euclaise/mathqa_programs huggingface dataset:
Problem: a caterer ordered 200 ice - cream bars and 200 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.40 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: "let price of a sundae = s price of ice cream bar = . 4 $ 200 * . 4 + 200 * s = 200 = > 200 * s = 200 = > s = 0.6 answer a"
Answer: a
Python program:
a = 200 * 0
b = 200 - 0
c = b / 200
Problem: what is the least value of k . so that 123 k 578 is divisible by 11 .
Options: a ) 8 , b ) 7 , c ) 5 , d ) 6 , e ) 4
Rationale: explanation : the difference of the sum of the digits at odd place and the sum of the digits at even place of the number , is either 0 or a number divisible by 11 . ( 1 + 3 + 5 + 8 ) - ( 2 + k + 7 ) = 17 - 9 - k = 8 - k therefore if k = 8 , then the value become zero . k = 8 is the least value so that 123 k 578 is divisible by 11 . answer : option a
Answer: a
Python program:
a = math.lcm(123, 578)
b = a / 578
c = b / 4
d = c / 4
Problem: local kennel has cats and dogs in the ratio of 3 : 4 . if there are 8 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 28 , b ) 26 , c ) 24 , d ) 32 , e ) 30
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 3 : 4 or cats 3 dogs 4 we can write number of cats as 3 x and number of dogs as 4 x and we know that 4 x - 3 x = 8 ( therefore x = 8 ) then # of dogs = 4 x 8 = 32 answer is d"
Answer: d
Python program:
a = 8 * 4
Problem: the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 142 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 145 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 142 . so , total number of ducks and frogs in the pond , = 2 * 142 = 284 . therefore , number of frogs , = ( 284 * 39 ) / 76 = 145 . answer : option d"
Answer: d
Python program:
a = 37 + 39 
b = a + 2 
c = b / 2
d = 142 / c
e = 39 * d
Problem: john had a stock of 1400 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 71.3 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1400 - n = 1400 - 402 = 998 percentage books not sold / total number of books = 998 / 1400 = 0.713 = 71.3 % correct answer b"
Answer: b
Python program:
a = 75 + 50 
b = 64 + 78 
c = a + b 
d = c + 135 
e = 1400 - d
f = e / 1400
g = f * 100
Problem: two numbers a and b are such that the sum of 8 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 4 : 3 , d ) 1 : 3 , e ) 3 : 2
Rationale: "explanation : 8 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 8 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 8 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 24 a + 12 b = 12 a + 16 b ⇒ 12 a = 4 b ⇒ ab = 4 / 12 ⇒ a : b = 1 : 3 answer : option d"
Answer: d
Python program:
a = 8 / 100
b = a * 4
c = b / 3
d = 4 / 100
e = c - d
f = 8 / 100
g = 6 / 100
h = g * 4
i = h / 3
j = f - i
k = e / j
Problem: the compound ratio of 5 : 6 , 3 : 4 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 1 : 87 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 6 * 3 / 4 * 4 / 5 = 1 / 2 1 : 2 answer : e"
Answer: e
Python program:
a = 5 * 3
b = 6 * 4
c = a / b
d = 3 * 4
e = 4 * 5
f = d / e
g = c / f
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.1 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 6 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.1 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.1 ) < = > k = 0.7 / 0.6 = 7 / 6 . required ratio = 7 / 6 : 1 = 7 : 6 . answer : a
Answer: a
Python program:
a = 15 - 8
b = 16 - 4
c = a / b
Problem: a man purchased 4 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 4 * 100 + 5 * 150 = 1150 1500 – 1150 = 350 b"
Answer: b
Python program:
a = 10 * 150
b = 4 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: of 70 players on a football team , 31 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 57 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 31 rest = 70 - 31 = 39 left handed = 39 / 3 = 13 right handed = 26 if all thrower are right handed then total right handed is 31 + 26 = 57 so a . 57 is the right answer"
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 31
d = b * c
e = d + 31
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars 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 53 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 ) 54
Rationale: "amount earned by james = 40 * x + 13 * 2 x = 66 x therefore , amount earned by harry = 66 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 66 x ] ] so x * ( 1.5 y - 45 + 30 ) = 66 x or x * ( 1.5 y - 15 ) = 66 x so 1.5 y - 15 = 66 so 1.5 y = 81 so y = 54 answer is e"
Answer: e
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 9 , what is the measure of side xy ?
