euclaise/mathqa_programs huggingface dataset:
Problem: if a * b * c = 130 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these
Rationale: "explanation : a ∗ b ∗ c / b ∗ c ∗ d = 130 / 65 = > a / d = 2 d ∗ e ∗ f / c ∗ d ∗ e = 250 / 1000 = > f / c = 14 a / d * f / c = 2 * 1 / 4 = 1 / 2 answer : a"
Answer: a
Python program:
a = 130 * 250
b = 1000 * 65
c = a / b
Problem: calculate the largest 5 digit number which is exactly divisible by 77 ?
Options: a ) 99111 , b ) 99946 , c ) 99869 , d ) 99792 , e ) 99654
Rationale: "largest 4 digit number is 99999 after doing 99999 ÷ 77 we get remainder 53 hence largest 5 digit number exactly divisible by 77 = 99999 - 53 = 99946 b"
Answer: b
Python program:
a = 100 + 2 
b = a * 77
Problem: working at a constant rate , p can finish a job in 4 hours . q , also working at a constant rate , can finish the same job in 20 hours . if they work together for 3 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 21 , e ) 24
Rationale: "each hour they complete 1 / 4 + 1 / 20 = 3 / 10 of the job . in 3 hours , they complete 3 ( 3 / 10 ) = 9 / 10 of the job . the time for p to finish is ( 1 / 10 ) / ( 1 / 4 ) = ( 2 / 5 ) hour = 24 minutes the answer is e ."
Answer: e
Python program:
a = 1/(4)
b = 1/(20)
c = a + b 
d = c * 3
e = 1 - d
f = 1/(4)
g = e / f
h = g * const_60
Problem: two stations p and q are 290 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10 am , b ) 12 am , c ) 10.30 am , d ) 12.30 pm , e ) 2 pm
Rationale: "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 290 = > 20 x + 25 ( x - 1 ) = 290 = > 45 x = 315 = > x = 7 means , they meet after 7 hours after 7 am , ie , they meet at 2 pm answer is e ."
Answer: e
Python program:
a = 290 + 25 
b = 20 + 25 
c = a / b
d = c + 7
Problem: free notebooks were distributed in a class among all the students . each student got notebooks which were 1 / 8 th of the number of student . if number of student been half , then each child would have received 16 notebooks in total . find the total number of books distributed among students ?
Options: a ) 430 , b ) 450 , c ) 460 , d ) 480 , e ) 512
Rationale: let suppose total number of students in class are x . then from the question we can conclude it that , x ∗ 18 x = x 2 ∗ 16 = > x = 64 total notebooks , = 18 x 2 = ( 18 ∗ 64 ∗ 64 ) = 512 e
Answer: e
Python program:
a = 1 / 2
b = a * 16
c = b * 8
d = c * 8
Problem: what is the least number to be subtracted from 990 to make it a perfect square ?
Options: a ) 100 , b ) 90 , c ) 30 , d ) 71 , e ) 80
Rationale: "the numbers less than 990 and are squares of certain number is 900 . the least number that should be subtracted from 990 to make it perfect square = 990 - 900 = 90 . answer : b"
Answer: b
Python program:
a = 3 * 2
b = 10 + a 
c = 100 * b
d = c - 990
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 36 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 1 / 3 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 36 = ( 2 / 3 ) * ( 2 / 3 ) therefore probability that the next one she draws is pink = 1 / 3 option ( d )"
Answer: d
Python program:
a = 16 / 36
b = math.sqrt(a)
c = 1 - b
Problem: if x is a sum of all even integers on the interval 13 . . . 65 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 13 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 64 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 64 ) / 2 * 26 = 39 * 26 . gcd of 26 and 39 * 26 is 26 . answer : c ."
Answer: c
Python program:
a = 13 - 10
b = a + 2 
c = 13 - 10
d = c + 2 
e = b * d
Problem: a child want to buy 5 new toys . if there are 15 toys that satisfy the child ' s criteria , in how many different ways can the child select the 5 new toys if the order of selection does n ' t matter .
Options: a ) 210 , b ) 1365 , c ) 3003 , d ) 5005 , e ) 3030
Rationale: the number of ways of choosing 5 toys out of 15 are counted by = 15 c 5 ways = 3003 answer : option c
Answer: c
Python program:
a = math.comb(15, 5)
Problem: two boys started running simultaneously around a circular track of length 4800 m from the same point at speeds of 60 km / hr and 100 km / hr . when will they meet for the first time any where on the track if they are moving in opposite directions ?
