euclaise/mathqa_programs huggingface dataset:
Problem: an object thrown directly upward is at a height of h feet after t seconds , where h = - 15 ( t - 3 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 90 , b ) 98 , c ) 106 , d ) 120 , e ) 136
Rationale: we see that h will be a maximum h = 150 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 15 ( 5 - 3 ) ^ 2 + 150 = - 15 ( 4 ) + 150 = 90 the answer is a .
Answer: a
Python program:
a = negate * (
b = 3 + 2 
c = b - 3
d = c ** 2
e = a + d
Problem: the average of 6 observations is 13 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: let seventh observation = x . then , according to the question we have = > ( 78 + x ) / 7 = 12 = > x = 6 . hence , the seventh observation is 6 . answer : d
Answer: d
Python program:
a = 13 - 1
b = 6 + 1 
c = a * b
d = 13 * 6
e = c - d
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 4 ) and ( 9 , 4 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 4 , b ) 2 , c ) 1 / 4 , d ) 2 / 5 , e ) 5 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 2 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 2 ) is 2 / 5 . the answer is d ."
Answer: d
Python program:
a = 9 - 1
b = a + 4 
c = b / 4
d = 1 / c
Problem: a test has 100 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 100 . thus 5 c < = 260 and so c < = 52 . then 40 < = c < = 52 and c can have 13 possible values . the answer is e ."
Answer: e
Python program:
a = 100 - 40
b = a / 5
c = b + 1 
d = c + 1
Problem: a women in her conversation said ` ` if u reverse my own age , in figures represent my husbands age . he is of course senior to me and difference between our age is one 0 ne - eleventh of their sum . what is the woman ' s and her husbands age ?
Options: a ) 4554 , b ) 4657 , c ) 8457 , d ) 3458 , e ) 5254
Rationale: let man , s age be xy the woman ' s age is yx then 10 x + y - 10 y - x = 1 / 11 ( 10 x + y + 10 y + x ) 9 x - 9 y = x + y 8 x = 10 y x / y = 10 / 8 = 5 / 4 so xy = 54 and yx = 45 answer : a
Answer: a
Python program:
a = 1000 * 1
b = a * 4
c = 1000 * 1
d = c / 2
e = b + d 
f = 4 + 1 
g = f * 10
h = e + g
Problem: if 4 men working 10 hours a day earn rs . 600 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 320 , c ) rs 810 , d ) rs 680 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 600 : x hence 4 * 10 * x = 9 * 6 * 600 or x = 9 * 6 * 600 / 4 * 10 = 810 answer : c"
Answer: c
Python program:
a = 9 * 6
b = 4 * 10
c = a / b
d = c * 600
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability q that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 q = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"
Answer: c
Python program:
a = 5 / 6
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 20.25 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 45 , d ) 47 , e ) 97
Rationale: "money collected = ( 20.25 x 100 ) paise = 2025 paise numbers of members = 2025 squareroot = 45 answer c"
Answer: c
Python program:
a = 20 * 25
b = math.sqrt(a)
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 12 sec . what is the length of the platform ?
Options: a ) 187 m , b ) 350 m , c ) 267 m , d ) 287 m , e ) 675 m
Rationale: "speed = 300 / 12 = 25 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 = > x = 675 m . answer : e"
Answer: e
Python program:
a = speed * (
b = a - 39
Problem: mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8510 / - . find out the amount that he borrowed .
Options: a ) s . 5266 , b ) s . 5269 , c ) s . 5228 , d ) s . 5218 , e ) s . 5526
Rationale: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8510 = p + ( 54 p / 100 ) 8510 = ( 100 p + 54 p ) / 100 8510 = 154 p / 100 p = ( 8510 * 100 ) / 154 = rs . 5525.974 answer : e"
Answer: e
Python program:
a = 6 * 9
b = a / 100
c = 1 + b 
d = 8510 / c
Problem: if the sum of two numbers is 24 and the sum of their squares is 400 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 24 and x ^ 2 + y ^ 2 = 400 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 24 ^ 2 = 400 + 2 xy so xy = 176 / 2 = 88 answer : d"
Answer: d
Python program:
a = 24 ** 2
b = a - 400
c = b / 2
Problem: if the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 9 , e ) 18
Rationale: "let length of rectangle = l 6 ^ 2 = l * 4 = > l = 36 / 4 = 9 answer d"
Answer: d
Python program:
a = 6 ** 2
b = a / 4
Problem: how many integer values t are there for x such that 1 < 3 x + 5 < 17 ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: 1 < 3 x + 5 < 17 = > - 4 < 3 x < 12 = > - 4 / 3 < x < 4 x can take integer values t - 10 , 1 , 2 , 3 answer d
Answer: d
Python program:
a = 17 - 5
b = a / 5
c = 1 - 5
d = c / 5
e = b - d
f = math.floor(e)
g = f + 2
Problem: the sum of 3 consecutive multiples of 3 is 117 . what is the largest number ?
