euclaise/mathqa_programs huggingface dataset:
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 18 % , then the cost price of the article is :
Options: a ) 500 , b ) 474.6 , c ) 222 , d ) 297 , e ) 111
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 118 = rs . 474.6 answer : b"
Answer: b
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 18 
g = e / f
Problem: how many integers from 10 to 180 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 45 , b ) 49 , c ) 50 , d ) 52 , e ) 56
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 10 to 180 , inclusive is ( 168 - 21 ) / 21 + 1 = 8 ; 57 - 8 = 49 . answer : b ."
Answer: b
Python program:
a = 180 / 10
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required
Options: a ) 8 days , b ) 3 days , c ) 7 days , d ) 5 days , e ) 6 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 10 = 8 days . a"
Answer: a
Python program:
a = 12 * 10
b = a * 8
c = 8 * 15
d = b / c
Problem: if x is an integer and 2.134 × 10 ^ x is less than 220,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 220,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 220,000 to remain true , the greatest number is 213,400 , which makes x = 5 c . 5"
Answer: c
Python program:
a = 220 / 0
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
Problem: calculate 469157 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none
Rationale: "answer 469157 x 9999 = 469157 x ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 . option : c"
Answer: c
Python program:
a = 469157 * 9999
Problem: the area of a square field is 400 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 4 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 400 km 2 . then , each side of field = √ 400 = 20 km distance covered by the horse = perimeter of square field = 20 × 4 = 80 km ∴ time taken by horse = distances / peed = 80 / 20 = 4 h answer c
Answer: c
Python program:
a = math.sqrt(400)
b = 4 * a
c = b / 20
Problem: there are 10 dozen mangoes in a box . if there are 36 such boxes , how many mangoes are there in all the boxes together ?
Options: a ) 516 , b ) 3096 , c ) 6192 , d ) 628 , e ) 4320
Rationale: number of mangoes = 12 dozens = 12 × 10 = 120 ∴ number of mangoes in 36 boxes = 36 × 120 = 4320 answer e
Answer: e
Python program:
a = 36 * 10
b = 10 + 2 
c = a * b
Problem: if a and b are in the ratio 3 : 4 , and b and c in the ratio 12 : 13 , then a and c will be in the ratio
Options: a ) 3 : 13 , b ) 9 : 13 , c ) 36 : 13 , d ) 13 : 9 , e ) none
Rationale: solution : ( a / b ) * ( b / c ) = ( 3 / 4 ) * ( 12 / 13 ) ; or , a / b = 36 / 39 = 9 : 13 . answer : option b
Answer: b
Python program:
a = 3 * 3
b = a / 13
Problem: the sum of a number and the number preceding it is 33 . by how much is two less than 6 times the number ?
Options: a ) 196 , b ) 94 , c ) 90 , d ) 100 , e ) 120
Rationale: two numbers must be 16 and 17 16 + 17 = 33 required number is 17 six times of this number = 6 * 17 = 102 two less than 102 = 102 - 2 = 100 answer : d
Answer: d
Python program:
a = 4 * 4
b = 33 - a
c = b * 6
d = c - 2
Problem: 4,18 , 100,294 , ___
Options: a ) 1000 , b ) 1100 , c ) 1210 , d ) 1452 , e ) 1552
Rationale: "2 ^ 3 - 2 ^ 2 = 4 ; 3 ^ 3 - 3 ^ 2 = 18 ; 5 ^ 3 - 5 ^ 2 = 100 ; 7 ^ 3 - 7 ^ 2 = 294 ; so , 11 ^ 3 - 11 ^ 2 = 1210 answer : c"
Answer: c
Python program:
a = 4 / 18
b = a * 100
Problem: a bag holds 5 red marbles and 5 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 6 , b ) 2 / 5 , c ) 3 / 10 , d ) 2 / 9 , e ) 1 / 2
Rationale: "probability of selecting first red marble = 5 / 10 probability of selecting second red marble without replacement = 4 / 9 final probability = 5 / 10 * 4 / 9 = 2 / 9 the correct answer is d ."
Answer: d
Python program:
a = math.comb(5, 5)
b = 2 + 0 
c = math.comb(b, 2)
d = a / c
Problem: what is the smallest integer x for which 27 ^ x > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ x > 3 ^ 24 converting into the same bases : 27 ^ x > 27 ^ 8 therefore for the equation to hold true , x > 8 or x = 9 option c"
Answer: c
Python program:
a = 24 / 3
b = math.floor(a)
c = b + 1
Problem: a man can row downstream at 16 kmph and upstream at 12 kmph . find the speed of the man in still water .