Options: a ) 4 , b ) 4 √ 2 , c ) 8 , d ) 6 , e ) can not be determined from the information provided
Rationale: "ans d . . 6 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 9 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 6"
Answer: d
Python program:
a = math.sqrt(9)
b = math.sqrt(2)
c = a * b
d = c ** 2
e = math.sqrt(9)
f = math.sqrt(2)
g = e * f
h = g ** 2
i = d + h 
j = math.sqrt(i)
Problem: yesterday ' s closing prices of 1980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer .
Answer: b
Python program:
a = 100 + 20 
b = a / 100
c = b + 1 
d = 1980 / c
e = 1980 - d
Problem: a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is ?
Options: a ) 2267 , b ) 1162 , c ) 2276 , d ) 1250 , e ) 1262
Rationale: "explanation : speed = ( 5 x 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 x 15 x 60 ) m = 1250 m . answer : d"
Answer: d
Python program:
a = 5 * 1000
b = a / const_60
c = b * 15
Problem: a 75 m long train is running at 54 km / hr . in how much time will it cross an electric pole ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: speed of the train = ( 54 * 5 / 18 ) m / sec = 15 m / sec . length of the train = ( speed x time ) time = ( length of the train / speed ) = ( 75 / 15 ) = 5 sec answer : a
Answer: a
Python program:
a = 54 * 1000
b = a / 3600
c = 75 / b
Problem: a reduction of 24 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.8 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 3.16
Rationale: "100 * ( 24 / 100 ) = 24 - - - 10 ? - - - 1 = > rs . 2.4 100 - - - 76 ? - - - 2.4 = > rs . 3.16 answer : e"
Answer: e
Python program:
a = 24 / 100
b = a * 100
c = b / 10
d = 24 / 100
e = d * 100
f = c / e
g = f * 100
Problem: what is the least number that should be added to 1077 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1077 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ."
Answer: d
Python program:
a = 1077 / 23
b = math.floor(a)
c = 1 + b 
d = 1077 / 23
e = c - d
f = e * 23
Problem: how many pieces of 0.63 meteres can be cut from a rod 32.5 meteres long
Options: a ) 30 , b ) 40 , c ) 51 , d ) 60 , e ) 70
Rationale: "explanation : we need so simple divide 32.5 / 0.63 , = ( 3250 / 63 ) = 51 option c"
Answer: c
Python program:
a = 32 / 5
Problem: how many terminating zeroes q does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Python program:
a = 4 + 1 
b = 200 / a
c = 4 + 1 
d = 4 + 1 
e = c * d
f = 200 / e
g = b + f
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 17 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 17 w 19 + 9 x = 17 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c"
Answer: c
Python program:
a = 17 - 9
b = 19 - 17
c = a / b
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 2 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 218 , c ) 400 , d ) 388 , e ) 211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 2 = > x = 400 answer : c ) rs 400"
Answer: c
Python program:
a = 5 * 4
b = a * 10
c = b * 2
Problem: a city with a population of 218,000 is to be divided into 10 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 19,920 , b ) 19,940 , c ) 19,960 , d ) 19,980 , e ) 20,000
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 218,000 = p + 9 ( 1.1 ) p 10.9 p = 218,000 p = 20,000 the answer is e ."