Options: a ) 45 , b ) 48 , c ) 51 , d ) 42 , e ) 54
Rationale: let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 117 9 x = 108 x = 12 largest number = 3 x + 6 = 42 answer : d
Answer: d
Python program:
a = 117 / 3
b = a + 3
Problem: if the cost price of 81 chocolates is equal to the selling price of 45 chocolates , the gain percent is :
Options: a ) 80 % , b ) 85 % , c ) 82 % , d ) 70 % , e ) 75 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 45 chocolates = rs . 45 ; s . p . of 45 chocolates = rs . 81 . . ' . gain % = 36 * 100 / 45 = 80 % answer : a"
Answer: a
Python program:
a = 81 - 45
b = 45 / a
c = 100 / b
Problem: company z has 50 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 50 . now , plug options for x . only a and e give an integer value for y . but only for e x > y as needed . answer : e ."
Answer: e
Python program:
a = 4 + 3 
b = 50 / a
c = math.floor(b)
d = c + 1 
e = 4 + d
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 18 % ?
Options: a ) 37.5 % , b ) 48 % , c ) 50.5 % , d ) 28.125 % , e ) 56 %
Rationale: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 82 gain % = 18 / 64 * 100 = 28.125 % . answer : option d"
Answer: d
Python program:
a = 100 - 18
b = a / 64
c = b - 1
d = c * 100
Problem: the average age of 39 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 51 years , d ) 54 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 40 * 15 - 39 * 14 ) years = 54 years . answer : d"
Answer: d
Python program:
a = 39 + 1
Problem: how many times are the hands of a clock at right angle in 2 weeks ?
Options: a ) 616 , b ) 611 , c ) 661 , d ) 116 , e ) 666
Rationale: "in 1 day , they are at right angles 44 times . in 14 days , they are at right angles 616 times . answer : option a"
Answer: a
Python program:
a = 12 * 2
b = a * 2
c = 12 * 4
d = c - 4
e = b * d
f = 12 * 2
g = e / f
Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be maths teachers ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 24 , e ) 1 / 12
Rationale: probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( e )
Answer: e
Python program:
a = 3 + 4 
b = a + 2 
c = 3 / b
d = 3 + 4 
e = d + 2 
f = e - 1
g = 2 / f
h = c * g
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 75 questions and secures 125 marks , the number of questions he attempts correctly , is :
Options: a ) 38 , b ) 40 , c ) 26 , d ) 25 , e ) 11
Rationale: "explanation : let the number of correct answers be x . then numbers of incorrect answers will be 75 – x we get 4 x – ( 75 – x ) × 1 = 125 on solving the equation we get x = 40 answer : b"
Answer: b
Python program:
a = 125 + 75 
b = 4 + 1 
c = a / b
Problem: the value of x . 320 ã · 2 ã · 3 = x
Options: a ) 53.33 , b ) 46.33 , c ) 15.36 , d ) 15.45 , e ) 15.48
Rationale: 320 ã · 2 ã · 3 = 320 ã — 1 / 2 ã — 1 / 3 = 160 / 3 = 53.33 correct answer : a
Answer: a
Python program:
a = 1 + 4 
b = a * 10
c = 3 + b 
d = 3 * 10
e = d + 3 
f = e / 100
g = c + f
Problem: v is the volume of a cylinder ; the radius of the cylinder is 3.5 . the height of the cylinder is 650 % more than the radius . which of the following is true ?
