euclaise/mathqa_programs huggingface dataset:
Problem: there are 6 positive and 8 negative numbers . 4 numbers are choosen at random and multiplied . the probability that the product is positive is :
Options: a ) 500 / 1001 , b ) 503 / 1001 , c ) 303 / 1001 , d ) 301 / 1001 , e ) 505 / 1001
Rationale: 6 c 4 / 14 c 4 + ( 6 c 2 * 8 c 2 ) / 14 c 4 + 8 c 4 / 14 c 4 = 505 / 1001 case 1 : only 4 positive no . case 2 : 2 positive and 2 negative no . case 3 : 4 negative no . answer : e
Answer: e
Python program:
a = math.factorial(6)
b = math.factorial(4)
c = math.factorial(2)
d = b * c
e = a / d
f = math.factorial(8)
g = math.factorial(4)
h = math.factorial(4)
i = g * h
j = f / i
k = e + j 
l = math.factorial(6)
m = math.factorial(4)
n = math.factorial(2)
o = m * n
p = l / o
q = math.factorial(8)
r = math.factorial(6)
s = math.factorial(2)
t = r * s
u = q / t
v = p * u
w = k + v 
x = 6 + 8 
y = math.factorial(x)
z = 6 + 8 
A = z - 4
B = math.factorial(A)
C = math.factorial(4)
D = B * C
E = y / D
F = w / E
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 35 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 979923 , c ) 1009125 , d ) 2356677 , e ) 1083875
Rationale: required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 35 / 100 ) = 1009125 c
Answer: c
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1000000 * h
Problem: f ( x ) is a function such that f ( x ) + 3 f ( 8 - x ) = x for all real numbers x . find the value of f ( 2 ) .
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: f ( x ) + 3 f ( 8 - x ) = x : given f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation . correct answer is d ) 2
Answer: d
Python program:
a = 3 * 3
b = a * 2
c = 2 - b
d = 3 * 3
e = 1 - d
f = c / e
Problem: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 105 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 60 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 105 ⇒ 1.75 x = 105 ⇒ x = 60 coins answer d"
Answer: d
Python program:
a = 1/(4)
b = 1/(2)
c = a + b 
d = c + 1 
e = 105 / d
Problem: john can complete a given task in 20 days . jane will take only 10 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 16 , e ) 20
Rationale: in such questions , you need to start from the end . last 5 days john works alone and completes 5 * ( 1 / 20 ) = 1 / 4 of the work . so 3 / 4 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 10 = 3 / 20 time taken to complete 3 / 4 of the work = ( 3 / 4 ) / ( 3 / 20 ) = 5 days . so total number of days taken to complete the work = 5 + 5 = 10 days . b
Answer: b
Python program:
a = 20 * 10
b = 10 * 5
c = a - b
d = 10 + 20 
e = c / d
f = 5 + e
Problem: a man sold 20 articles for $ 60 and gained 10 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 10 % ) / 20 = $ 2.70 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 2.70 = 40 thus , solution c is correct ."
Answer: c
Python program:
a = original_price_before_loss / (
Problem: list k consists of 10 consecutive integers . if - 4 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 4
Rationale: "answer = e = 4 if least = - 4 , then largest = 5 range = 5 - 1 = 4"
Answer: e
Python program:
a = 10 - 4
b = a - 1
c = b - 1
Problem: in a school of 400 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 41 , b ) 63 , c ) 72 , d ) 63 , e ) 50
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 400 * 18 / 100 = 72 answer : c"
Answer: c
Python program:
a = 44 + 28 
b = a + 10 
c = 100 - b
d = 400 * c
e = d / 100
Problem: a train 120 m in length crosses a telegraph post in 6 seconds . the speed of the train is ?
Options: a ) 72 kmph , b ) 88 kmph , c ) 54 kmph , d ) 18 kmph , e ) 19 kmph
Rationale: "s = 120 / 6 * 18 / 5 = 72 kmph answer : a"
Answer: a
Python program:
a = 120 / 6
b = const_3_6 * a
Problem: two boats are heading towards each other at constant speeds of 3 miles / hr and 21 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 1 / 3 , e ) 3 / 15
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 3 + 21 = 24 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 24 * 1 / 60 = 3 / 15 miles apart . answer : e ."