Answer: e
Python program:
a = 1000 * 100
b = 3600 - 100
c = b - 1000
d = a - c
e = d / 1000
f = 10 / 100
g = 1 + f 
h = 10 - 1
i = g * h
j = i + 1 
k = e / j
Problem: two trains of equal are running on parallel lines in the same direction at 47 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 50 , b ) 88 , c ) 66 , d ) 55 , e ) 22
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 47 - 36 = 11 km / hr . = 11 * 5 / 18 = 55 / 18 m / sec . 2 x / 36 = 55 / 18 = > x = 55 . answer : d"
Answer: d
Python program:
a = 47 - 36
b = a * 1000
c = b / 3600
d = 36 * c
e = d / 2
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 30 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 450 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: pastry is divided in 30 customers equally . so , total number of pastry must be a multiple of 30 only option a satisfies the condition , and hence is the answer
Answer: a
Python program:
a = 49 * 6
b = 49 - 30
c = a / b
d = c * 30
Problem: if x and y are positive integers and x = 5 y + 7 , what is the remainder when x is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that x and y are positive integers and x = 5 y + 7 . we ' re asked for the remainder when x is divided by 5 . if . . . . y = 1 x = 12 12 / 5 = 2 remainder 2 final answer : c"
Answer: c
Python program:
a = 7 + 1 
b = a / 5
Problem: on a certain road 14 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 17.5 % , d ) 22 % , e ) 30 %
Rationale: "answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 14 % + 0,2 x id est x = 17,5 %"
Answer: c
Python program:
a = 14 / 100
b = 20 / 100
c = a * b
d = c * 100
e = 100 / d
Problem: the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
Options: a ) 90 , b ) 93 , c ) 56 , d ) 80.5 , e ) 78
Rationale: "total increase in weight = 8 × 6 = 48 if x is the weight of the new person , total increase in weight = x − 45 = > 48 = x - 45 = > x = 48 + 45 = 93 answer : b"
Answer: b
Python program:
a = 8 * 6
b = a + 45
Problem: how many digits 2 ^ 300 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 91 , e ) 101
Rationale: 2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 90 therefore 91 digits would be my best guess d
Answer: d
Python program:
a = math.log(2)
b = math.log(10)
c = a / b
d = c * 300
e = 1 + d 
f = math.floor(e)
Problem: after distributing the sweets equally among 25 children , 8 sweets remain . had the number of children been 28 , 22 sweets would have been left after equal distribution . what was the total number of sweets ?
Options: a ) 328 , b ) 348 , c ) 358 , d ) 362 , e ) data inadequate
Rationale: explanation : let the total number of sweets be ( 25 x + 8 ) . then , ( 25 x + 8 ) - 22 is divisible by 28 ( 25 x - 14 ) is divisible by 28 28 x - ( 3 x + 14 ) is divisible by 28 ( 3 x + 14 ) is divisible by 28 x = 14 . therefore total number of sweets = ( 25 x 14 + 8 ) = 358 . answer : c
Answer: c
Python program:
a = 25 - 1
b = a / 2
c = 28 * b
d = c + 22
Problem: a batsman scored 150 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 60 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 150 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 150 - 60 = 90 required % = ( 90 / 150 ) × 100 = 60 % answer : option b"
Answer: b
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 150 - c
e = d / 150
f = e * 100
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 120 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 3000 , d ) 1000 , e ) 2871
Rationale: ( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 120 x = 3000 answer : c
Answer: c
Python program:
a = 6 * 2500
b = a / 100
c = 120 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.000168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 7 digits after decimal total no . of decimals = 9 req . no . of digits = ( n - 1 ) = ( 9 - 1 ) = 8 answer : e
Answer: e
Python program:
a = 52 / 416
Problem: the average age of a class of 23 students is 22 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 46 , d ) 42 , e ) 49
Rationale: "total age of all students = 23 ã — 22 total age of all students + age of the teacher = 24 ã — 23 age of the teacher = 24 ã — 23 â ˆ ’ 23 ã — 22 = 23 ( 24 â ˆ ’ 22 ) = 23 ã — 2 = 46 answer is c ."
