euclaise/mathqa_programs huggingface dataset:
Problem: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio t of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio t of ann ' s time to bob ' s time is 3 : 2 . answer : b .
Answer: b
Python program:
a = 1 / 3
b = 1 + a 
c = 2 / b
Problem: if 6 x = 10 y = 14 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 213 , b ) 58 , c ) 84 , d ) 122 , e ) 168
Rationale: answer = d = 122 6 x = 10 y = 14 z 3 x = 5 y = 7 z 3 ( 5 * 7 ) = 5 ( 3 * 7 ) = 7 ( 3 * 5 ) addition = 35 + 21 + 15 = 71 answer would be multiple of 71 which is 213 answer : a
Answer: a
Python program:
a = 10 * 14
b = a * 6
c = b / 4
Problem: tough and tricky questions : percents . over the course of a year , a certain microbrewery increased its beer output by 20 percent . at the same time , it decreased its total working hours by 30 percent . by what percent did this factory increase its output per hour ?
Options: a ) 171.4 , b ) 171.5 , c ) 171.6 , d ) 171.7 , e ) none of the above
Rationale: lets assume the initial production was 100 litres of beer for 100 hr . with the 20 % increase the total amount of beer production will be 120 litres and with 30 % decrease in total hours will be reduced to 70 hr . 100 hr - - - - > 100 lts 1 hr - - - - - > 1 lts 70 hr - - - - - > 120 lts 1 hr - - - - - > 1.714 lts total increase in production for 1 hr = 171.4 % answer a
Answer: a
Python program:
a = 100 + 20 
b = 100 - 30
c = a / b
d = c * 100
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 8 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let t = usual time = distance / usual speed t + 8 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 32 the answer is d ."
Answer: d
Python program:
a = 5 / 4
b = a - 1
c = 8 / b
Problem: an inspector rejects 0.08 % of the meters as defective . how many will be examine to project ?
Options: a ) 2000 , b ) 2300 , c ) 2700 , d ) 2500 , e ) 250
Rationale: let the number of meters to be examined be x . then , 0.08 % of x = 2 [ ( 8 / 100 ) * ( 1 / 100 ) * x ] = 2 x = [ ( 2 * 100 * 100 ) / 8 ] = 2500 answer is d .
Answer: d
Python program:
a = 2 * 100
b = a * 100
c = 0 * 8
d = b / c
Problem: a can do a piece of work in 15 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 8 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 * 5 = 1 / 2 remaining work = 1 â ˆ ’ 1 / 2 = 1 / 2 a can finish work = 15 â ˆ — 1 / 2 = 7.5 days answer is c"
Answer: c
Python program:
a = 1 / 15
b = 1 / 10
c = a + b 
d = 1 / c
Problem: a couple decides to have 3 children . if they succeed in having 3 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 1 girl and 2 boys ?
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 5 / 8 , d ) 1 , e ) 1 / 4
Rationale: sample space = 2 ^ 3 = 8 favourable events = { bgg } , { bgb } , { bbb } , { ggg } , { gbg } , probability = 5 / 8 = 5 / 8 . ans ( c ) .
Answer: c
Python program:
a = math.factorial(3)
b = math.factorial(2)
c = a / b
d = 1 / 2
e = d ** 3
f = c * e
g = 1 - f
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 60 / r years . if pat ' s parents invested $ 7,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 20 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 14000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 60 / r years , then for r = 6 it ' ll double in 60 / 6 = ~ 10 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 20 years investment will become $ 7,000 * 2 = $ 14,000 . answer : b"
Answer: b
Python program:
a = 2 + 3 
b = a * 1000
c = b * 6
d = c / 2
Problem: find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 28 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 12 , 6,16 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: "let the numbers be a , b and c . a : b : c = 3 : 2 : 4 given , ( a + b ) + ( c - b ) = 21 = > a + c = 28 = > 3 x + 4 x = 28 = > x = 4 a , b , c are 3 x , 2 x , 4 x a , b , c are 12 , 8 , 16 . answer : c"
Answer: c
Python program:
a = 4 * 3
b = a / 3
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 570 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 38 / 15 , d ) 5 / 8 , e ) 5 / 3
Rationale: "distance traveled by eddy = 570 km time taken by eddy = 3 hours average speed of eddy = 570 / 3 = 190 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 190 / 75 = 38 / 15 answer c"
Answer: c
Python program:
a = 570 / 3
b = 300 / 4
c = a / b
Problem: two trains 180 m and 360 m long run at the speed of 60 kmph and 30 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 21.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 30 = 90 kmph * 5 / 18 = 25 m / s distance covered in crossing each other = 180 + 360 = 540 m required time = 540 * 1 / 25 = 21.6 sec answer is a"
Answer: a
Python program:
a = 180 + 360 
b = 60 + 30 
c = b * const_0_2778
d = a / c
Problem: if 5 ^ 10 x 2 ^ 10 = 10 ^ n what is the value of n ?