Answer: e
Python program:
a = 21 + 3 
b = a / const_60
Problem: two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 15 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 10 + 6 = 16 m / sec . required time = ( 120 + 120 ) / 16 = 15 sec . answer : d"
Answer: d
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 20 % . their gross income from sales for one month increases by what percent ?
Options: a ) 2 % , b ) 4 % , c ) 5 % , d ) 8 % , e ) 12 %
Rationale: "let list price of an item = 100 discount on each item = 10 % discounted price of an item = . 9 * 100 = 90 if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 20 % originally if 10 items were sold in a month , with the new discount 12 items will be sold original revenue = no of items * price of an item = 10 * 100 = 1000 new revenue = 12 * 90 = 1080 increase in gross income = 1080 - 1000 = 80 % increase in gross revenue = 80 / 1000 * 100 % = 8 % answer d"
Answer: d
Python program:
a = 20 - 10
b = 20 / 10
c = a - b
Problem: a reduction of 48 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.6 , b ) 8.6 , c ) 7.6 , d ) 3.6 , e ) 1.6
Rationale: "explanation : 40 * ( 48 / 100 ) = 19.2 - - - 64 ? - - - 12 = > rs . 3.6 answer : d"
Answer: d
Python program:
a = 48 / 100
b = 48 * a
c = b / 64
d = 12 * c
Problem: the s . i . on a certain sum of money for 3 years at 8 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 3000 , b ) 2802 , c ) 1750 , d ) 2990 , e ) 2982
Rationale: "c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 1750 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 4000 * c
e = d - 4000
f = e / 2
g = 8 / 100
h = 3 * g
i = f / h
Problem: in plutarch enterprises , 70 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 60,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 220,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 7 marketers , 2 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 60,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 420,000 - $ 160,000 = $ 220,000 . the correct answer is e ."
Answer: e
Python program:
a = 70 + 20 
b = a * 1000
c = b * 100
d = 70 + 20 
e = d * 1000
f = 20 * e
g = c - f
h = 20 / 2
i = h * 20
j = i * 1000
k = j * 70
l = g - k
m = l / 20
Problem: a person buys an article at rs . 460 . at what price should he sell the article so as to make a profit of 18 % ?
Options: a ) 542 , b ) 882 , c ) 772 , d ) 662 , e ) 521
Rationale: "cost price = rs . 460 profit = 18 % of 460 = rs . 82 selling price = cost price + profit = 460 + 82 = 542 answer : a"
Answer: a
Python program:
a = 18 / 100
b = 460 * a
c = 460 + b
Problem: if an integer n is to be chosen at random from the integers 1 to 86 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 55 / 86 , e ) 3 / 4
Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 86 , there are 43 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 43 + 12 ) / 96 = 55 / 86 ans isd"
Answer: d
Python program:
a = 86 / 2
b = 86 / 8
c = a + b 
d = c / 86
Problem: a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 600 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 377.78
Rationale: let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 277.78 d
Answer: d
Python program:
a = 40 / 100
b = a * 600
c = 60 / 100
d = b / c
e = 40 / 100
f = d * e
g = 60 / 100
h = f / g
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 1,000 ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 7 , e ) 6
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 9 = 512 < 1,000 , then the greatest possible length of integer z is 9 . the answer is c ."
Answer: c
Python program:
a = 2 ** 10
b = math.log(a)
Problem: in a group of 6 boys and 4 girls are to be selected . in how many different ways can they be selected such that at least one boy should be there ?
Options: a ) 209 , b ) 200 , c ) 210 , d ) 225 , e ) 221
Rationale: no of boys = 6 no of girls = 4 therefore , no of ways at least 1 boy can be selected = 6 c 4 * 4 c 0 + 6 c 3 * 4 c 1 + 6 c 2 * 4 c 2 + 6 c 1 * 4 c 3 = 15 + 80 + 90 + 24 = 209 ans - a
Answer: a
Python program:
a = 6 + 4 
b = math.factorial(a)
c = math.factorial(4)
d = math.factorial(6)
e = c * d
f = b / e
Problem: the youngest of 4 children has siblings who are 1 , 4 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 17 , what is the age of the youngest sibling ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "x + ( x + 1 ) + ( x + 4 ) + ( x + 8 ) = 68 4 x + 12 = 68 4 x = 56 x = 14 the answer is e ."
