euclaise/mathqa_programs huggingface dataset:
Problem: an exam consists of 7 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16
Rationale: if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 219 / 256 . d
Answer: d
Python program:
a = 1 / 2
b = a ** 7
c = 1 / 2
d = c ** 7
e = 7 * d
f = b + e 
g = 7 * 3
h = 1 / 2
i = h ** 7
j = g * i
k = f + j 
l = 1 - k
m = l / 10
n = 1 / 2
o = n ** 7
p = 1 / 2
q = p ** 7
r = 7 * q
s = o + r 
t = 7 * 3
u = 1 / 2
v = u ** 7
w = t * v
x = s + w 
y = 1 - x
z = m + y
Problem: what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 7
Options: a ) 2 / 15 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a
Answer: a
Python program:
a = 4 / 5
b = 2 / 3
c = a - b
Problem: last year department store x had a sales total for december that was 5 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 5 / 16 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 50 year total = 11 * 10 + 50 = 160 answer = 50 / 160 = 5 / 16 = d"
Answer: d
Python program:
a = 12 - 1
b = a + 5 
c = 5 / b
Problem: if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 6.2 ] + [ - 3.4 ] + [ 12.7 ] ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 6.2 ] = - 7.0 [ - 3.4 ] = - 4.0 [ 12.7 ] = 12.0 therefore , answer is : - 7.0 - 4.0 + 12.0 = - 1.0 option a ."
Answer: a
Python program:
a = 3 + 4 
b = a - 6
Problem: a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is :
Options: a ) 13 % , b ) 14 % , c ) 18 % , d ) 20 % , e ) 28 %
Rationale: let original length = x and original breadth = y . decrease in area = xy - ( 80 / 100 * x * 90 / 100 * y ) = ( xy - 18 / 25 * xy ) = 7 / 25 * xy . decrease % = ( 7 / 25 * xy * 1 / xy * 100 ) % = 28 % . answer is e
Answer: e
Python program:
a = 100 - 20
b = a / 100
c = 100 - 10
d = c / 100
e = b * d
f = 1 - e
g = f * 100
Problem: at what rate percent per annum will the simple interest on a sum of money be 2 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 74 % , c ) 64 % , d ) 74 % , e ) 94 %
Rationale: let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 2 x ) / ( x * 5 * 10 ) = 4 % answer : a
Answer: a
Python program:
a = 2 / 5
b = a * 100
c = b / 10
Problem: a cycle is bought for rs . 900 and sold for rs . 1125 , find the gain percent ?
Options: a ) 27 % , b ) 20 % , c ) 80 % , d ) 30 % , e ) 25 %
Rationale: "900 - - - - 225 100 - - - - ? = > 25 % answer : e"
Answer: e
Python program:
a = 1125 - 900
b = a / 900
c = b * 100
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 5 , 0 ) , ( 1 , 2 ) and ( 5 , 2 ) 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 ) 3 , b ) 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 3 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 3 , 1 ) is 1 / 3 . the answer is c ."
Answer: c
Python program:
a = 5 - 1
b = a + 2 
c = b / 2
d = 1 / c
Problem: a 140 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 43.2 sec , e ) none of the above
Rationale: speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 140 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 660 m time = distance / speed = 660 x 18 / ( 5 x 55 ) = 43.2 sec ans is : d
Answer: d
Python program:
a = 140 + 520 
b = 55 * const_0_2778
c = a / b
Problem: how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 80 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 50 * 4 = 200 m time taken = 200 * 2 / 5 = 80 sec answer is a"
Answer: a
Python program:
a = 50 * 4
b = 1000 / 3600
c = 9 * b
d = a / c
Problem: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 28 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 9 , e ) 1 / 9
Rationale: "28 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 28 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 28 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 27 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 27 = r ^ 3 r = 3 a"
Answer: a
Python program:
a = 28 - 1
b = 1 / 3
c = a ** b
Problem: 19 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 38 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 19 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 19 * 21 * 8 = 14 * x * 6 x = 38 answer : c"
Answer: c
Python program:
a = 21 * 8
b = 19 * 3
c = a * b
d = 21 * 2
e = d * 6
f = c / e
g = math.floor(f)
h = g + 1
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,056 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 400 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1056 / 1000 ) - 1 = 0.053 = 5.3 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.056 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.056 - 0.01 x = - 0.004 x = - 0.004 / - 0.01 = 4 / 10 = 40 % so x = 40 % of the 1000 which is 400 answer : b"
Answer: b
Python program:
a = 5 * 2
b = a * 100
c = 5 * 2
d = c * 100
e = 5 * 2
f = e * 5
g = f + 4 
h = d + g 
i = 5 * 2
j = i * 100
k = h - j
l = k * 100
m = 5 * 2
n = m * 100
o = 5 * n
p = l - o
q = b - p
Problem: there are two inlets and one outlet to a cistern . one of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern . both of the inlets are turned on at 8 : 30 am with the cistern completely empty , and at 10 : 30 am , the outlet is turned on and it takes 1 more hour to fill the cistern completely . how much time does the outlet working alone takes to empty the cistern when the cistern is full ?
