euclaise/mathqa_programs huggingface dataset:
Problem: in the coordinate plane , points ( x , 6 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x * y =
Options: a ) 52 , b ) 46 , c ) 60 , d ) 50 , e ) 35
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 6 ) = ( 12 , 6 ) and ( 10 , y ) = ( 10,5 ) - - > x * y = 12 * 5 = 60 . answer : c"
Answer: c
Python program:
a = 10 * 2
b = 6 / 2
c = a * b
Problem: a vessel of capacity 3 litre has 25 % of alcohol and another vessel of capacity 5 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 27.5 % . , d ) 29 % . , e ) 51 % .
Rationale: "25 % of 3 litres = 0.75 litres 40 % of 5 litres = 2 litres therefore , total quantity of alcohol is 2.75 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.5 % c"
Answer: c
Python program:
a = 25 / 100
b = a * 3
c = 40 / 100
d = c * 5
e = b + d 
f = e / 10
g = f * 100
Problem: a jar contains 18 balls . 3 blue balls are removed from the jar and not replaced . now the probability of getting a blue ball is 1 / 5 then how many blue balls jar contains initially ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: x / 15 = 1 / 5 x = 3 3 + 3 ( removed 3 blue balls ) = 6 answer : e
Answer: e
Python program:
a = 18 - 3
b = 1 / 5
c = a * b
d = 3 + c
Problem: a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt ?
Options: a ) 680 rs , b ) 540 rs , c ) 480 rs , d ) 640 rs , e ) 280 rs
Rationale: area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a
Answer: a
Python program:
a = 80 / 100
b = 110 * 65
c = 110 - 5
d = 65 - 5
e = c * d
f = b - e
g = a * f
Problem: a motorcyclist goes from nagpur to delhi , a distance of 600 kms at an average of 60 kmph speed . another man starts from nagpur by car 5 â ½ hours after the first , and reaches delhi â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 7 , c ) 1 : 9 , d ) 1 : 5 , e ) 2 : 5
Rationale: t = 600 / 60 = 10 h t = 10 - 6 = 4 time ratio = 10 : 4 = 5 : 2 speed ratio = 2 : 5 answer : e
Answer: e
Python program:
a = 600 / 60
b = a - 5
c = 1/(2)
d = b - c
e = 1/(2)
f = d - e
g = 600 / f
h = 60 / g
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 120 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? d"
Answer: d
Python program:
a = 3 * 10
b = 120 + a
Problem: there are 20 balls in a jar . you take out 2 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Rationale: "12 = 3 blue balls + 18 / 2 answer : a"
Answer: a
Python program:
a = 20 - 2
b = a / 5
c = b + 2
Problem: a = { 20 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 , - 620 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 5 / 12 , d ) 4 / 9 , e ) 1 / 2
Rationale: for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 3 / 6 * 3 / 6 = 9 / 36 ; p ( negative , negative ) = 2 / 6 * 3 / 6 = 6 / 36 . p = 9 / 36 + 6 / 36 = 15 / 36 = 5 / 12 . answer : c .
Answer: c
Python program:
a = 2 * 3
b = 3 * 2
c = a + b 
d = 1 + 4 
e = d ** 2
f = c / e
g = 1 + 4 
h = g ** 2
i = 2 / h
j = f - i
Problem: if x is 40 percent greater than 88 , then x =
Options: a ) 68 , b ) 70.4 , c ) 123.2 , d ) 105.6 , e ) 108
Rationale: "x = 88 * 1.4 = 123.2 so the answer is c ."