Options: a ) 105 , b ) 106 , c ) 107 , d ) 108 , e ) 109
Rationale: time taken to meet for the first time anywhere on the track = length of the track / relative speed = 4800 / ( 60 + 100 ) 5 / 18 = 4800 * 18 / 160 * 5 = 108 seconds . answer : d
Answer: d
Python program:
a = 60 * const_0_2778
b = 100 * const_0_2778
c = a + b 
d = 4800 / c
Problem: a contractor is engaged for 30 days on the condition that he receives rs . 25 for each dayhe works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many dayswas he absent ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 17
Rationale: "30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b"
Answer: b
Python program:
a = 30 * 7
b = a + 425 
c = 25 + 7 
d = b / c
e = 30 - d
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 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 28 years later ?
Options: a ) $ 160,000 , 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 $ 40,000 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 28 years , the investment will get doubled 28 / 14 = 2 times . so the amount invested will get doubled thrice . so , 40000 * 2 = 80000 80000 * 2 = 160000 hence , the answer is a ."
Answer: a
Python program:
a = 3600 / 10
Problem: in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each 100 m in length both trains running with a speed of 80 kmph ?
Options: a ) 4.5 sec , b ) 4.8 sec , c ) 4.2 sec , d ) 5.0 sec , e ) 5.2 sec
Rationale: d = 100 m + 100 m = 200 m * 1 / 1000 = 0.2 kms rs = 80 + 80 = 160 kmph t = ( 0.2 / 160 ) * 3600 = 4.5 sec answer : a
Answer: a
Python program:
a = 100 + 100 
b = 80 + 80 
c = b * const_0_2778
d = a / c
Problem: the profit earned by selling an article for 892 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1005 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: let the profit or loss be x and 892 – x = 448 + x or , x = 444 ⁄ 2 = 222 \ cost price of the article = 892 – x = 448 + x = 670 \ sp of the article = 670 × 150 ⁄ 100 = 1005 answer b
Answer: b
Python program:
a = 892 + 448 
b = a / 2
c = 50 / 100
d = 1 + c 
e = b * d
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 720 . find the sum ?
Options: a ) s . 7000 , b ) s . 9000 , c ) s . 14000 , d ) s . 12000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 720 = > 30 x / 100 - 24 x / 100 = 720 = > 6 x / 100 = 720 = > x = 12000 . answer : d"
Answer: d
Python program:
a = 15 - 12
b = a * 2
c = b / 100
d = 720 / c
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 4 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 45 % , b ) 13 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 4 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 4 or 45 * 18 - 45 * x + 36 * x = 400 or - 9 x = 400 - 45 * 18 or x = 410 / 9 = 45 % = 45 % a"
Answer: a
Python program:
a = 18 / 100
b = 18 / 100
c = 18 * 2
d = b * c
e = 4 - d
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: in a building there are 5 rooms . each having a equal area . the length of the room is 4 m and breadht is 5 m . the height of the rooms are 2 m . if 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room ?
Options: a ) 320
b ) 340
c ) 300
d ) 330
e ) 360
Rationale: explanation : area of the floor = 4 m x 5 m = 20 m 2 17 bricks are needed to make 1 m 2 area . so to make 20 m 2 no of bricks needed = 17 x 20 = 340 answer : b
Answer: b
Python program:
a = 4 * 5
b = a * 17
Problem: meena wrote all the numbers from 1 to 69,999 inclusive . how many digits did she write in total ?
Options: a ) 278,889 , b ) 308,889 , c ) 338,889 , d ) 368,889 , e ) 398,889
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 69999 = > 5 * 60,000 = 300,000 the answer is 338,889 the answer is c ."