Options: a ) 100 < v < 300
b ) 300 < v < 500
c ) 500 < v < 700
d ) 700 < v < 900
e ) 900 < v < 1100
Rationale: as we see the answers are in form of range we can use approximation volume of cylinder is π r ^ 2 h given π = 22 / 7 and r = 3.5 so r ^ 2 ~ 12 and h = 6.5 * 3.5 ~ 23 so 22 / 7 * 12 * 23 ~ 868 so answer should be d . 700 < v < 900 answer : d
Answer: d
Python program:
a = 3 ** 5
b = math.pi * a
c = 650 / 100
d = 3 * 5
e = b * d
Problem: two employees x and y are paid a total of rs . 580 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 263 , b ) s . 283 , c ) s . 293 , d ) s . 300 , e ) s . 383
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 580 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 580 ⇒ y [ 12 / 10 + 1 ] = 580 ⇒ 22 y / 10 = 580 ⇒ 22 y = 5800 ⇒ y = 5800 / 22 = rs . 263 a )"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = 580 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: two trains of length 120 m and 300 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 ) 21 sec , b ) 32 sec , c ) 82 sec , d ) 20 sec , e ) 89 sec
Rationale: relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 300 = 420 m . the time required = d / s = 420 / 20 = 21 sec . answer : a
Answer: a
Python program:
a = 120 + 300 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: two trains of length 100 m and 220 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 ) 18 sec , b ) 70 sec , c ) 21 sec , d ) 20 sec , e ) 16 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 220 = 320 m . the time required = d / s = 320 / 20 = 16 sec . answer : e"
Answer: e
Python program:
a = 100 + 220 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: what positive number , when squared , is equal to the cube of the positive square root of 18 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 9
Rationale: "let the positive number be x x ^ 2 = ( ( 18 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 81 = > x = 9 answer e"
Answer: e
Python program:
a = 1 / 2
b = 18 ** a
c = b ** 3
d = math.sqrt(c)
Problem: a train 360 m long is running at a speed of 54 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 11 sec , c ) 88 sec , d ) 33.33 sec , e ) 10 sec
Rationale: "speed = 54 * 5 / 18 = 15 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 15 = 33.33 sec answer : d"
Answer: d
Python program:
a = 54 - 140
b = a * const_0_2778
c = 360 / b
Problem: 210 college students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: 120 = 60 ( mac ) + x ( window ) + 20 ( both ) = > x = 40 answer : b
Answer: b
Python program:
a = 210 - 90
b = a - 60
c = 210 - 90
d = c - 60
e = d / 3
f = b - e
Problem: if a truck is traveling at a constant rate of 36 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 18 , b ) 24 , c ) 60 , d ) 36 , e ) 48
Rationale: "speed = 36 km / hr = > 36,000 m / hr in one minute = > 36000 / 60 = 600 meters in one sec = > 600 / 60 = 10 meters time = total distance need to be covered / avg . speed = > 600 / 10 = 60 and hence the answer : c"
Answer: c
Python program:
a = 600 / 1000
b = a / 36
c = b * 3600
Problem: solve this 6 + 7 = 12 8 + 9 = 16 5 + 6 = 10 7 + 8 = 14 then , 3 + 3 = ? ?
Options: a ) 11 , b ) 12 , c ) 5 , d ) 14 , e ) 18
Rationale: 5 answer : c
Answer: c
Python program:
a = 12 - 6
b = 7 - a
c = 3 - b
d = 3 + c
Problem: | x + 3 | – | 4 - x | = | 8 + x | how many solutions zwill this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "z = | x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Python program:
a = 4 + 3 
b = a * 2
c = b / 8
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 1.26 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 42 , e ) 84
Rationale: the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 1.26 - - > 15 p - 13.5 p = 126 - - > p = 84 . answer : e .
Answer: e
Python program:
a = 15 / 100
b = 10 / 100
c = 1 - b
d = 15 / 100
e = c * d
f = a - e
g = 1 / 26
Problem: if 3 / p = 8 & 3 / q = 18 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 3 / 8 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 3 / 8 ) - ( 1 / 6 ) = 5 / 24 answer : a"
Answer: a
Python program:
a = 3 / 8
b = 3 / 18
c = a - b
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 147 , d ) 165 , e ) 315
Rationale: "ans : 147 7 c 1 * 7 c 2 answer c )"
Answer: c
Python program:
a = 7 * 3
b = a * 7
Problem: mohit sold an article for $ 18000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 25000 , c ) 15000 , d ) 18000 , e ) 17000
Rationale: "c 15000 let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 18000 - 10 / 100 ( 18000 ) = 18000 - 1800 = $ 16200 = > 1.08 x = 16200 = > x = 15000"
Answer: c
Python program:
a = 18000 * 10
b = a / 100
c = 18000 - b
d = 100 + 8 
e = c / d
f = e * 100
Problem: a is twice as fast as b . if b alone can do a piece of work in 30 days , in what time can a and b together complete the work ?