Options: a ) 14 , b ) 13 , c ) 12 , d ) 16 , e ) 15
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 16 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 28 = > x = 14 , y = 2 . answer : a"
Answer: a
Python program:
a = 16 + 12 
b = a / 2
c = b / 2
Problem: a shopkeeper sold an article offering a discount of 4 % and earned a profit of 38 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 44
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 138 let marked price be rs . x . then , 96 / 100 x = 138 x = 13800 / 96 = rs . 143.75 now , s . p . = rs . 143.75 , c . p . = rs . 100 profit % = 44 % . answer : e"
Answer: e
Python program:
a = 100 + 38 
b = a * 100
c = 100 - 4
d = b / c
e = d - 100
Problem: two trains of length 160 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 82 sec , d ) 24 sec , e ) 89 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 160 + 320 = 480 m . the time required = d / s = 480 / 20 = 24 sec . answer : d"
Answer: d
Python program:
a = 160 + 320 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: solve ( 0.76 × 0.76 × 0.76 − 0.008 ) / ( 0.76 × 0.76 + 0.76 × 0.2 + 0.04 )
Options: a ) 0.56 , b ) 0.62 , c ) 0.5 , d ) 0.48 , e ) 0.52
Rationale: 0.56 option ' a '
Answer: a
Python program:
a = 0 * 76
b = a * 0
c = b - 0
d = 0 * 76
e = 0 * 76
f = d + e 
g = f + 0 
h = c / g
Problem: if the average ( arithmetic mean ) of 2 x , 4 x , and 8 x is 140 , what is the value of x ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 33 , e ) 31
Rationale: "am of 2 x , 4 x and 8 x = 2 x + 4 x + 8 x / 3 = 14 x / 3 given that 14 x / 3 = 140 x = 30 answer is b"
Answer: b
Python program:
a = 4 * 2
b = 2 * 2
c = a - b
Problem: if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 10 inclusive ?
Options: a ) 7 / 32 , b ) 11 / 64 , c ) 35 / 128 , d ) 49 / 128 , e ) 65 / 128
Rationale: "one possible case is : rainy - rainy - rainy - not rainy - not rainy - not rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 7 = 1 / 128 the number of possible cases is 7 c 3 = 35 . p ( exactly 3 rainy days ) = 35 * 1 / 128 = 35 / 128 the answer is c ."
Answer: c
Python program:
a = 1 / 2
b = a ** 4
c = 4 * b
Problem: what is the positive difference between the sum of the squares of the first 5 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 = 55 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 55 is 14 . so the answer is ( d ) ."
Answer: d
Python program:
a = 2 ** 2
b = 1 + a 
c = 3 ** 2
d = b + c 
e = 4 ** 2
f = d + e 
g = 4 + 1 
h = g ** 2
i = f + h 
j = 5 ** 2
k = i + j 
l = 4 + 3 
m = l + 5 
n = 2 + 3 
o = 4 + 1 
p = n + o 
q = 4 + 3 
r = p + q 
s = 2 + 3 
t = s + 5 
u = r + t 
v = m + u 
w = k - v
Problem: find the value of 80641 x 9999 = m ?
Options: a ) 807518799 , b ) 806436469 , c ) 807538799 , d ) 806329359 , e ) 817431046
Rationale: "80641 x 9999 = 80641 x ( 10000 - 1 ) = 80641 x 10000 - 80641 x 1 = 806410000 - 80641 = 806329359 d"
Answer: d
Python program:
a = 9999 - 4
b = a * 80641
Problem: 3889 + 12.952 – ? = 3854.002
Options: a ) 47.095 , b ) 47.752 , c ) 47.932 , d ) 47.95 , e ) none
Rationale: explanation let 3889 + 12.952 – x = 3854.002 . then x = ( 3889 + 12.952 ) – 3854.002 = 3901.952 – 3854.002 = 47.95 . answer d
Answer: d
Python program:
a = 3889 + 12 
b = a - 3854
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 9 inches on a side and costs $ 10 , and a large pizza that measures 14 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches
b ) 10 square inches
c ) 15 square inches
d ) 25 square inches
e ) 34 square inches
Rationale: in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 9 * 9 = 81 ) for the small pizza and ( 14 * 14 = 196 ) for the large pizza . in total sq inches that would be ( 81 + 196 ) * 2 = 554 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 196 = 588 sq inches . hence , the difference is 34 square inches more ( 588 - 554 ) . the correct answer is e
Answer: e
Python program:
a = 14 ** 2
b = a * 3
c = 9 ** 2
d = 14 ** 2
e = c + d 
f = 9 ** 2
g = 14 ** 2
h = f + g 
i = e + h 
j = b - i
Problem: which number is a factor of 20 ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 18 , e ) 9
Rationale: a whole number that divides exactly into another whole number is called a factor 20 / 5 = 4 answer b
Answer: b
Python program:
a = 2 ** 2
Problem: there are 2 sections a and b in a class , consisting of 24 and 16 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?