Answer: c
Python program:
a = 40 / 100
b = a * 88
c = 88 + b
Problem: the perimeter of an isosceles right triangle is 4 + 4 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 2.82 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 4 + 4 sqrt 2 or , a . ( 2 + sqrt 2 ) = 4 ( 1 + sqrt 2 ) a = 4 . ( 1 + sqrt 2 ) / 2 + sqrt 2 = 4 * 2.414 / 3.414 = then hypotenuse = 2.82 a"
Answer: a
Python program:
a = math.sqrt(2)
b = 4 * a
c = b / 2
Problem: how many different positive integers are factors of 36 ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 9 , e ) 11
Rationale: "6 × 6 = 3 ^ 2 × 2 ^ 2 so total factors = ( 2 + 1 ) ( 2 + 1 ) = 9 answer : d"
Answer: d
Python program:
a = 2 ** 2
b = a + 2
Problem: the list price of an article is rs . 65 . a customer pays rs . 57.33 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 12 % , e ) 2 %
Rationale: "option e explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 57.33 x = 2 %"
Answer: e
Python program:
a = 10 / 100
b = 65 * a
c = 65 - b
d = c - 57
e = 10 / 100
f = 65 * e
g = 65 - f
h = d / g
i = h * 100
Problem: the supplementary of an angle is thrice its complimentary . find the angle .
Options: a ) 60 , b ) 45 , c ) 90 , d ) 180 , e ) 120
Rationale: let angle = x ; by question - - 180 - x = 3 ( 90 - x ) x = 45 answer : b
Answer: b
Python program:
a = 100 - 10
b = 3 * a
c = 100 - 10
d = c * 2
e = b - d
f = e / 2
Problem: 9 log 9 ( 2 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 2 ) = 2 correct answer b
Answer: b
Python program:
a = 9 * 9
b = math.log(a)
c = math.log(10)
d = b / c
Problem: there are 2 vessels a & b containing 25 liters each of pure milk and pure water respectively . 5 liters of milk from a is taken and poured into b , then 6 liters of mixture from b is taken and poured in a . what is ratio of water a and b respectively .
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 1 : 6 , e ) 1 : 7
Rationale: at first a cotain milk = 25 water = 0 b cotain milk = 00 water = 25 5 litres of milk taken from a and poured in b then a cotain milk = 20 water = 0 b cotain milk = 5 water = 25 6 litres ( 1 lit milk & 5 lit water ) of mixture from b and poured in a . so , finally a cotain milk = 21 water = 5 b cotain milk = 4 water = 20 ratio of water in a & b is 5 : 20 = 1 : 4 answer : b
Answer: b
Python program:
a = 25 + 5 
b = 5 / a
c = b * 6
d = 25 - 5
e = d / 5
f = c / e
Problem: tim and é lan are 150 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 45 miles . , d ) 90 miles . , e ) 100 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice e meet the 2 : 1 ( tim : elan = 100 : 50 ) ratio of maintaining total distance traveled 150 miles socorrect answer e"
Answer: e
Python program:
a = 5 + 10 
b = 10 / a
c = b * 150
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 4 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 4 girls = 8 ã — 6 / 4 + 12 = 12 + 4 = 16 girls 9 days to complete the work answer : option e"
Answer: e
Python program:
a = 1 / 6
b = a / 24
c = 4 * b
d = 1 / 6
e = d / 16
f = 8 * e
g = c + f 
h = 1 / g
Problem: 30 pens and 75 pencils were purchased for 630 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 16
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 630 – 150 ) = 480 ∴ average price of a pen = 480 ⁄ 60 = 16 answer e"
Answer: e
Python program:
a = 75 * 2
b = 630 - a
c = b / 30
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 1,600 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 5.55 % , b ) 5.65 % , c ) 5.75 % , d ) 5.85 % , e ) 5.95 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 8400 = 5 / 84 which is about 5.95 % the answer is e ."
Answer: e
Python program:
a = 100 * 100
b = 5 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: find the cost of fencing around a circular field of diameter 34 m at the rate of rs . 2 a meter ?
Options: a ) 215 , b ) 212 , c ) 278 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 17 = 106 106 * 2 = rs . 212 answer : b"
Answer: b
Python program:
a = 34 / 2
b = circumface * (
Problem: a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the the distance in km ?