Options: a ) 13 , b ) 10 , c ) 16 , d ) 50 , e ) 23
Rationale: "option b explanation : a can do the work in 30 / 2 i . e . , 15 days . a and b ' s one day ' s work = 1 / 15 + 1 / 30 = ( 2 + 1 ) / 30 = 1 / 10 so a and b together can do the work in 10 days ."
Answer: b
Python program:
a = 1 / 30
b = 1 / 30
c = b * 2
d = a + c 
e = 1/(d)
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability c that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability c = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Python program:
a = 3 * 5
b = 3 + 5 
c = 5 + 2 
d = b * c
e = d / 2
f = a / e
Problem: the total cost of a vacation was divided among 4 people . if the total cost of the vacation had been divided equally among 5 people , the cost per person would have been $ 50 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 400 , d ) $ 500 , e ) $ 1000
Rationale: "c for cost . p price per person . c = 4 * p c = 5 * p - 250 substituting the value of p from the first equation onto the second we get p = 250 . plugging in the value of p in the first equation , we get c = 1000 . which leads us to answer choice e"
Answer: e
Python program:
a = 5 * 4
b = 5 - 4
c = 50 / b
d = a * c
Problem: by mixing two brands of coffee and selling the mixture at the rate of $ 177 per kg . a shopkeeper makes a profit of 18 % . if to every 2 kg of one brand costing $ 200 per kg , 3 kg of the other brand is added , then how much per kg does the other brand cost ?
Options: a ) $ 110.66 , b ) $ 132.66 , c ) $ 116.66 , d ) $ 126.66 , e ) $ 118.66
Rationale: c $ 116.66 let the cost of the brand be $ x per kg . c . p . of 5 kg = ( 2 * 200 + 3 * x ) = $ ( 400 + 3 x ) s . p of 5 kg = $ ( 5 * 177 ) = $ 885 [ 885 - ( 400 + 3 x ) ] / ( 400 + 3 x ) * 100 = 18 24250 - 150 x = 3600 + 27 x 177 x = 20650 = > x = 116 2 / 3 so , cost of the other brand = $ 116.66 .
Answer: c
Python program:
a = 2 + 3 
b = a * 177
c = 2 * 200
d = 18 / 100
e = 1 + d 
f = c * e
g = b - f
h = 18 / 100
i = 1 + h 
j = 3 * i
k = g / j
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.75 ?
Options: a ) 1280 , b ) 1145 , c ) 1040 , d ) 950 , e ) 260
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.75 - $ 0.65 = $ 1.10 the charge for the next 1000 grams is $ 1.00 which leaves a charge of $ 0.10 the weight is somewhere between 1250 and 1350 . the answer is a ."
Answer: a
Python program:
a = 65 / 100
b = 1 - 75
c = 10 / 100
d = c / 100
e = d * 250
f = b + e 
g = 10 / 100
h = g / 100
i = f / h
Problem: johnny makes $ 6.75 per hour at his work . if he works 10 hours , how much money will he earn ?
Options: a ) $ 67.50 , b ) $ 54 , c ) $ 28.50 , d ) $ 12.50 , e ) $ 9.60
Rationale: 6.75 * 10 = 67.50 . answer is a .
Answer: a
Python program:
a = 6 * 75
Problem: machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 6 hours and machine y produces k bottles in 3 hours . how many hours does it take machines x and y , working simultaneously , to produce 12 k bottles ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 18 , e ) 24
Rationale: "x rate = k / 6 y rate = k / 3 k / 6 + k / 3 = 12 k / t solving t = 24 answer e"
Answer: e
Python program:
a = 6 + 3 
b = a / 3
c = 12 * b
d = c / 3
Problem: 34 , 45 , 56 , 67,78 , _ ?
Options: a ) 33 , b ) 82 , c ) 99 , d ) 89 , e ) 27
Rationale: answer : d
Answer: d
Python program:
a = negate - (
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 4 days . b can do the work alone in ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 24 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 4 6 / x = 1 / 4 = > x = 24 so , b takes 12 hours to finish the work . answer : d"
Answer: d
Python program:
a = 1 + 2 
b = a + 3 
c = b * 4