Options: a ) 16 , b ) 14 , c ) 12 , d ) 10 , e ) 18
Rationale: "5 ^ 10 * 2 ^ 10 = 10 ^ n or 10 ^ 10 = 10 ^ n n = 10 d"
Answer: d
Python program:
a = 2 ** 10
b = 5 ** 10
c = a * b
d = math.log(c)
e = math.log(10)
f = d / e
Problem: the average of 55 results is 28 and the average of other 28 results is 55 . what is the average of all the results ?
Options: a ) 37 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 83 result = sum of 55 result + sum of 28 result . = 30 x 20 + 20 x 30 = 3080 correct option : a"
Answer: a
Python program:
a = 55 * 28
b = 28 * 55
c = a + b 
d = 55 + 28 
e = c / d
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 90 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 98 , e ) 95
Rationale: "total score on 3 tests = 90 * 3 = 270 jerry wants the average to be = 92 hence total score on 4 tests should be = 92 * 4 = 368 score required on the fourth test = 368 - 270 = 98 option d"
Answer: d
Python program:
a = 90 + 2 
b = 4 * a
c = 90 * 3
d = b - c
Problem: 36 men can complete a piece of work in 18 days . in how many days will 9 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 88 , d ) 72 , e ) 21
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 9 : 36 : : 18 : x x = 72 answer : d ) 72 days"
Answer: d
Python program:
a = 18 * 36
b = a / 9
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 4,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6.85 % , b ) 7.25 % , c ) 7.76 % , d ) 8.33 % , e ) 8.75 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 6000 = 1 / 12 which is about 8.33 % the answer is d ."
Answer: d
Python program:
a = 100 * 100
b = 5 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: the diameter of a garden roller is 1.4 m and it is 4 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 80 m 2 , b ) 84 m 2 , c ) 88 m 2 , d ) 86 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â  „ 7 ã — 0.7 ã — 4 = 88 m 2 answer c"
Answer: c
Python program:
a = 22 / 7
b = 4 * a
c = 1 / 4
d = b * c
e = d * 4
f = 5 * e
Problem: at a certain high school , the senior class is twice the size of the junior class . if 7 / 8 of the seniors and 1 / 2 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 4 , d ) 3 / 8 , e ) 5 / 16
Rationale: "start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 7 / 8 ) * 200 = 175 and ( 1 / 2 ) * 100 = 50 . 175 + 50 = 225 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 225 total students in japanese , so 225 students in japanese / 300 total students equals 3 / 4 of the students in both classes that study japanese . answer : a"
Answer: a
Python program:
a = 8 + 2 
b = 2 / a
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 400 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the distance between the nest and the ditch is 400 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 400 = 12000 . d = st 12000 / 1.5 = t , i think we can take 12000 meters as 12 km , then only we get t = 8 . ( 1000 meters = 1 km ) d )"
Answer: d
Python program:
a = 15 * 2
b = 400 * a
c = b / 1000
d = 15 / 10
e = c / d
Problem: what is the total cost of 2 sandwiches at $ 2.44 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.36 , d ) $ 10.08 , e ) $ 11.85
Rationale: "answer = c 2 * 2.44 + 4 * 0.87 = 2 ( 2.50 - 0.06 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.12 - 0.52 = 9 - 0.64 = 8.36"
Answer: c
Python program:
a = 2 * 2
b = 4 * 0
c = a + b
Problem: average of 5 numbers is 12 . if one number is excluded the average becomes 10 . the excluded number is
Options: a ) 35 , b ) 20 , c ) 40 , d ) 30 , e ) 67
Rationale: explanation : number is ( 5 * 12 ) - ( 4 * 10 ) = 60 - 40 = 20 answer : option b
Answer: b
Python program:
a = 5 * 12
b = 10 * 4
c = a - b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 200 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 1000 , b ) 1429 , c ) 1977 , d ) 2778 , e ) 2711
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 200 100 % - - - - ? = > rs . 1429 answer : b"
Answer: b
Python program:
a = 200 * 100
b = 100 + 4 
c = 100 - 10
d = b - c
e = a / d
Problem: set a contains all the even numbers between 12 and 60 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 850 , b ) 1250 , c ) 1650 , d ) 2050 , e ) 2450
Rationale: "each term in set b is 50 more than the corresponding term in set a . the difference of the sums = 25 * 50 = 1250 . the answer is b ."
