euclaise/mathqa_programs huggingface dataset:
Problem: a can complete a certain job in 7 days . b is 40 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 5 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 4.8
Rationale: "let , total work unit = 70 units a can finish in 7 days = 70 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 40 / 100 ) * 10 = 14 unit work days in which b will complete the work alone = 70 / 14 = 5 days answer : option a"
Answer: a
Python program:
a = 7 * 40
b = a / 100
Problem: the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit t on the height of vehicles that are allowed to use the tunnel ?
Options: a ) 5 ½ ft
b ) 7 ½ ft
c ) 8 ½ ft
d ) 9 ½ ft
e ) 10 ft
Rationale: let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer t is 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b
Answer: b
Python program:
a = 12 / 2
b = 1 / 2
c = a - b
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 miles , e ) 160
Rationale: let v and t be initial parameter vt = d from the stem ( t + 1 ) ( v + 5 ) = 70 + d = > v + 5 t = 65 - - - - - - - 1 ) we need the additional distance traveled second time at v + 10 and t + 2 ( t + 2 ) ( v + 10 ) = vt + 2 v + 10 t + 20 but vt = d hence d + 2 ( v + 5 t ) + 20 but v + 5 t = 65 hence the additional distance traveled is 2 ( v + 5 t ) + 20 = 2 * 65 + 20 = 130 + 20 = 150 d
Answer: d
Python program:
a = 70 - 5
b = a * 2
c = 2 * 10
d = b + c
Problem: a glass was filled with 40 ounces of water , and 0.01 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.005 % , b ) 0.02 % , c ) 0.5 % , d ) 5 % , e ) 20 %
Rationale: "we are given that 0.01 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20 . this gives us : 0.01 x 20 = 0.2 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.2 / 40 ) x 100 % = 0.5 % answer c"
Answer: c
Python program:
a = 0 * 1
b = a / 40
c = b * 100
Problem: a family pays $ 800 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,600 , e ) $ 2,000
Rationale: assuming the medical expenses are $ 1000 or more , the family pays $ 800 + $ 400 = $ 1200 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 600 when the medical expenses are $ 1600 . the answer is d .
Answer: d
Python program:
a = 1000 - 800
Problem: mike and his friend are going on a road trip and hoping to miss traffic . if they are driving at a rate of 6 miles per minute , what is their speed in kilometers per hour ? [ 1 km = 0.6 miles ]
Options: a ) 60 , b ) 30 , c ) 300 , d ) 600 , e ) none of the above
Rationale: to calculate the equivalent of kilometres in a mile 6 miles = 6 * ( 0.6 ) ^ - 1 = 10 kilometres in 1 hour there are 60 minutes speed in kmph = 10 * 60 = 600 correct answer - d
Answer: d
Python program:
a = 6 * const_60
b = a / 0
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 30,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 240,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 450,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 30,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 30000 * 2 ^ 3 = 240000 hence , the answer is a ."
Answer: a
Python program:
a = 3600 / 10
Problem: the average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 6 kg = > ( 120 - x ) / 10 = 6 = > x = 60 answer : b"
Answer: b
Python program:
a = 10 * 6
b = 120 - a
Problem: the length of a rectangular landscape is 4 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 3 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90
b ) 100
c ) 120
d ) 130
e ) 140
Rationale: sol . x * 4 x = 3 * 1200 x = 30 length = 4 * 30 = 120 c
Answer: c
Python program:
a = 4 * 3
b = a * 10
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 2 x = 42 x dollars ; we know that harry also earned the same 42 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 12 x additional dollars . since for each additional hour he gets 2 x dollars then he worked for 12 x / 2 x = 6 additional hours , so harry worked for total of 30 + 6 = 36 hours . answer : b ."