Options: a ) 2 hours , b ) 2.5 hours , c ) 3 hours , d ) 3.5 hours , e ) 8 hours
Rationale: "the combined inflow rate of the two inlets is 1 / 4 + 1 / 8 = 3 / 8 cistern / hour . thus , working together , it takes 8 / 3 hours ( time is reciprocal of rate ) to fill the cistern . from 8 : 30 am to 10 : 30 am , so in 2 hours , the inlet pipes will fill ( time ) * ( rate ) = 2 * 3 / 8 = 3 / 4 th of the cistern . then the outlet is turned on and the remaining 1 / 4 th of the cistern is filled in 1 hour . letting x to be the rate of the outlet , we would have : 3 / 8 - x = 1 / 4 - - > x = 1 / 8 cistern / hour , which means that it takes 8 hours the outlet working alone to empty the cistern . answer : e ."
Answer: e
Python program:
a = 2 - 0
b = 8 - a
c = 10 - b
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 80 , how much more remains to be paid ?
Options: a ) $ 640 , b ) $ 680 , c ) $ 720 , d ) $ 760 , e ) $ 800
Rationale: "90 % remains to be paid so the remaining amount is 9 * 80 = $ 720 . the answer is c ."
Answer: c
Python program:
a = 100 / 10
b = 80 * a
c = b - 80
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 22 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 777 , c ) 780 , d ) 867 , e ) 232
Rationale: "if mike had scored 22 marks more , he could have scored 30 % therefore , mike required 212 + 22 = 234 marks let the maximum marks be m . then 30 % of m = 234 ( 30 / 100 ) × m = 234 m = ( 234 × 100 ) / 30 m = 23400 / 30 m = 780 answer : c"
Answer: c
Python program:
a = 212 + 22 
b = 30 / 100
c = a / b
Problem: if shares of two persons in profits are rs . 400 and rs . 500 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 4 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 400 : 500 = 4 : 5 answer : b"
Answer: b
Python program:
a = 400 / 500
Problem: in the xy - plane , the point ( 2 , 1 ) is the center of a circle . the point ( - 2 , 1 ) lies inside the circle and the point ( 2 , - 5 ) lies outside the circle . if the radius r of the circle is an integer , then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 2 , 1 ) and the point inside the circle ( - 2 , 1 ) is 4 units ( both points are on y = 1 line so the distance will simply be 2 - ( - 2 ) = 4 ) so the radius must be more than 4 units . the distance between the center ( 2,1 ) and the point outside the circle ( 2 , - 5 ) is 6 units ( both points are on x = 2 line so the distance will simply be 1 - ( - 5 ) = 6 ) so the radius must be less than 6 units , which implies 4 < r < 6 , thus as r is an integer then r = 5 . answer : b .
Answer: b
Python program:
a = 2 + 2 
b = a + 1
Problem: the sum of three consecutive integers is 102 . find the lowest of the three ?
