
m = 75 - l
n = 3 / 7
o = 75 * n
p = 75 - o
q = 3 / 7
r = p * q
s = m - r
t = s - 3
u = j / t
Problem: - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 150 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
Options: a ) 100 , b ) 250 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 150 students answered yes only for subject m , then the remaining 350 students who answered yes for subject m , also answered yes for subject r . so , 350 students answered yes for both subjects . if 350 students answered yes for both subjects , then 400 - 350 = 50 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 50 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 50 + 300 ) = 250 students did not answer yes for either subject . answer : b ."
Answer: b
Python program:
a = 500 - 150
b = 150 + a 
c = 500 - 150
d = 400 - c
e = b + d 
f = 800 - e
Problem: a bag contains 6 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 12 / 55 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 6 + 2 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 6 c 1 * 2 c 1 * 4 c 1 = 48 probability = 48 / 220 = 12 / 55 answer is a"
Answer: a
Python program:
a = math.comb(4, 2)
b = 6 + 2 
c = math.comb(b, 1)
d = a * c
e = 6 + 2 
f = e + 4 
g = math.comb(f, 6)
h = d / g
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 50 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 30 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 50 % means total women in company 50 % ( assume total people in company 100 % ) no of men employees attended picnic = 50 x ( 20 / 100 ) = 10 no of women employees attend picnic = 50 x ( 40 / 100 ) = 20 total percentage of employees attend the picnic = 10 + 20 = 30 % answer : a"
Answer: a
Python program:
a = 50 / 100
b = 20 / 100
c = a * b
d = 100 - 50
e = d / 100
f = 40 / 100
g = e * f
h = c + g 
i = h * 100
Problem: a trader sells 80 meters of cloth for rs . 10000 at the profit of rs . 7 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 118 , b ) 88 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 8925 / 85 = rs . 125 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 125 - rs . 7 = rs . 118 answer : a"
Answer: a
Python program:
a = 10000 / 80
b = a - 7
Problem: the present ratio of students to teachers at a certain school is 35 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "we are given that the ratio of students to teacher is 35 to 1 . we can rewrite this using variable multipliers . students : teachers = 35 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 35 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 35 x + 50 25 x + 125 = 35 x + 50 7.5 = x x ~ 8 since x is the present number of teachers , currently there are 8 teachers . answer b ."
Answer: b
Python program:
a = 35 + 25 
b = a / 25
Problem: if x and y are the two digits of the number 653 xy . such that this number is divisible by 80 , then x + y is equal to
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 0
Rationale: since 653 xy is divisible by 5 as well as 2 . so y = 0 now 653 x 0 must be divisible by 8 so 3 x 0 must be 8 this happens when x = 2 hence , x + y = 2 + 0 = 2 answer b 2
Answer: b
Python program:
a = 653 * 100
b = reminder / (
Problem: 22 + 23 + 24 + . . . 61 + 62 + 63 = ?
Options: a ) 1361 , b ) 1362 , c ) 1363 , d ) 1364 , e ) 1785
Rationale: "sum = 22 + 23 + 24 + . . . 61 + 62 + 63 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 63 positive integers = 63 * 64 / 2 sum of first 21 positive integers = 21 * 22 / 2 sum = 22 + 23 + 24 + . . . 61 + 62 + 63 = 63 * 64 / 2 - 21 * 22 / 2 = 1376 answer : e"
Answer: e
Python program:
a = 61 + 22 
b = 61 * a
c = b / 23
Problem: matt and peter can do together a piece of work in 24 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 10 days . in how many days peter complete the work separately .
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "together they complete the job in 24 days means they complete 12 / 24 of the job after 12 days . peter completes the remaining ( 12 / 24 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . x = 12 / ( 12 / 24 ) = 24 a"
Answer: a
Python program:
a = 1 / 24
b = 12 * a
c = 1 - b
d = 10 / c
Problem: a train which has 600 m long , is running 60 kmph . in what time will it cross a person moving at 6 kmph in same direction ?
Options: a ) 42 sec , b ) 44 sec , c ) 46 sec , d ) 40 sec , e ) 50 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 600 / ( ( 60 - 6 ) ( 5 / 18 ) = 600 / 54 * ( 5 / 18 ) = 600 / 15 = 40 sec answer : d"
Answer: d
Python program:
a = 60 / const_3_6
b = 6 / 2
c = b / const_3_6
d = a - c
e = 600 / d
Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 3 / 8 , e ) 1 / 2
Rationale: "winning scenario is if we ' ll have either three tails ( ttt ) or three heads ( hhh ) : 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 = 1 / 4 . answer : b ."