Answer: b
Python program:
a = 40 + 2 
b = a - 30
c = b / 2
d = c + 30
Problem: the sum of 3 numbers is 98 . the ratio of the first to the second is 2 / 3 , and the ratio of the second to the third is 5 / 8 . the second number is :
Options: a ) 20 , b ) 30 , c ) 60 , d ) 70 , e ) 10
Rationale: b 30 let the three numbers be x , y and z . sum of the numbers is 98 . x + y + z = 98 … … … … … … ( i ) the ratio of the first to the second is 2 / 3 . x / y = 2 / 3 . x = 2 / 3 × y . x = 2 y / 3 . the ratio of the second to the third is 5 / 8 . y / z = 5 / 8 . z / y = 8 / 5 . z = 8 / 5 × y . z = 8 y / 5 . put the value of x = 2 y / 3 and z = 8 y / 5 in ( i ) . 2 y / 3 + y + 8 y / 5 = 98 49 y / 15 = 98 . 49 y = 98 × 15 . 49 y = 1470 . y = 1470 / 49 . y = 30 . therefore , the second number is 30 .
Answer: b
Python program:
a = 3 * 5
b = 98 * a
c = 3 * 5
d = 2 * 5
e = c + d 
f = 8 * 3
g = e + f 
h = b / g
Problem: a trader sold an article on a certain price with 20 % profit . if he sold double of previous selling price then find its profit %
Options: a ) 140 % , b ) 120 % , c ) 100 % , d ) 90 % , e ) 80 %
Rationale: let cost price = 100 % selling price = 120 % new s . p . = 240 % p % = 240 - 100 = 140 % answer is a
Answer: a
Python program:
a = 100 + 20 
b = 2 * a
c = b - 100
Problem: if a and b get profits of rs . 6000 and rs . 4000 respectively at the end of year the ratio of their investments are ?
Options: a ) 1 : 4 , b ) 3 : 2 , c ) 2 : 3 , d ) 2 : 5 , e ) none of these
Rationale: "profit = investment * time so , 6000 = i 1 * 1 = 6000 4000 = i 2 * 1 = 4000 i 1 / i 2 = 6000 / 4000 = 3 / 2 answer : b"
Answer: b
Python program:
a = 3 * 2
b = a * 100
c = b * 100
d = 3 * 2
e = d * 100
f = e * 100
g = 2 + 3 
h = g * 2
i = f / h
j = c / i
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 57 kmph , find the speed of the stream ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 18 , e ) 16
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 57 / 3 = 19 kmph . answer : c"
Answer: c
Python program:
a = 57 * 2
b = a / 3
c = 57 - b
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 650 grams per kg , what is his percent ?
Options: a ) 15 % , b ) 25 % , c ) 65 % , d ) 53.8 % , e ) 35 %
Rationale: "explanation : 650 - - - 350 100 - - - ? = > 53.8 % answer : d"
Answer: d
Python program:
a = 100 / 650
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: the slant height of a cone is 12 cm and radius of the base is 4 cm , find the curved surface of the cone .
Options: a ) 33 , b ) 88 , c ) 48 , d ) 77 , e ) 27
Rationale: "π * 12 * 4 = 48 answer : c"
Answer: c
Python program:
a = math.pi * 4
b = a * 12
Problem: the sum of ages of 4 children born 2 years different each is 40 yrs . what is the age of the elder child ?
Options: a ) 13 , b ) 9 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 40 4 x + 12 = 40 = > 4 x = 28 x = 7 x + 6 = 7 + 6 = 13 answer : a"
Answer: a
Python program:
a = 2 + 4 
b = 2 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 40 
g = f / 4
Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 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 200 liters of water , how many liters of detergent will it contain ?
Options: a ) 60 , b ) 55 , c ) 50 , d ) 45 , e ) 40
Rationale: "b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 200 dnew = wnew / 5 = 200 / 5 = 40 so , answer will be e"
Answer: e
Python program:
a = 200 / 100
b = 40 / 2
c = a * b
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 75 paise per sq m is
Options: a ) rs . 258 , b ) rs . 358 , c ) rs . 458 , d ) rs . 558 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) × h ] + ( l × b ) = [ 2 ( 25 + 12 ) × 6 ] + ( 25 × 12 ) = 744 sq m cost of plastering = 744 × ( 75 / 100 ) = rs . 558 answer : d"
Answer: d
Python program:
a = 75 / 100
b = 25 * 12
c = 25 * 6
d = 2 * c
e = 12 * 6
f = e * 2
g = d + f 
h = b + g 
i = a * h
Problem: it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 140 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 42 , e ) 30
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 140 / 50 = 42 minutes to print 140 pages ( answer d )"
Answer: d
Python program:
a = 4 * 2
b = a + 4 
c = 140 * b
d = c / 40
Problem: there is a total of 100 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 7 / 10 , d ) 9 / 20 , e ) 11 / 20
Rationale: "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 20 / 20 - 5 / 20 - 4 / 20 = 11 / 20 the answer is e ."