Answer: b
Python program:
a = 62 - 12
b = 60 - 12
c = b / 2
d = c + 1 
e = a * d
Problem: a worker earns $ 20 on the first day and spends $ 15 on the second day . the worker earns $ 20 on the third day and spends $ 15 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 90 ?
Options: a ) 28 , b ) 29 , c ) 31 , d ) 34 , e ) 36
Rationale: "every two days , the net total is $ 5 . after 28 days , the worker will have $ 70 . on day 29 , the worker will receive $ 20 for a net total of $ 90 . the answer is b ."
Answer: b
Python program:
a = 20 - 15
b = 20 / a
c = b * 2
d = c + 1
Problem: log 3 n + log 9 n what is 3 digit number n that will be whole number
Options: a ) 629 , b ) 729 , c ) 829 , d ) 929 , e ) 727
Rationale: "no of values n can take is 1 9 ^ 3 = 729 answer : b"
Answer: b
Python program:
a = 9 ** 3
Problem: an employee ’ s annual salary was increased $ 15,000 . if her new annual salary now equals $ 90,000 , what was the percent increase ?
Options: a ) 15 % , b ) 16 2 ⁄ 3 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: "new annual salary = $ 90,000 salary increase = $ 15,000 . original salary = $ 90,000 - $ 15,000 . = $ 75,000 % increase = ( $ 15,000 / $ 75,000 ) * 100 = 20 % hence c ."
Answer: c
Python program:
a = 100 - 10
b = a * 1000
c = 100 - 10
d = c * 1000
e = const_0_25 * 100
f = e * 1000
g = d - f
h = b / g
i = h - 1
j = i * 100
Problem: how many zeros does 50 ! end with ?
Options: a ) 20 , b ) 24 , c ) 25 , d ) 12 , e ) 32
Rationale: "according to above 50 ! has 50 / 5 + 50 / 25 = 10 + 2 = 12 trailing zeros . answer : d ."
Answer: d
Python program:
a = 4 + 1 
b = 50 / a
c = 4 + 1 
d = 50 - c
e = 4 + 1 
f = e ** 2
g = d / f
h = b + g 
i = 4 + 1 
j = 50 - i
k = 4 + 1 
l = k ** 3
m = j / l
n = h + m
Problem: when 1 + 2 = 23 , 2 + 3 = 65 , 3 + 4 = 127 , then 4 + 5 = ?
Options: a ) 209 , b ) 250 , c ) 265 , d ) 280 , e ) 225
Rationale: "1 + 2 = > 1 x 2 = 2 & 1 + 2 = 3 = > 2 & 3 = > 23 2 + 3 = > 2 ã — 3 = 6 & 2 + 3 = 5 = > 6 & 6 = > 65 3 + 4 = > 3 ã — 4 = 12 & 3 + 4 = 7 = > 12 & 7 = > 127 then 4 + 5 = > 4 ã — 5 = 20 & 4 + 5 = 9 = > 20 & 9 = > 209 answer : a"
Answer: a
Python program:
a = 4 * 5
b = a * 10
c = b + 1
Problem: paul sells encyclopedias door - to - door . he earns $ 150 on every paycheck , regardless of how many sets he sells . in addition , he earns commission as follows : commission sales 10 % $ 0.00 - $ 1000.00 5 % $ 1000.01 - - - > he does not earn double commission . that is , if his sales are $ 12000 , he earns 10 % on the first $ 10000 and 5 % on the remaining $ 2000 . his largest paycheck of the year was $ 1320 . what were his sales for that pay period ?