Options: a ) 35.29 kg , b ) 37.25 kg , c ) 42 kg , d ) 38 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 24 * 40 + 16 * 35 = 1520 average weight of the class is = 1520 / 40 = 38 kg answer is d"
Answer: d
Python program:
a = 24 * 40
b = 16 * 35
c = a + b 
d = 24 + 16 
e = c / d
Problem: if n divided by 5 has a remainder of 4 , what is the remainder when 3 times n is divided by 5 ?
Options: a ) 1 , b ) 4 , c ) 3 , d ) 2 , e ) 0
Rationale: "as per question = > n = 5 p + 4 for some integer p hence 3 n = > 15 q + 12 but again , 12 can be divided by 5 to get remainder 2 for some integer q hence d"
Answer: d
Python program:
a = 3 * 4
Problem: a man can row downstream at 18 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 2
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 28 = > x = 14 , y = 4 . answer : d"
Answer: d
Python program:
a = 18 + 10 
b = a / 2
c = b / 2
Problem: if four machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 48 , b ) 60 , c ) 75 , d ) 80 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 4 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 8 / 3 = 10 / 3 * x x = 4 / 5 hour so 48 minutes answer : a"
Answer: a
Python program:
a = 3 / 5
b = 3 / 4
c = b / 5
d = c / 30
e = d * 2
f = a / e
Problem: the ratio of number of boys and girls in a school is 2 : 5 . if there are 210 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 210 number of girls in the school = 5 * 210 / 7 = 150 answer is a"
Answer: a
Python program:
a = 210 / 3
b = a * 5
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 10 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 5020
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , and 2 * 5 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 = 2520 the answer is d ."
Answer: d
Python program:
a = math.lcm(1, 10)
Problem: there are two positive integers a and b . what is the probability that a + b is odd /
Options: a ) 3 / 2 , b ) 6 / 7 , c ) 1 / 2 , d ) 7 / 2 , e ) 4 / 5
Rationale: s = adding two numbers is ( even + even ) , ( even + odd ) , ( odd + odd ) , ( odd + even ) n ( s ) = 4 e = ( even + odd ) , ( odd + even ) are the points in the event . n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 4 = 1 / 2 answer is option c
Answer: c
Python program:
a = 2 / 4
b = a * 100
Problem: of the 150 employees at company x , 60 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 80 answer : option d"
Answer: d
Python program:
a = 150 - 60
b = a - 20
Problem: if f is the smallest positive integer such that 3,150 multiplied by f is the square of an integer , then f must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by f is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x f = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , y = 7 x 2 = 14 answer is e .
Answer: e
Python program:
a = 10 + 4
Problem: what is the least number . which should be added to 0.0355 to make it a perfect square ?
Options: a ) 0.0005 , b ) 0.0016 , c ) 0.0056 , d ) 0.0066 , e ) 0.0006
Rationale: "0.0355 + 0.0006 = 0.0361 ( 0.19 ) ^ 2 answer : e"
Answer: e
Python program:
a = 12 + 4 
b = a + 2 
c = b / 100
d = 12 + 4 
e = d + 2 
f = e / 100
g = c * f
h = g - 0
Problem: if x + 4 y = 5 and 5 x + 6 y = 7 , then 3 x + 5 y = ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: add the left terms and right terms of the two equation to obtain a new equation x + 5 x + 4 y + 6 y = 5 + 7 group and simplify 6 x + 10 y = 12 divide all terms of the above equation by 2 to obtain a new equation 3 x + 5 y = 6 correct answer a
Answer: a
Python program:
a = 5 * 5
b = a - 7
c = 5 * 4
d = c - 6
e = b / d
f = 5 * e
g = 5 * 5
h = g - 7
i = 5 * 4
j = i - 6
k = h / j
l = k * 4
m = 5 - l
n = m * 3
o = f + n
Problem: the distance from steve ' s house to work is 10 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 10 km = > speed = 5 kmph a"
Answer: a
Python program:
a = 10 / 2
b = 10 + a 
c = b / 6
d = c * 2
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 35 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 35 % = 63 responded as satisfied , so remaining satisfied are 120 - 63 = 57 so 57 is what percentage of 300 - 19 % so the answer should be a
Answer: a
Python program:
a = 40 / 100
b = a * 300
c = 35 / 100
d = 60 / 100
e = 300 * d
f = c * e
g = b - f
h = g / 300
i = h * 100
Problem: a work can be finished in 30 days by 30 women . the same work can be finished in fifteen days by 15 men . the ratio between the capacity of a man and a woman is
Options: a ) 1 : 3 , b ) 4 : 3 , c ) 2 : 3 , d ) 4 : 1 , e ) 2 : 4
Rationale: "work done by 30 women in 1 day = 1 / 30 work done by 1 woman in 1 day = 1 / ( 30 × 30 ) work done by 15 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 × 15 ) ratio of the capacity of a man and woman = 1 / ( 15 × 15 ) : 1 / ( 30 × 30 ) ) = 1 / 225 : 1 / 900 = 1 / 1 : 1 / 4 = 4 : 1 option d"
Answer: d
Python program:
a = 30 + 2 
b = a * 10
c = 1 / b
d = 30 * 10
e = 1 / d
f = c / e
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 8 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 ) 1 / 16 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 8 = 8 c 2 total possible outcomes - 2 ^ 8 ( each child can be either a girl or a boy ) probability = 2 c 1 * 8 c 2 / 2 ^ 8 = 2 * 8 / 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 16 / 256 = 1 / 16 ans = d"
Answer: d
Python program:
a = 2 / 8
Problem: ? % of 360 = 126
Options: a ) 277 , b ) 35 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 126 or , ? = 126 × 100 / 360 = 35 answer b"
Answer: b
Python program:
a = 126 * 100
b = a / 360
Problem: the area of a circle of radius 5 is numerically what percent of its circumference ?