Answer: c
Python program:
a = 10 - 1
b = 100 - 10
c = b * 2
d = a + c 
e = 100 - 10
f = e * 3
g = d + f 
h = 100 - 10
i = h * 4
j = g + i
Problem: harkamal purchased 9 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1120 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 9 kg grapes = 70 × 9 = 630 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 630 + 490 = 1120 a"
Answer: a
Python program:
a = 9 * 70
b = 9 * 55
c = a + b
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 100 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 142
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 100 = > 2 * ( 2 ) ^ 2 + y = 100 = > 8 + y = 100 = > y = 92 f ( 5 ) = 2 * ( 5 ) ^ 2 + 92 = 142 answer e"
Answer: e
Python program:
a = 2 ** 2
b = a * 2
c = 100 - b
d = 5 ** 2
e = 2 * d
f = c + e
Problem: a sum of rs . 2717 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1672 , b ) 1640 , c ) 1677 , d ) 1698 , e ) 1679
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2717 - x ) * 3 * 5 ) / 100 24 x / 100 = 40755 / 100 - 15 x / 100 39 x = 40755 = > x = 1045 second sum = 2717 â € “ 1045 = 1672 answer : a"
Answer: a
Python program:
a = 3 * 5
b = a * 2717
c = 3 * 5
d = 8 * 3
e = c + d 
f = b / e
g = 2717 - f
Problem: if 35 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 110 , b ) 330 , c ) 572 , d ) 430 , e ) 880
Rationale: "students enrolled in biology are 35 % and therefore not enrolled are 65 % . so of 880 is 880 * . 65 = 572 answer is c 572"
Answer: c
Python program:
a = 880 / 100
b = 100 - 35
c = a * b
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 28 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 16 , b ) 24 , c ) 32 , d ) 40 , e ) 48
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.28 ( 800 ) = 216 the answer is a ."
Answer: a
Python program:
a = 160 / 800
b = a * 100
c = 100 - b
d = c - 28
e = 100 - 75
f = d - e
g = f * 800
h = g / 100
i = 100 - 75
j = i * 800
k = j / 100
l = h - k
Problem: a sum of rs . 1700 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1700 = > 17 x / 12 = 1700 = > 1700 x 12 / 17 = rs . 1200 hence , b ’ s share = rs . ( 1200 / 4 ) = rs . 300 . answer d"
Answer: d
Python program:
a = 1700 / 10
b = a * 2
c = b - 12
d = c - 12
Problem: on a certain island , 5 % of the 10000 inhabitants are one - legged and half of the others go barefooted . what is the least number of shoes needed in the island ?
Options: a ) 10200 , b ) 10000 , c ) 9500 , d ) 9000 , e ) none
Rationale: explanation : = > one - legged = 5 % of 10000 = 500 = > remaining = 10000 - 500 = 9500 = > barefooted = 9500 / 2 = 4750 = > remaining people = 9500 - 4750 = 4750 = > hence required number of shoes = 4750 * 2 + 500 * 1 = 10000 hence ( b ) is the correct answer . answer : b
Answer: b
Python program:
a = 5 / 100
b = a * 10000
c = 10000 - b
d = c / 2
e = d * 2
f = 5 / 100
g = f * 10000
h = g * 1
i = e + h
Problem: a person borrows rs . 9000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 9000 * 6 * 2 ) / 100 ] - [ ( 9000 * 4 * 2 ) / 100 ] 1080 - 720 = 360 gain in 1 year = ( 360 / 2 ) = 180 rs answer : d"
Answer: d
Python program:
a = 9000 * 6
b = a * 2
c = b / 100
d = 9000 * 4
e = d * 2
f = e / 100
g = c - f
h = g / 2
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 7 gallons of water and 14 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 105 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 14 gallons salt is added and 7 gallons of water is added . so salt now becomes - > ( 0.2 x + 14 ) and water - - > ( 0.6 x + 7 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 14 ) = ( 0.6 x + 7 ) / 2 = > 0.2 x = 21 solving , x = 105 answer : c"
Answer: c
Python program:
a = 14 * 2
b = a - 7
c = 20 / 100
d = 1 - c
e = 20 / 100
f = 1 - e
g = 1 / 4
h = f * g
i = d - h
j = 20 / 100
k = 2 * j
l = i - k
m = b / l
Problem: a car takes 12 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 4 th of the previous time ?
Options: a ) 25 kmph , b ) 60 kmph , c ) 100 kmph , d ) 120 kmph , e ) 180 kmph
Rationale: "time = 12 distence = 540 3 / 4 of 12 hours = 12 * 3 / 4 = 9 hours required speed = 540 / 9 = 60 kmph b )"
Answer: b
Python program:
a = 12 * 3
b = a / 4
c = 540 / b
Problem: a soccer team played 140 games and won 50 percent of them . how many games did it win ?
Options: a ) 140 , b ) 94 , c ) 104 , d ) 70 , e ) 80
Rationale: "50 % of 140 = x 0.50 * 140 = x 70 = x answer : d"
Answer: d
Python program:
a = 50 * 140
b = a / 100
Problem: how many 11 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 12345654321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 900000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the 11 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 10 th 9 th , 8 th , 7 th , 6 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the , 5 th , 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 11 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 900000 ways ) answer : e"
Answer: e
Python program:
a = 11 * 10
b = a * 10
c = b * 10
d = c * 10
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 224 different signs . if the company used 222 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 224 signs ?