Options: a ) 33 , b ) 37 , c ) 40 , d ) 38 , e ) 27
Rationale: "let the distance be x km , the speed in which he moved = v kmph time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes ⇒ xv − xv + 3 = 4060 ⇒ x [ 1 v − 1 v + 3 ] = 23 ⇒ x [ v + 3 − vv ( v + 3 ) ] = 23 ⇒ 2 v ( v + 3 ) = 9 x . . . . . . . . . . . . . . . . ( equation 1 ) time taken when moving 2 kmph slower - time taken when moving at normal speed = 40 minutes ⇒ xv − 2 − xv = 4060 ⇒ x [ 1 v − 2 − 1 v ] = 23 ⇒ x [ v − v + 2 v ( v − 2 ) ] = 23 ⇒ x [ 2 v ( v − 2 ) ] = 23 ⇒ x [ 1 v ( v − 2 ) ] = 13 ⇒ v ( v − 2 ) = 3 x . . . . . . . . . . . . . . . . ( equation 2 ) equation 1 equation 2 ⇒ 2 ( v + 3 ) ( v − 2 ) = 3 ⇒ 2 v + 6 = 3 v − 6 ⇒ v = 12 substituting this value of v in equation 1 ⇒ 2 × 12 × 15 = 9 x = > x = 2 × 12 × 159 = 2 × 4 × 153 = 2 × 4 × 5 = 40 hence distance = 40 km answer : c"
Answer: c
Python program:
a = 40 / const_60
b = 2 * a
c = 40 / const_60
d = 3 * c
e = b + d 
f = 3 - 2
g = e / f
h = 2 * g
i = 40 / const_60
j = 2 * i
k = h + j 
l = 40 / const_60
m = k / l
n = 40 / const_60
o = 2 * n
p = 40 / const_60
q = 3 * p
r = o + q 
s = 3 - 2
t = r / s
u = m * t
Problem: if x + y = 280 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 240 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 280 x - y = 200 2 x = 80 x = 40 y = 240 answer is b"
Answer: b
Python program:
a = 280 + 200 
b = a / 2
Problem: there are 10 students named alphabetically from a to j . what is the probability that a and d do not sit together if all 10 sit around a circular table ?
Options: a ) 2 / 9 , b ) 2 / 5 , c ) 7 / 9 , d ) 4 / 5 , e ) 8 / 9
Rationale: number of students = 10 number of ways 10 students can sit around a circular table = ( 10 - 1 ) ! = 9 ! number of ways a and d sit together ( consider a and d as one entity ) = ( 9 - 1 ) ! = 8 ! * 2 number of ways a and d do not sit together = 9 ! - ( 8 ! * 2 ) probability = ( 9 ! - ( 8 ! * 2 ) ) / 9 ! = 1 - 2 / 9 = 7 / 9 answer : c
Answer: c
Python program:
a = 2 / 10
b = 1 - a
Problem: a pipe can empty 2 / 3 rd of a cistern in 10 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 3 / 7 , c ) 8 / 15 , d ) 3 / 8 , e ) 4 / 7
Rationale: "2 / 3 - - - - 10 ? - - - - - 8 = = > 8 / 15 c"
Answer: c
Python program:
a = 2 / 3
b = a * 8
c = b / 10
Problem: if $ 10 be allowed as true discount on a bill of $ 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :
Options: a ) $ 18.33 , b ) $ 22.33 , c ) $ 28.33 , d ) $ 26.23 , e ) $ 16.23
Rationale: s . i . on $ ( 110 - 10 ) for a certain time = $ 10 . s . i . on $ 100 for double the time = $ 20 . t . d . on $ 120 = $ ( 120 - 100 ) = $ 20 . t . d . on $ 110 = $ ( 20 / 120 * 100 ) = $ 18.33 answer : a
Answer: a
Python program:
a = 2 * 10
b = 110 + 10 
c = a / b
d = c * 110
Problem: if you multiply two integers together and then add 4 , the result is 40 . which of the following could not be the sum of the two numbers ?
Options: a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 20
Rationale: let the two integers equal x and y , and then create the following equation and simplify : xy + 4 = 40 xy = 36 so x and y are a pair of integers that equal 36 . try adding all possible combinations of two integers that multiply out to 36 : 1 × 36 = 36 1 + 36 = 37 2 × 18 = 36 2 + 18 = 20 3 × 12 = 36 3 + 12 = 15 4 × 9 = 36 4 + 9 = 13 6 × 6 = 36 6 + 6 = 12 this list of sums includes 12 , 13 , 15 , and 20 , but not 18 . thus , no pair of integers both satisfies the original equation and adds up to 18 correct answer d ) 18
Answer: d
Python program:
a = 40 - 4
b = a / 2
Problem: a train 460 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 87 , c ) 48 , d ) 21 , e ) 14
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 460 + 140 = 600 m required time = 600 * 2 / 25 = 48 sec answer : c"
Answer: c
Python program:
a = 45 - 140
b = a * const_0_2778
c = 460 / b
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what might be the weight of the new person ?