Answer: e
Python program:
a = 4 * 17
b = 4 + 4 
c = b + 7 
d = a - c
e = d / 4
Problem: a , b , c weighted separately 1 st like a , b , c , then a & b , then b & c , then c & a at last a & b & c , the last weight was 167 , then what will be the average weight of the 7 reading ?
Options: a ) 95 , b ) 95.42 , c ) 95.45 , d ) 94 , e ) 93
Rationale: the sum of 7 weights = weights of [ a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] = weights of [ 4 * ( a + b + c ) = 4 * 167 = 668 therefore the average weight of 7 readings is 668 / 7 = 95.428 answer : b
Answer: b
Python program:
a = 4 * 167
b = a / 7
Problem: a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a plce and come back , how far is the place ?
Options: a ) 2 km , b ) 2.4 km , c ) 2.5 km , d ) 3.4 km , e ) none
Rationale: "sol . speed downstream = ( 5 + 1 ) kmph = 6 kmph ; speed upstream = ( 5 - 1 ) kmph = 4 kmph . let the required distance be x km . then , x / 6 + x / 4 = 1 ⇔ 2 x + 3 x = 12 ⇔ 5 x = 12 ⇔ x = 2.4 km . answer b"
Answer: b
Python program:
a = 5 - 1
b = a * 3
c = b / 5
Problem: a box contains 24 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 24 / 77 , e ) none
Rationale: "solution p ( none is defective ) = 20 c 2 / 24 c 2 = 53 / 77 . p ( at least one is defective ) = ( 1 - 53 / 77 ) = 24 / 77 . answer d"
Answer: d
Python program:
a = 24 - 4
b = math.comb(a, 2)
c = math.comb(24, 2)
d = b / c
e = 1 - d
Problem: in a sample of christ college students , 30 percent are third year students and 90 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 3 / 4 , b ) 2 / 3 , c ) 4 / 7 , d ) 1 / 2 , e ) 1 / 7
Rationale: = 10 / 70 . = 1 / 7 my answer is e too
Answer: e
Python program:
a = 100 - 30
b = 90 - 30
c = a - b
d = 100 - 30
e = c / d
Problem: an electric pump can fill a tank in 3 hours . because of a leak in the tank , it took 12 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 4 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 15 hours
Rationale: "work done by the leak in 1 hour = 1 / 3 - 1 / 12 = 1 / 4 the leak will empty the tank in 4 hours answer is a"
Answer: a
Python program:
a = 12 / 1
Problem: in a school of 800 students , 45 % wear blue shirts , 23 % wear red shirts , 15 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 120 , b ) 128 , c ) 136 , d ) 144 , e ) 152
Rationale: "45 + 23 + 15 = 83 % 100 – 83 = 17 % 800 * 17 / 100 = 136 the answer is c ."
Answer: c
Python program:
a = 45 / 100
b = a * 800
c = 23 / 100
d = c * 800
e = b + d 
f = 15 / 100
g = f * 800
h = e + g 
i = 800 - h
Problem: what is the hcf of 2 / 3 , 4 / 12 and 6 / 5
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 1 / 30 , e ) 9 / 45
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 12 , 5 ) = 2 / 60 = 1 / 30 answer : option d"
Answer: d
Python program:
a = 2 / 5
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 10 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 127 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: "since michelle earns 10 % interest compounded semiannually , then she earns 5 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 5 % * 5 = 25 % . but , since the interest is compounded every 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 25 % , only answer choice a fits . answer : a"
Answer: a
Python program:
a = 10 / 100
b = a / 2
c = 1 + b 
d = 2 + 3 
e = c ** d
f = e * 100
Problem: john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 70 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 70 = 30 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 30 / 100 ) * 100 = ( 0.3 ) * 100 = 30 % . b"
Answer: b
Python program:
a = 100 - 70
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 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 ) 22 , d ) 20 , e ) 14
Rationale: "let the total number of workers be x . then , 8000 x = ( 10000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 28000 = x = 14 . answer : e"
Answer: e
Python program:
a = 10000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: a picture is copied onto a sheet of paper 8.5 inches by 10 inches . a 1.5 inch margin is left all around . what area in square inches does the picture cover ?
Options: a ) 76
b ) 65
c ) 59.5
d ) 49
e ) 38.5
Rationale: area covered by picture = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e
Answer: e
Python program:
a = 1 * 5
b = 8 - 5
c = 1 * 5
d = 10 - c
e = b * d
Problem: a cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm . find the total area of the wet surface .