Answer: b
Python program:
a = 2 ** 3
b = 1 / a
Problem: machine p can print one lakh books in 8 hours . machine q can print the same number of books in 10 hours while machine r can print the same in 12 hours . all the machines started printing at 9 a . m . machine p is stopped at 11 a . m . and the remaining two machines complete work . approximately at what time will the printing of one lakh books be completed ?
Options: a ) 3 pm , b ) 2 pm , c ) 1 : 00 pm , d ) 11 am , e ) 12 am
Rationale: explanation : work done by p in 1 hour = 1 / 8 work done by q in 1 hour = 1 / 10 work done by r in 1 hour = 1 / 12 work done by p , q and r in 1 hour = 1 / 8 + 1 / 10 + 1 / 12 = 37 / 120 work done by q and r in 1 hour = 1 / 10 + 1 / 12 = 22 / 120 = 11 / 60 from 9 am to 11 am , all the machines were operating . ie , they all operated for 2 hours and work completed = 2 × ( 37 / 120 ) = 37 / 60 pending work = 1 - 37 / 60 = 23 / 60 hours taken by q an r to complete the pending work = ( 23 / 60 ) / ( 11 / 60 ) = 23 / 11 which is approximately equal to 2 hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm answer : option c
Answer: c
Python program:
a = 11 - 9
b = 1 / 12
c = 1 / 8
d = 1 / 10
e = c + d 
f = b + e 
g = a * f
h = 1 - g
i = 1 / 10
j = 1 / 12
k = i + j 
l = h / k
m = 11 + l 
n = math.floor(m)
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 30 . the largest number is :
Options: a ) 33 , b ) 77 , c ) 36 , d ) 18 , e ) 16
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 30 15 x = 90 x = 6 largest number = 6 x = 36 . answer : c"
Answer: c
Python program:
a = 4 * 6
b = a * 100
c = 5 * 6
d = b + c
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 10 points after 5 games , what is the least number of the remaining matches it has to win to reach the 45 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 45 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10"
Answer: e
Python program:
a = 45 - 10
b = 20 - 5
c = a - b
d = c / 2
e = math.floor(d)
f = e + 1
Problem: the price of lunch for 15 people was $ 208.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.60 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 208 is for 115 then we have to calculate for 100 for 115 208 for 100 x so by cross multiplication we get 115 x = 100 * 208 = > x = 100 * 208 / 110 by simplifying we get x as 189 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 189 / 15 = 12.6 so our answer is b )"
Answer: b
Python program:
a = 100 + 15 
b = 208 / 0
c = b * 100
d = 1 / 15
e = c * d
Problem: if the area of a circle decreases by 36 % , then the radius of a circle decreases by
Options: a ) 20 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 36 ) % = ( 100 − 10 √ 64 ) % = 100 - 80 = 20 % answer a"
Answer: a
Python program:
a = 100 - 36
b = a / 100
c = math.sqrt(b)
d = 1 - c
e = d * 100
Problem: if n is a positive integer and n ^ 2 is divisible by 450 , then what is the largest positive integer that must divide n ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "450 = 2 * 3 ^ 2 * 5 ^ 2 if 450 divides n ^ 2 , then n must be divisible by 2 * 3 * 5 = 30 the answer is c ."
Answer: c
Python program:
a = 450 / 2
b = math.sqrt(a)
c = b * 2
Problem: if the given two numbers are respectively 7 % and 14 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 50 % , e ) none of these
Rationale: "here , l = 7 and m = 14 therefore , first number = l / m x 100 % of second number = 7 / 14 x 100 % of second number = 50 % of second number answer : d"
Answer: d
Python program:
a = 7 / 100
b = 14 / 100
c = a / b
d = c * 100
Problem: the average of first 9 prime numbers is ?
Options: a ) 10.11 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11
Rationale: "sum of 10 prime no . = 100 average = 100 / 9 = 11.11 answer : b"
Answer: b
Python program:
a = 9 + 1
Problem: a trailer carries 3 , 4 and 6 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 720
Rationale: "max no . of crates = 6 . max weight = 120 kg max . weight carried = 6 * 120 = 720 kg = e"
Answer: e
Python program:
a = 6 * 120
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 21 years . the ratio of their ages after 8 years will be
Options: a ) 2 : 3 , b ) 20 : 17 , c ) 5 : 4 , d ) 3 : 5 , e ) 6 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 21 x = 3 mini ’ s age = 12 years and minakshi ’ s age = 9 years ratio of their ages after 8 years = ( 12 + 8 ) : ( 9 + 8 ) = 20 : 17 answer : b"
Answer: b
Python program:
a = 4 + 3 
b = 21 / a
c = 4 * b
d = c + 8 
e = 4 + 3 
f = 21 / e
g = 3 * f
h = g + 8 
i = d / h
Problem: a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 1.7 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 0.9 , b ) 1.2 , c ) 1.5 , d ) 1.8 , e ) 2.1
Rationale: "72 km / hr = 1.2 km / min the total distance is 1.8 km . 1.8 / 1.2 = 1.5 minutes the answer is c ."