Options: a ) 13,400 , b ) 14,800 , c ) 16,400 , d ) 15,800 , e ) 19,600
Rationale: his pay check was $ 1320 . out of this , $ 150 was his fixed salary so the total commission he earned was $ 1320 - $ 150 = $ 1170 he earns 10 % on the sales of first $ 10,000 which gives a commission of $ 1000 . he earns 5 % on every subsequent dollar . since he earns another $ 170 , he must have had sales of another 170 * ( 100 / 5 ) = 3400 so his total sales must have been $ 10,000 + $ 3400 = $ 13,400 a
Answer: a
Python program:
a = 10 + 4 
b = a - 1
c = 4 / 10
d = b + c
Problem: if an article is sold at 19 % profit instead of 12 % profit , then the profit would be $ 84 more . what is the cost price ?
Options: a ) $ 900 , b ) $ 1200 , c ) $ 1500 , d ) $ 1800 , e ) $ 2100
Rationale: "7 % * cost price = $ 84 1 % * cost price = $ 84 / 7 = $ 12 the cost price is $ 1200 . the answer is b ."
Answer: b
Python program:
a = 84 / 12
b = a * 100
Problem: if 213 × 16 = 3408 , then 16 × 21.3 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 16 × 21.3 = ( 16 x 213 / 10 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d"
Answer: d
Python program:
a = 16 * 21
Problem: a , b and c invest in a partnership in the ratio : 7 / 24 / 36 / 5 . after 4 months , a increases his share 50 % . if the total profit at the end of one year is rs . 21600 , then what is b ' s share in the profit ?
Options: a ) 1000 , b ) 2000 , c ) 3000 , d ) 4000 , e ) 5000
Rationale: ratio of the initial investment = 7 / 2 : 4 / 3 : 6 / 5 = 105 : 40 : 36 therefore , let the initial investments of a , b and c be 105 x , 40 x and 36 x respectively a increases his share 50 % after 4 months . hence the ratio of their investments = ( 105 x × 4 ) + ( 105 x × 150 / 100 × 8 ) : 40 x × 12 : 36 x × 12 = 105 + ( 105 × 3 / 2 × 2 ) : 40 × 3 : 36 × 3 = 105 × 4 : 40 × 3 : 36 × 3 = 35 × 4 : 40 : 36 = 35 : 10 : 9 b ' s share = total profit × 10 / 54 = 21600 × 10 / 54 = 4000 answer is d .
Answer: d
Python program:
a = 21600 * 10
b = 36 + 24 
c = b - 5
d = c - 1
e = a / d
Problem: if x and y are numbers such that ( x + 3 ) ( y - 3 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: "from ( x + 3 ) ( y - 3 ) = 0 it follows that either x = - 3 or y = 3 . thus either x ^ 2 = 9 or y ^ 2 = 9 . now , if x ^ 2 = 9 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 9 + 0 = 9 . similarly if y ^ 2 = 9 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 9 = 9 . answer : d ."
Answer: d
Python program:
a = 3 ** 2
Problem: a bag contains 6 black and 3 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 1 / 3 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 3 ) = 9 . number of white balls = 3 . p ( drawing a white ball ) = 3 / 9 = 1 / 3 . option b ."