Answer: e
Python program:
a = 1 / 4
b = 1 / 5
c = a + b 
d = 1 - c
Problem: you and your friend spent a total of $ 11 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 7 , d ) $ 6 , e ) $ 5
Rationale: "my lunch = l , my friends lunch = l + 1 ( l ) + ( l + 3 ) = 11 l + l + 3 - 3 = 11 - 3 2 l = 8 l = 4 my friends lunch l + 3 = 4 + 3 = $ 7 , the answer is c"
Answer: c
Python program:
a = 11 - 3
b = a / 2
c = b + 3
Problem: 3 business people wish to invest in a new company . each person is willing to pay one third of the total investment . after careful calculations , they realize that each of them would pay $ 2200 less if they could find two more equal investors . how much is the total investment in the new business ?
Options: a ) $ 11,000 , b ) $ 50,000 , c ) $ 16,500 , d ) $ 6,600 , e ) $ 3,600
Rationale: total investment between 5 : ( x / 5 ) total investment including 2200 less between 3 people ( x - ( 2200 * 3 ) ) / 3 set both eq . equal to each other . 16,500 answer c )
Answer: c
Python program:
a = 3 + 2 
b = 2200 * 3
c = b / 2
d = a * c
e = reminder / (
Problem: haresh went to buy fruits . she bought 1 apple , 3 bananas , 5 oranges and paid 21 rupees . another person bought 7 apple , 5 bananas , 3 oranges and paid 51 rupees . if i want to buy 1 apple , 1 banana , 1 orange then how much i have to pay ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 7
Rationale: there can be multiple possible rates of apple , banana and orange to satisfy given conditions , but cost of 1 apple , 1 banana , 1 orange will be rs 9 . 1 x + 3 y + 5 z = 21 . . . . . . . . ( 1 ) 7 x + 5 y + 3 z = 51 . . . . . . . . ( 2 ) adding ( 1 ) and ( 2 ) , we get 8 x + 8 y + 8 z = 72 8 * ( x + y + z ) = 72 x + y + z = 9 answer : b
Answer: b
Python program:
a = 21 + 51 
b = 1 + 7 
c = a / b
Problem: mahesh can do a piece of work in 60 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 30
Rationale: "work done by mahesh in 60 days = 20 * 1 / 60 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 2 / 3 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 3 / 2 = 45 days answer is a"
Answer: a
Python program:
a = 1 / 60
b = 20 * a
c = 1 - b
d = c / 30
e = 1 / d
Problem: a land owner needs to fence his semicircular land leaving an opening of length of 3 m for access . the radius of the semicircular plot is 7 m . how long would be the fence in meters ?
Options: a ) 22 , b ) 33 , c ) 36 , d ) 44 , e ) 51
Rationale: perimeter of the semicircle = ï € xd / 2 + d = ï € x 7 + 14 = 22 + 14 = 36 m length of the fence = 36 - 3 = 33 m answer : b
Answer: b
Python program:
a = 2 + 10 
b = a + 10 
c = b / 7
d = 7 * c
e = 2 * 7
f = d + e 
g = f - 3
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has travelled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 222 km , b ) 333 km , c ) 555 km , d ) 444 km , e ) 666 km
Rationale: d 444 km 1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444
Answer: d
Python program:
a = 21 - 16
b = 60 / a
c = b * 16
d = 21 - 16
e = 60 / d
f = e * 21
g = c + f
Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 10000 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 10000 n = 100 satisfies this . d"
Answer: d
Python program:
a = 1 / 10000
b = 1000 * a
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × q , what is the value of q ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × q = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x q = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x q = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x q q = 7 ^ 2 = 49 answer d"
Answer: d
Python program:
a = 105 ** 3
b = 21 * 25
c = b * 45
d = a / c
Problem: what number should replace the question mark ? 5 , 24 , 11 , 20 , 17 , 16 , - - - ?