Options: a ) 200
b ) 225
c ) 240
d ) 250
e ) none
Rationale: solution required % = [ π x ( 5 ) 2 / 2 π x 5 x 100 ] % ‹ = › 250 % . answer d
Answer: d
Python program:
a = circle_area / (
b = 100 * a
Problem: jony walks along sunrise boulevard daily . he starts walking at 07 : 00 from block 10 and walks to block 90 where he turns around and walks back to block 70 , where he stops at 07 : 40 . the blocks along the boulevard are numbered sequentially ( 1 , 2,3 ) , and each block measures 40 meters . what is jony ' s speed in meters per minute ?
Options: a ) 88 , b ) 100 , c ) 198 , d ) 216 , e ) 252
Rationale: total distance from 10 to 90 = 80 + from 90 to 70 = 20 so the dist is 100 × 40 ( per block dist ) speed = 4000 mts / 40 min = 100 m / min b is the answer
Answer: b
Python program:
a = 90 - 10
b = a * 40
c = 90 - 70
d = c * 40
e = b + d 
f = e / 40
Problem: car a is 40 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 ) 5 , b ) 6 , c ) 7 , d ) 5.5 , e ) 6.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 40 miles and drive 8 miles ahead so to drive 48 miles it ' ll need 48 / 8 = 6 hours . answer : b"
Answer: b
Python program:
a = 40 + 8 
b = 58 - 50
c = a / b
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , - 8 ) . what is the least possible value of the slope of line l ?
Options: a ) - 6.5 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 10
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 8 ) should satisfy the equation . hence x = t and y = - 8 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 8 - 5 ) / ( 4 - 2 ) = - 6.5 imo option a is correct answer ."
Answer: a
Python program:
a = 8 - 5
b = 9 + 8 
c = math.sqrt(b)
d = 5 + 9 
e = math.sqrt(d)
f = c - e
g = a / f
Problem: find the compound interest on $ 1200 for 4 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 1288 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 4 = $ 2488 ci = $ 1288 answer is c"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 4
d = 1200 * c
e = d - 1200
Problem: in a company 10 % of male staff are same in number as 1 / 4 th of the female staff . what is the ratio of male staff to female staff
Options: a ) 3 : 2 , b ) 5 : 2 , c ) 2 : 1 , d ) 4 : 3 , e ) 1 : 2
Rationale: 10 % of ms = 1 / 4 th of fs - > 10 ms / 100 = 1 / 4 fs - > ms = 5 / 2 fs : . ms / fs = 5 / 2 = ms : fs = 5 : 2 answer : b
Answer: b
Python program:
a = 1 / 4
b = 10 / 100
c = a / b
Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 25 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 75 / 2 , e ) 35
Rationale: "b : d : w = 2 : 25 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 25 ) = ( 2 / 75 ) dnew / wnew = ( 1 / 2 ) * ( 25 / 100 ) = ( 1 / 8 ) wnew = 300 dnew = wnew / 5 = 300 / 8 = 75 / 2 so , answer will be d"
Answer: d
Python program:
a = 300 / 100
b = 25 / 2
c = a * b
Problem: the average weight of 10 persons increases by 6.3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 176 kg , b ) 80 kg , c ) 185 kg , d ) 90 kg , e ) 128 kg
Rationale: "solution total weight increased = ( 10 x 6.3 ) kg = 63 kg . weight of new person = ( 65 + 63 ) kg = 128 kg . answer e"
Answer: e
Python program:
a = 10 * 6
b = 65 + a
Problem: a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number t of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average t sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Python program:
a = 1 + 2 
b = 66 * a
c = 70 * 2
d = b - c