Options: a ) 65 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "a 65 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 64 + 20 ) kg = 65 kg ."
Answer: a
Python program:
a = 8 * 2
b = a + 45
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 187 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 247 , b ) s . 248 , c ) s . 264 , d ) s . 329 , e ) s . 412
Rationale: "given that sp = rs . 187 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 187 ) / 85 = 20 * 6 = rs . 220 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 220 * 120 ) / 100 = rs . 264 answer : c"
Answer: c
Python program:
a = 15 / 100
b = 1 - a
c = 187 / b
d = 15 / 100
e = 1 - d
f = 187 / e
g = 20 / 100
h = f * g
i = c + h
Problem: if 9 a - b = 10 b + 65 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 11 , b ) - 5 , c ) 0 , d ) 5 , e ) 11
Rationale: "( i ) 9 a - 11 b = 65 ( ii ) 2 a + 22 b = - 65 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Python program:
a = 65 / 2
b = a * 2
c = negate * (
Problem: find the average of all numbers between 1 and 76 which are divisible by 5
Options: a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 + 75 ) / 15 = 600 / 15 = 40 answer : option a"
Answer: a
Python program:
a = 5 * 3
b = 5 * 2
c = 5 + b 
d = a + c 
e = 5 * 4
f = d + e 
g = 4 + 1 
h = g * 5
i = f + h 
j = i / 5
Problem: a cricketer makes a score of 134 runs in the 22 nd inning and thus increases his average by 3.5 . find his average after 22 nd inning .
Options: a ) 40 , b ) 60.5 , c ) 52 , d ) 55 , e ) 36
Rationale: explanation : let the average after 22 nd innings = x then average after 21 th innings = ( x - 3.5 ) therefore 21 ( x - 3.5 ) + 134 = 22 x therefore x = 60.5 answer : b
Answer: b
Python program:
a = 3 * 5
b = 134 - a
c = b + 3
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 30 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 percent , c ) 25 % , d ) 28 % , e ) 27 %
Rationale: "total sales = 800 commission = ( 20 / 100 ) * 500 + ( 30 / 100 ) * 300 = 100 + 90 = 190 % commission = ( 190 / 800 ) * 100 = 23.7 ~ 24 % answer is b"
Answer: b
Python program:
a = 20 / 100
b = a * 500
c = 30 / 100
d = 800 - 500
e = c * d
f = b + e 
g = f / 800
h = g * 100
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 6 rows in all and a total of 135 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 19 , e ) 24
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 + x - 5 = 135 6 x - 15 = 135 6 x = 120 x = 20 answer : b"
Answer: b
Python program:
a = 135 - 1
b = a - 2
c = b - 3
d = c - 4
e = d / 6
Problem: the average marks of a class of 25 students is 50 and that of another class of 40 students is 65 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 59 , e ) 52.9
Rationale: "sum of the marks for the class of 25 students = 25 * 50 = 1250 sum of the marks for the class of 40 students = 40 * 65 = 2600 sum of the marks for the class of 65 students = 1250 + 2600 = 3850 average marks of all the students = 4850 / 65 = 59 . answer : d"
Answer: d
Python program:
a = 25 * 50
b = 40 * 65
c = a + b 
d = 25 + 40 
e = c / d
Problem: how many plants will be there in a circular bed whose outer edge measure 34 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 23 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 34 cm area of circular bed = ( 34 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 34 ) 2 â  „ 4 ï € ã · 4 = 22.98 = 23 ( approx ) answer c"
Answer: c
Python program:
a = 2 * math.pi
b = 34 / a
c = circle_area / (
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 550 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 10 % of 500 = rs . 50 selling price = cost price + profit = 500 + 50 = 550 answer : a"
Answer: a
Python program:
a = 10 / 100
b = 500 * a
c = 500 + b
Problem: stacy and helon are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour faster than helon ' s constant rate of 5 miles / hour . if helon starts her journey 24 minutes after stacy , how far from the original destination has helon walked when the two meet ?