Options: a ) 20 , b ) 23 , c ) 22 , d ) 21 , e ) 26
Rationale: "answer : b 5 , 24 , 11 , 20 , 17 , 16 , 23 ? there are two alternate sequences : + 6 and - 4 ."
Answer: b
Python program:
a = 5 + 5 
b = a + 5 
c = b + 5
Problem: the average ( arithmetic mean ) of 4 different integers is 72 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 21 , d ) 30 , e ) 33
Rationale: total of integers = 72 * 4 = 288 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 288 - ( 90 + 89 + 88 ) = 288 - 267 = 21 answer : c
Answer: c
Python program:
a = 72 * 4
b = a - 90
c = 90 - 1
d = b - c
e = 90 - 2
f = d - e
Problem: stacy has a 66 page history paper due in 6 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 11 , d ) 8.5 , e ) 6
Rationale: 66 / 6 = 11 answer : c
Answer: c
Python program:
a = 66 / 6
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent w ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . w = [ ( 2 - 1 ) / 1 ] * 100 % = 100 %
Answer: c
Python program:
a = 100 - 80
b = a - 10
c = 10 / b
d = c * 100
Problem: diana took out a charge account at the general store and agreed to pay 7 % simple annual interest . if she charges $ 75 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 79.25 , b ) $ 79.50 , c ) $ 79.75 , d ) $ 80.00 , e ) $ 80.25
Rationale: 1.07 * $ 75 = $ 80.25 the answer is e .
Answer: e
Python program:
a = 7 / 100
b = a * 75
c = 75 + b
Problem: a rower whose speed is 9 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "time upstream = d / 6 time downstream = d / 12 total time = d / 6 + d / 12 = d / 4 average speed = 2 d / ( d / 4 ) = 8 km / hr the answer is b ."
Answer: b
Python program:
a = 9 - 0
b = 9 + 3 
c = a + b 
d = c / 2
Problem: a man completes of a job in 10 days . at this rate , how many more days will it takes him to finish the job ?
Options: a ) 6 , b ) 12 , c ) 7 , d ) 15 , e ) 5
Rationale: work done = 5 / 8 balance work = ( 1 - 5 / 8 ) = 3 / 8 let the required number of days be x . then , ( 5 / 8 ) : ( 3 / 8 ) = : : 10 : x ( 5 / 8 ) * x = ( 3 / 8 ) * 10 x = ( 3 / 8 ) * 10 * ( 8 / 5 ) x = 6 . answer is a .
Answer: a
Python program:
a = 2 + 3 
b = 2 * 4
c = a / b
d = 1 - c
e = 10 * d
f = 2 + 3 
g = 2 * 4
h = f / g
i = e / h
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 74 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 56 , d ) 208 , e ) 256
Rationale: "sophomores = 26 % juniors = 22 % seniors = 160 / 800 = 20 % total : 68 % 1 - 68 % = 32 % ( freshmen ) 0,32 * 800 - 0,26 * 800 = 256 - 208 = 48 . answer choice b"
Answer: b
Python program:
a = 160 / 800
b = a * 100
c = 100 - b
d = c - 22
e = 100 - 74
f = d - e
g = f * 800
h = g / 100
i = 100 - 74
j = i * 800
k = j / 100
l = h - k
Problem: a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
Rationale: "60 % = 180 marks 1 % = 3 marks 100 % = 300 marks the answer is b ."
Answer: b
Python program:
a = 80 + 100 
b = 60 / 100
c = a / b
Problem: a football player scores 2 goals in his fifth match thus increasing his average goals score by 0.1 . the total number of goals in his 5 matches would be
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer c = 8 goals if . . . . total goals = 8 goals 5 th game = 2 goals 1 st 4 games = 6 goals avg . for 1 st 4 games = 6 / 4 = 1.5 goal / game avg . for all 5 games = 8 / 5 = 1.6 goals / game this is an exact match for what we ' re told in the prompt , so answer c must be the answer ."
Answer: c
Python program:
a = 4 * 2
b = 4 * 5
c = b * 0
d = a - c
e = d + 2