Answer: c
Python program:
a = 23 + 1 
b = 22 + 1 
c = a * b
d = 23 * 22
e = c - d
Problem: x is a positive integer less than 600 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 600 n = 25.42 or n = 25 answer : - e"
Answer: e
Python program:
a = reminder * (
b = a + 3 
c = b - reminder
Problem: if the radius of a circle is increased by 30 % then the area is increased by :
Options: a ) 44 % , b ) 69 % , c ) 144 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 130 / 100 r then area = pi * ( 130 r / 100 ) 2 area = 169 r / 100 that is area increases from 100 to 169 = increase in area = 69 % answer : b"
Answer: b
Python program:
a = 100 / 100
b = 100 / 100
c = 30 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
Problem: the length of a rectangle hall is 5 m more than its breadth . the area of the hall is 750 m 2 . the length of the hall is :
Options: a ) 15 m
b ) 22.5 m
c ) 25 m
d ) 30 m
e ) none of these
Rationale: solution let breadth = x metres . then , length = ( x + 5 ) metres . then x ( x + 5 ) = 750 ⇔ x 2 + 5 x − 750 = 0 ⇔ ( x + 30 ) ( x + 25 ) = 0 ⇔ x = 25 . ∴ length = ( x + 5 ) = 30 m . answer d
Answer: d
Python program:
a = 750 / 5
b = a / 5
Problem: what is the perimeter of a square with area p ^ 2 / 16 ?
Options: a ) 3 p / 4
b ) 3 p ^ 2 / 4
c ) p
d ) 3 p ^ 2
e ) 4 p / 3
Rationale: area of square , ( side ) ^ 2 = ( p / 4 ) ^ 2 therefore side of the square = p / 4 perimeter of square = 4 * side = 4 * ( p / 4 ) = p answer is c .
Answer: c
Python program:
a = 2 / 16
b = math.pi ** a
c = math.sqrt(b)
d = c * 4
Problem: 65 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64
b ) 128
c ) 151
d ) 216
e ) 256
Rationale: 65 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 65 = 151 hence , c is the answer .
Answer: c
Python program:
a = cube_edge_by_volume + ( 
b = volume_cube - (
Problem: how long does a train 100 m long traveling at 60 kmph takes to cross another train of 170 m in length has a speed of 40 kmph ?
Options: a ) 1.42 sec , b ) 16.8 sec , c ) 5 sec , d ) 1.68 sec , e ) 3.6 sec
Rationale: "d = 100 m s = ( 60 + 40 ) * 5 / 18 = 250 / 3 t = 100 * 9 / 250 = 3.6 sec answer : e"
Answer: e
Python program:
a = 100 + 170 
b = 60 * const_0_2778
c = a / b
Problem: in the coordinate plane , line a has a slope of - 1 and an x - intercept of 2 . line b has a slope of 5 and a y - intercept of - 10 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation of line a is y = - x + 2 the equation of line b is y = 5 x - 10 5 x - 10 = - x + 2 x = 2 y = 0 the point of intersection is ( 2,0 ) and then a + b = 2 . the answer is c .
Answer: c
Python program:
a = 10 - 5
b = a - 1
c = b / 2
Problem: if 9 is added to thrice a number and this sum is multiplied by 6 , the result is the same as if the number is multiplied by 7 and 10 is added to the product . what is the number ?
Options: a ) - 7 , b ) - 8 , c ) - 9 , d ) - 10 , e ) - 11
Rationale: let the number be x ; 6 ( 9 + 3 x ) = 7 x + 10 ; x = - 11 answer : e
Answer: e
Python program:
a = 9 * 6
b = a - 10
c = 3 * 6
d = 7 - c
e = b / d
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 20 + 29 + 8 ) = 5 % basic astrophysics . 5 % of 360 ° is 18 ° . answer : c ."
Answer: c
Python program:
a = 14 + 24 
b = a + 20 
c = b + 29 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Python program:
a = 5 ** 2
b = 2 * 12
c = b * 4
d = a + c 
e = math.sqrt(d)
f = 5 + e 
g = 2 * 2
h = f / g
i = 5 ** 2
j = 2 * 12
k = j * 4
l = i + k 
m = math.sqrt(l)
n = 5 - m
o = 2 * 2
p = n / o
q = h - p
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is b ."
Answer: b
Python program:
a = 4 + 2 
b = a / 1
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 27 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 27 ) / 5 = ( 5 x + 40 ) / 5 = x + 8 median = x + 4 thus mean - median = x + 8 - ( x + 4 ) = 4 answer = d"
Answer: d
Python program:
a = 2 + 4 
b = a + 7 
c = b + 27 
d = 4 + 1 
e = c / d
f = e - 4