Options: a ) 246 , b ) 248 , c ) 892 , d ) 15,128 , e ) 20,256
Rationale: "# of 2 - letter codes possible from 224 different signs = 224 * 224 . # of 2 - letter codes possible from 222 different signs = 222 * 222 . the difference = 224 ^ 2 - 222 ^ 2 = ( 224 - 222 ) ( 224 + 222 ) = 892 . answer : c ."
Answer: c
Python program:
a = 224 - 222
b = 222 * a
c = 224 - 222
d = b * c
Problem: a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and captain ) to a nearby port . altogether , these passengers have 15 heads and 42 legs . how many cats does the ship host ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "sa ' s + co + ca + cats = 15 . sa ' s + 1 + 1 + cats = 15 or sa ' s + cats = 13 . sa ' s ( 2 ) + 2 + 2 + cats * 4 = 42 sa ' s * 2 + cats * 4 = 38 or sa ' s + cats * 2 = 19 or 13 - cats + cat * 2 = 19 then cats = 6 b"
Answer: b
Python program:
a = 42 - 1
b = 15 - 1
c = b * 2
d = a - c
e = 15 - 1
f = e * 4
g = 15 - 1
h = g * 2
i = f - h
j = d / i
k = 15 - 1
l = j * k
Problem: in 6 successive games , a baseball team scored 1 runs once , 4 runs twice , and 5 runs 3 times . what was the average ( arithmetic mean ) number of runs the team scored per game over the 6 - game period ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: 1 runs once ( one game ) 4 runs twice ( two game ) 5 runs three times ( three games ) so we have ( 1 * 1 + 4 * 2 + 5 * 3 ) / 6 = 24 / 6 = 4 . ans : e .
Answer: e
Python program:
a = 5 * 3
b = 1 * 1
c = 4 * 2
d = b + c 
e = a + d 
f = e / 6
Problem: a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.2 hrs , e ) 30 hrs
Rationale: "net part filled in 1 hour = 1 / 5 - 1 / 6 = 1 / 30 therefore the cistern will be filled in 30 hours . answer : e"
Answer: e
Python program:
a = 1 / 5
b = 1 / 6
c = a - b
d = 1 / c
Problem: one hour before john started walking from p to q , a distance of 23 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 15 miles
Rationale: ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 23 - 3 = 20 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 20 miles so it will take them 20 / 5 = 4 hours to meet . in 4 hrs , ann would have covered 4 hrs * 3 miles per hour = 12 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 12 = 15 miles . answer ( e )
Answer: e
Python program:
a = 3 + 2 
b = 23 / a
c = b * 2
Problem: ( 128.5 x 60 ) + ( 13.8 x 65 ) = ? x 25
Options: a ) 524.48 , b ) 344.28 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 60 ) + ( 13.8 x 65 ) / 25 = 7710 + 897 / 25 = 344.28 answer : option b"
Answer: b
Python program:
a = 4 + 1 
b = a ** 4
c = 128 * 5
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 11 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 1 to 5 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 11 k waiters . the new ratio is 1 : 5 which equals 3 : 15 . 15 k = 11 k + 12 k = 3 there are 9 cooks . the answer is c ."
Answer: c
Python program:
a = 12 / 4
b = 12 / 5
c = a * b
Problem: on a certain day , tim invested $ 600 at 10 percent annual interest , compounded annually , and lana invested 1,000 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5.5 , b ) $ 15.5 , c ) $ 23.5 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 600 ( 1.10 ) ^ 2 = 600 ( 1.21 ) = 726 and lana would have 1,000 ( 1.05 ) ^ 2 = 1,000 ( 1.1025 ) = 1102.5 thus , tim earned 126 dollars , while lana earned 102.5 dollars the difference is $ 23.5 and the answer is c ."
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 600 * c
e = d - 600
f = 5 / 100
g = 1 + f 
h = g ** 2
i = h * 1
j = i - 1
k = e - j
Problem: john has 10 pairs of matched socks . if he loses 9 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "because we have to maximize the pair of matched socks , we will remove 4 pairs ( 8 socks ) out of 10 pairs 1 sock from the 5 th pair . thus the no of matching socks pair remaining = 10 - 5 = 5 answer c"
Answer: c
Python program:
a = 10 - 3
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 8.5 ) = ( 500 ∗ 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 9 % ( option a ) answer : a"
Answer: a
Python program:
a = 3 * 500
b = 500 + a 
c = 8 / 5
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100