Answer: c
Python program:
a = 100 / 1000
b = 1 + 7 
c = b / 72
d = c * const_60
Problem: the difference between a number and its two - fifth is 510 . what is 5 % of that number ?
Options: a ) 425 , b ) 300 , c ) 255 , d ) 300 , e ) 400
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 5 % of 850 = 425 . answer : a"
Answer: a
Python program:
a = 4 + 1 
b = 510 * a
c = 1 + 2 
d = b / c
Problem: the contents of two vessels containing copper and tin in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4 . the resulting mixture will have copper and tin in the ratio ?
Options: a ) 15 : 32 , b ) 21 : 28 , c ) 31 : 74 , d ) 33 : 37 , e ) 41 : 92
Rationale: "the ratio of copper and tin the new vessel = ( 1 / 3 * 1 / 5 + 2 / 7 * 4 / 5 ) : ( 2 / 3 * 1 / 5 + 5 / 7 * 4 / 5 ) = 31 / 105 : 74 / 105 = 31 : 74 answer is c"
Answer: c
Python program:
a = 1 * 2
b = 2 * 2
c = a + b 
d = 2 * 2
e = 5 * 2
f = d + e 
g = c / f
Problem: a can do a piece of work in 4 days . b can do it in 8 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 8 days , c ) 67 days , d ) 1 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 8 = 1 / 8 = > 8 days answer : b"
Answer: b
Python program:
a = 4 * 8
b = 4 * 8
c = 4 * 8
d = c / 4
e = 4 * 8
f = e / 8
g = d + f 
h = g * 2
i = b - h
j = i / 2
k = a / j
Problem: a cargo ships engines failed 100 miles away from the port . due to the changing wind direction , it is moving 12 miles towards the port and 6 miles away from the port . if the wind pattern remains same , how many miles it will travel before reaching the port ?
Options: a ) a - 179 , b ) b - 240 , c ) c - 280 , d ) d - 100 , e ) e - 155
Rationale: ships overall distance covered per cycle is + 6 miles take 100 - 6 take 94 / 6 to lowest divisible number - 90 / 6 this means that it will take 15 ` ` overall ' ' actions to reach the 90 th mile . - 15 * 18 miles added later set cycle start at 90 . travel 10 miles and reach the anchor point - add 10 to total 15 * 18 + 10 = 280 miles in total answer : c
Answer: c
Python program:
a = 100 + 12 
b = a - 6
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 14 , c ) 22 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 2 + 12 = 14 . answer : b ."
Answer: b
Python program:
a = 18 - 6
b = 8 - 6
c = a + b
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 50 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 125 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 6 , so radius is 3 new area = 9 π increase in area is 5 π % increase in area = 5 / 4 * 100 so , % increase is 125 % answer will be ( d )"
Answer: d
Python program:
a = 50 * 2
b = a / 1000
c = b + 3 
d = c ** 2
e = d - 4
f = e / 4
g = f * 100
Problem: a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 3.5 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 3 , b ) 4.2 , c ) 3.4 , d ) 5.5 , e ) 5.7
Rationale: "72 km / hr = 1.2 km / min the total distance is 3.6 km . 3.6 / 1.2 = 3 minutes the answer is a ."
Answer: a
Python program:
a = 100 / 1000
b = 3 + 5 
c = b / 72
d = c * const_60
Problem: if 0.5 % of a = 80 paise , then the value of a is ?
Options: a ) rs . 170 , b ) rs . 160 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 80 / 100 ∴ a = rs . ( 80 / 0.5 ) = rs . 160 correct option : b"
Answer: b
Python program:
a = 80 / 0
Problem: it takes 2 team of farm workers 12 days to completely prepare a piece of land for planting . if both team of workers were to work separately , one of them can complete the work 10 days earlier than the other , how many days will it take each of them to separately complete the work ?