Answer: b
Python program:
a = math.factorial(3)
b = 3 - 2
c = math.factorial(b)
d = a / c
e = math.factorial(2)
f = d / e
g = math.factorial(6)
h = 6 - 2
i = math.factorial(h)
j = g / i
k = math.factorial(2)
l = j / k
m = f + l 
n = 6 + 3 
o = math.factorial(n)
p = 6 + 3 
q = p - 2
r = math.factorial(q)
s = o / r
t = math.factorial(2)
u = s / t
v = m / u
Problem: find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1437 , b ) 1250 , c ) 1540 , d ) 1600 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1200 = 6 x + 15 5 x = 1185 x = 237 large number = 237 + 1365 = 1437 a"
Answer: a
Python program:
a = 1200 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: due to construction , the speed limit along an 8 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 4.99 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 8 miles stretch = 8 * 60 / 55 = 8 * 12 / 11 = 8.72 new time in minutes to cross 8 miles stretch = 8 * 60 / 35 = 8 * 12 / 7 = 13.71 time difference = 4.99 ans : a"
Answer: a
Python program:
a = 55 + 8 
b = a - 1
c = 8 / 35
d = 8 / 55
e = c - d
f = b * e
g = max(f)
Problem: set a consists of all the prime numbers between 2 and 13 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 8
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 11 lowest number = 3 range = highest - lowest = 11 - 3 = 8 option e"
Answer: e
Python program:
a = 13 - 2
b = 2 + 4 
c = b + 1 
d = a - c
Problem: if the sum of a number and its square is 210 , what is the number ?
Options: a ) 16 , b ) 14 , c ) 25 , d ) 87 , e ) 171
Rationale: "explanation : let the integer be x . then , x + x 2 = 210 x 2 + x - 210 = 0 ( x + 15 ) ( x – 14 ) = 0 x = 14 answer : b"
Answer: b
Python program:
a = math.sqrt(210)
b = math.floor(a)
Problem: a train of length 240 m crosses a bridge of length 150 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 25 , d ) 70.2 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 240 + 150 ) = 20 x speed speed = 390 / 20 = 19.5 m / s = 70.2 km / h answer = d"
Answer: d
Python program:
a = 240 + 150 
b = a / 20
c = const_3_6 * b
Problem: three interviewers , a , b , and c are interviewing 50 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer a admitted 20 applicants , b admitted 22 applicants , and c admitted 20 applicants , at least how many applicants get the admission ?
Options: a ) 4 , b ) 0 , c ) 6 , d ) 8 , e ) 12
Rationale: "if a admitted 20 are overlapping with b admission of 22 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : b"
Answer: b
Python program:
a = 20 + 22 
b = a + 20 
c = b - 50
Problem: find the sum of first 100 odd numbers
Options: a ) 5500 , b ) 2005 , c ) 10000 , d ) 5800 , e ) 4960
Rationale: "explanation : n 2 = 1002 = 10000 answer : option c"
Answer: c
Python program:
a = 100 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 100 / e
g = f / 2
h = 100 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 100 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 6 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 30
Rationale: "let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 6 ] = ( 1 / 2 ) ( a + 6 ) 2 ( 2 a + 30 ) = 5 ( a + 6 ) a = 30 e"
Answer: e
Python program:
a = 1 / 2
b = 6 * a
c = 6 - b
d = 1 / 2
e = 2 / 5
f = d - e
g = c / f
Problem: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 1.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 6.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 1.50 + 1.50 ( x − 2 ) = 1.50 + 1.5 * 3 = 1.5 + 4.5 = 6 $ answer d"
Answer: d
Python program:
a = 18 - 2
b = a / 4
c = b + 1 
d = c - 2
e = 1 * 50
f = 1 + 50
Problem: a fraction in reduced form is such that when it is squared and then its numerator is reduced by 33 ( 1 / 3 ) % and denominator is reduced to 20 % , its result is twice the original fraction . the sum of numerator and denominator is :
Options: a ) 8 , b ) 13 , c ) 17 , d ) 15 , e ) none of these
Rationale: solution : let the fraction be x / y . when fraction is squared its numerator is reduced by 33 ( 1 / 3 ) and denominator is reduced by 20 % . according to question , ( x / y ) 2 * 33 ( 1 / 3 ) % / 20 % = 2 ( x / y ) . or , ( x / y ) 2 * ( 2 / 3 ) / ( 1 / 5 ) = 2 ( x / y ) . or , x / y = 3 / 5 . sum of numerator and denominator is , ( x + y ) = 3 + 5 = 8 . answer : option a
Answer: a
Python program:
a = 100 / 20
b = 3 + a
Problem: car a is 24 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 2.0 , c ) 2.5 , d ) 3.0 , e ) 4.0
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 24 miles and drive 8 miles ahead so to drive 32 miles it ' ll need 32 / 8 = 4 hours . answer : e ."
Answer: e
Python program:
a = 24 + 8 
b = 58 - 50
c = a / b