Options: a ) 5 miles , b ) 8 miles , c ) 6 miles , d ) 13 miles , e ) 12 miles
Rationale: original distance between s and h = 30 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 5 ) + 5 * t = 30 - - - > t = 138 / 55 hours . thus h has traveled for 138 / 55 hours giving you a total distance for h = 5 * 138 / 55 = 13 miles . d is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles .
Answer: d
Python program:
a = 5 + 1 
b = a * 24
c = b / const_60
d = 30 - c
e = 5 + 1 
f = 5 + e 
g = d / f
h = g * 5
Problem: if log 2 = 0.30103 and log 3 = 0.4771 , find the number of digits in ( 648 ) 5
Options: a ) 14.05 , b ) 14.02 , c ) 277 , d ) 288 , e ) 222
Rationale: "log ( 648 ) 5 = 5 log ( 648 ) = 5 log ( 81 × 8 ) = 5 [ log ( 81 ) + log ( 8 ) ] = 5 [ log ( 34 ) + log ( 23 ) ] = 5 [ 4 log ( 3 ) + 3 log ( 2 ) ] = 5 [ 4 × 0.4771 + 3 × 0.30103 ] = 5 ( 1.9084 + 0.90309 ) = 5 × 2.81149 ≈ 14.05 answer : a"
Answer: a
Python program:
a = 0 / 30103
b = 0 * 30103
Problem: if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is :
Options: a ) 15 : 12
b ) 15 : 14
c ) 15 : 16
d ) 15 : 22
e ) none of these
Rationale: explanation : a 2 / b 2 = 225 / 256 = 15 / 16 < = > 4 a / 4 b = 4 ∗ 15 / 4 ∗ 16 = 15 / 16 = 15 : 16 option c
Answer: c
Python program:
a = 225 / 256
b = math.sqrt(a)
Problem: what least number must be subtracted from 12702 to get number exactly 99 ?
Options: a ) 49 , b ) 30 , c ) 29 , d ) 31 , e ) 32
Rationale: "explanation : divide the given number by 99 and find the remainder . if you subtract the remainder from the given number then it is exactly divisible by 99 . 99 ) 12702 ( 128 99 280 198 822 792 30 required number is 30 . answer is b"
Answer: b
Python program:
a = 12702 / 99
b = math.floor(a)
c = b * 99
d = 12702 - c
Problem: if x is 20 percent greater than 40 , then x =
Options: a ) 48 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x is 20 % greater than 40 means x is 1.2 times 40 ( in other words 40 + 20 / 100 * 40 = 1.2 * 40 ) therefore , x = 1.2 * 40 = 48 answer : a"
Answer: a
Python program:
a = 20 / 100
b = a * 40
c = 40 + b
Problem: in a theater , the first row has 14 seats and each row has 2 more seats than previous row . if the last row has 56 seats , what is the total number of seats in the theater ?
Options: a ) 770 , b ) 780 , c ) 790 , d ) 800 , e ) 810
Rationale: "the number of seats in the theater is 14 + ( 14 + 2 ) + . . . + ( 14 + 42 ) = 22 ( 14 ) + 2 ( 1 + 2 + . . . + 21 ) = 22 ( 14 ) + 2 ( 21 ) ( 22 ) / 2 = 22 ( 14 + 21 ) = 22 ( 35 ) = 770 the answer is a ."
Answer: a
Python program:
a = 14 + 56 
b = a / 2
c = 56 - 14
d = c + 2 
e = d / 2
f = b * e
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 60 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 36 , b ) 96 , c ) 100 , d ) 76 , e ) 72
Rationale: "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 60 vehicles . hence 2 / 3 constitutes 120 speedster convertibls = 120 * 4 / 5 = 96 b"
Answer: b
Python program:
a = 2 / 3
b = 1 - a
c = 60 / b
d = 2 / 3
e = c * d
f = 4 / 5
g = e * f
Problem: a bag of potatoes weighs 12 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 18 lb , c ) 12 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 12 ÷ 1 = 12 . answer : c"
Answer: c
Python program:
a = 12 / 1