Options: a ) 12 and 22 , b ) 11 and 21 , c ) 15 and 25 , d ) 9 and 19 , e ) 20 and 30
Rationale: work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two team of workers would complete a job in 12 days . this means that ( individually ) each of team would take more than 12 days to do the job . answers d , a and b are illogical , since the individual times must both be greater than 12 days . so we can test the values for answers c and e . using the values for answers b and d . . . answer b : ( 15 ) ( 25 ) / ( 15 + 25 ) = 375 / 40 = 9.4 this is a match answer e : ( 20 ) ( 30 ) / ( 20 + 30 ) = 12 final answer : e
Answer: e
Python program:
a = 10 * 12
b = 10 * 2
c = a + b 
d = c * 10
e = 10 * 12
f = e * 10
g = d + f 
h = 3 + 4 
i = h * 10
j = i + 100 
k = g - j
l = 10 * 12
m = 10 * 2
n = l + m 
o = n * 10
p = k - o
q = 10 * 100
r = p + q
Problem: find compound interest on $ 8000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 3109 , b ) 3209 , c ) 3108 , d ) 3107 , e ) 3100
Rationale: time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 8000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 8000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 11109 . . : . c . i . = rs . ( 11109 - 8000 ) = $ 3109 . answer a .
Answer: a
Python program:
a = 15 / 100
b = 8000 * a
c = 15 / 100
d = 8000 * c
e = 8000 + d 
f = 15 / 100
g = e * f
h = b + g 
i = 15 / 100
j = 8000 * i
k = 8000 + j 
l = 15 / 100
m = 8000 * l
n = 8000 + m 
o = 15 / 100
p = n * o
q = k + p 
r = 15 / 100
s = r / 3
t = q * s
u = h + t
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 85 kg , d ) 80 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 8 ã — 2.5 = 20 if x is the weight of the new person , total increase in weight = x â ˆ ’ 45 = > 20 = x - 45 = > x = 20 + 45 = 65 answer : option b"
Answer: b
Python program:
a = 8 * 2
b = a + 45
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 54 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 6.67 , d ) 2.8 , e ) 2.1
Rationale: "speed = 54 * 5 / 18 = 15 m / sec time taken = 100 / 15 = 6.67 sec . answer : c"
Answer: c
Python program:
a = 54 * const_0_2778
b = 100 / a
Problem: find the area of a triangle whose sides are 41 cm , 28 cm , 15 cm . also , find the length of the altitude corresponding to the largest side of the triangle .
Options: a ) 4.1 cm
b ) 5.1 cm
c ) 6.1 cm
d ) 7.1 cm
e ) 8.1 cm
Rationale: semi - perimeter of the triangle = ( a + b + c ) / 2 = ( 41 + 28 + 15 ) / 2 = 84 / 2 = 42 cm therefore , area of the triangle = √ ( s ( s - a ) ( s - b ) ( s - c ) ) = √ ( 42 ( 42 - 41 ) ( 42 - 28 ) ( 42 - 15 ) ) cm ² = √ ( 42 × 1 × 27 × 14 ) cm ² = √ ( 3 × 3 × 3 × 3 × 2 × 2 × 7 × 7 ) cm ² = 3 × 3 × 2 × 7 cm ² = 126 cm ² now , area of triangle = 1 / 2 × b × h therefore , h = 2 a / b = ( 2 × 126 ) / 41 = 252 / 41 = 6.1 cm answer : option c
Answer: c
Python program:
a = triangle_area_three_edges * (
b = a / 2
Problem: alex takes a loan of $ 8,000 to buy a used truck at the rate of 6 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 480 , b ) 520 , c ) 460 , d ) 400 , e ) 520
Rationale: "from the details given in the problem principle = p = $ 8,000 and r = 6 % or 0.06 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 8,000 x 1 x 0.06 = 480.00 annual interest to be paid = $ 480 answer : a"
Answer: a
Python program:
a = 6 * 100
b = math.sqrt(100)
c = a * b
d = c * 6
e = d / 100
Problem: if john covers a certain distance in 1 hr . 24 min . by covering two third of the distance at 4 kmph and the rest at 5 kmph , then find the total distance
Options: a ) 4 km , b ) 6 km , c ) 6.8 km , d ) 7.2 km , e ) none of these
Rationale: explanation : let the total distance be y km . then , ( 2 / 3 ) y / 4 + ( 1 / 3 ) y / 5 = 7 / 5 y / 6 + y / 15 = 7 / 5 7 y = 42 y = 6 km answer b
Answer: b
Python program:
a = 2 / 3
b = 24 / const_60
c = 1 + b 
d = a * c
e = 4 * d
f = 2 / 3
g = 1 - f
h = 24 / const_60
i = 1 + h 
j = g * i
k = j * 5
l = e + k
Problem: in how many ways 4 boys and 3 girls can be seated in a row so that they are alternative ?
Options: a ) 120 , b ) 144 , c ) 160 , d ) 210 , e ) 180
Rationale: "4 boys can be seated in 4 ! three girls can be seated in 3 ! required number = 4 ! 3 ! = 144 answer is b"
Answer: b
Python program:
a = math.factorial(4)
b = math.factorial(3)
c = a * b