Options: a ) 142 m sqaure , b ) 122 m sqaure , c ) 135 m sqaure , d ) 188 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 2.25 + 9 * 2.25 ) ] + 9 * 6 = 122 m square option b"
Answer: b
Python program:
a = 25 / 100
b = a + 2 
c = b * 6
d = 25 / 100
e = d + 2 
f = e * 9
g = c + f 
h = 2 * g
i = 6 * 9
j = h + i
Problem: a tailor trims 4 feet from opposite edges of a square piece of cloth , and 3 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 18
b ) 20
c ) 24
d ) 26
e ) 40
Rationale: let the original side of the square be x . ( x - 8 ) * ( x - 6 ) = 120 = 10 * 12 x = 18 the answer is a .
Answer: a
Python program:
a = 2 * 4
b = 2 * 3
c = a + b 
d = 2 * 3
e = 2 * 4
f = d * e
g = 120 - f
h = 4 * g
i = 2 * 4
j = 2 * 3
k = i + j 
l = k ** 2
m = h + l 
n = math.sqrt(m)
o = c + n 
p = o / 2
Problem: in a company , 54 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 55 % , b ) 60 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 46 % of all employees are women , so non - union women are 46 % - 18 % = 28 % 40 % of all employees are non - union . the percent of non - union employees who are women is 28 % / 40 % = 70 % the answer is d .
Answer: d
Python program:
a = 100 - 54
b = 70 / 100
c = 60 * b
d = 60 - c
e = a - d
f = 100 - 60
g = e / f
h = 100 * g
Problem: 10 women can complete a work in 7 days & 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 5 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) 11 days
Rationale: 1 woman ' s 1 day ' s work = 1 / 70 1 child ' s 1 day ' s work = 1 / 140 5 women and 10 children 1 day work = ( 5 / 70 + 10 / 140 ) = 1 / 7 so 5 women and 10 children will finish the work in 7 days . b )
Answer: b
Python program:
a = 10 * 7
b = 1 / a
c = b * 5
d = 10 * 14
e = 1 / d
f = e * 10
g = c + f 
h = 1/(g)
Problem: 5 n + 7 > 12 and 7 n - 5 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 1 and 7 , e ) 2 and 9
Rationale: "5 n > 5 - - > n > 1 7 n < 49 - - > n < 7 1 < n < 7 answer : d"
Answer: d
Python program:
a = 7 * 10
b = 44 + 5 
c = b / 7
d = a + c
Problem: the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 30 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 360 , c ) $ 400 , d ) $ 500 , e ) $ 600
Rationale: "c for cost . p price per person . c = 3 * p c = 4 * p - 120 substituting the value of p from the first equation onto the second we get p = 120 . plugging in the value of p in the first equation , we get c = 360 . which leads us to answer choice b"
Answer: b
Python program:
a = 4 * 3
b = 4 - 3
c = 30 / b
d = a * c
Problem: a survey was sent to 75 customers , 7 of whom responded . then the survey was redesigned and sent to another 60 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 60 % , e ) 73 %
Rationale: "rate of first survey = 7 / 75 rate of second survey = 9 / 60 % response rate increase ( 9 / 60 - 7 / 75 ) / ( 7 / 75 ) = 60 % answer is d = 60 %"
Answer: d
Python program:
a = 9 / 60
b = 7 / 75
c = a - b
d = c * 100
e = math.floor(d)
Problem: mary ' s income is 60 % more than tim ' s income and tim ' s income is 20 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 128 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: even i got 96 % j = 100 t = 100 * 0.8 = 80 m = 80 * 1.6 = 128 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 128 * 100 / 100 = 128 ans : a
Answer: a
Python program:
a = 100 - 20
b = 100 - 20
c = 60 / 100
d = b * c
e = a + d
Problem: a train 125 m long passes a man , running at 9 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 50 , c ) 88 , d ) 65 , e ) 54
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 9 ) km / hr . x - 9 = 45 = = > x = 54 km / hr . answer : e"
Answer: e
Python program:
a = 9 * const_0_2778
b = a * 9
c = 125 - b
d = c / 9
e = d / const_0_2778
Problem: steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles . therefore , total distance covered = 80 + 240 = 320 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 320 / 5 = 64 miles per hour . choice d"
Answer: d
Python program:
a = 80 * 3
b = 40 * 2
c = a + b 
d = 3 + 2 
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g