Options: a ) 15 , b ) 33 , c ) 56 , d ) 96 , e ) 88
Rationale: "explanation : three consecutive numbers can be taken as ( p - 1 ) , p , ( p + 1 ) . so , ( p - 1 ) + p + ( p + 1 ) = 102 3 p = 102 = > p = 34 . the lowest of the three = ( p - 1 ) = 34 - 1 = 33 . answer b"
Answer: b
Python program:
a = 102 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 102 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 102 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 102 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 21,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 147 % , d ) 150 % , e ) 225 %
Rationale: "the percent increase is ( 21947 - 8902 ) / 8902 = 13045 / 8902 = 1.47 so the approximate answer is c"
Answer: c
Python program:
a = 21 - 947
b = a / 8
Problem: if k is the greatest positive integer such that 4 ^ k is a divisor of 16 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "16 / 4 = 4 16 / 16 = 1 4 + 1 = 5 k = 5 answer : c"
Answer: c
Python program:
a = 16 / 4
b = 1 + a
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 20 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 767 , e ) 432
Rationale: "1 h - - - - - 4 ? - - - - - - 60 12 h rs = 16 + 20 = 36 t = 12 d = 36 * 12 = 432 answer : e"
Answer: e
Python program:
a = 20 - 16
b = 60 / a
c = b * 16
d = 20 - 16
e = 60 / d
f = e * 20
g = c + f
Problem: johnny makes $ 8.25 per hour at his work . if he works 2 hours , how much money will he earn ?
Options: a ) $ 30.50 , b ) $ 16.50 , c ) $ 28.50 , d ) $ 12 , e ) $ 9.60
Rationale: 8.25 * 2 = 16.50 . answer is b .
Answer: b
Python program:
a = 8 * 25
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number t ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = t answer : b"
Answer: b
Python program:
a = 12 / 5
b = 1 + a 
c = 25 / 100
d = 1 - c
e = b - d
f = 30 / e
Problem: how many positive integers less than 5,000 are evenly divisible by neither 18 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 18 5000 / 18 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 18 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 18 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4428 answer d ."
Answer: d
Python program:
a = 4 + 18 
b = a - 1
c = math.factorial(b)
d = math.factorial(18)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70"
Answer: d
Python program:
a = 3 - 12
b = 8 * a
c = 4 - b
d = 5 - 11
e = c - negate
Problem: if xy denotes x is raised to the power y , find the last two digits of 19413844 + 19714181
Options: a ) 154 , b ) 677 , c ) 784 , d ) 148 , e ) 132
Rationale: "1941 ^ 3844 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 4 = 16 = 2 means last two digit = 61 and 1971 ^ 4181 unit digit = 1 10 th digit = 7 * 1 = 7 mean last two digit = 71 hence , 71 + 61 = 132"
Answer: e
Python program:
a = 100 ** 2
b = reminder - (
c = b - 100
d = c + 10 
e = d - 10
f = 100 ** 2
g = 19413844 / f
h = math.floor(g)
i = e - reminder
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 172 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 172 = > 4 x / 10 = 172 = > 4 x = 1720 = > x = 430 . answer : a"
Answer: a
Python program:
a = 100 - 70
b = 70 - a
c = b / 100
d = 172 / c
Problem: 12 buckets of water fill a tank when the capacity of each bucket is 55 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 5 litres ?
Options: a ) 142 , b ) 130 , c ) 132 , d ) 123 , e ) 120
Rationale: "capacity of the tank = ( 12 ã — 55 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 55 / 5 = 12 ã — 11 = 132 answer is c"
Answer: c
Python program:
a = 55 * 12
b = a / 5
Problem: yesterday i noticed that in my clock , there is time when the hour needle and the minute needle are exactly between 1 and 2 . also both the needles lie on top of each other . what time i and talking about ?
Options: a ) 10 : 00 , b ) 11 : 00 , c ) 09 : 00 , d ) 12 : 00 , e ) 07 : 00
Rationale: d 12 : 00 both minute and hour clock lie exactly between the number one and two in the number .
Answer: d
Python program:
a = 1 * 10
b = a + 2
Problem: a watch was sold at a loss of 46 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 280 , b ) 288 , c ) 279 , d ) 277 , e ) 290
Rationale: "54 % 104 % - - - - - - - - 50 % - - - - 140 100 % - - - - ? = > rs . 280 answer : a"
Answer: a
Python program:
a = 140 * 100
b = 100 + 4 
c = 100 - 46
d = b - c
e = a / d
Problem: ( 168 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 354 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 168 x 1265 / 100 ) ÷ 6 = 212520 / 600 = 354 answer : option a"
Answer: a
Python program:
a = 168 / 100
b = a * 1265
c = b / 6
Problem: there are 15 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 650 , b ) 750 , c ) 850 , d ) 950 , e ) 1050
Rationale: "the number of ways to choose two teams is 15 c 2 = 15 * 14 / 2 = 105 the total number of games in the season is 10 * 105 = 1050 . the answer is e ."
Answer: e
Python program:
a = 15 - 1
b = 15 * a
c = b * 10
d = c / 2
Problem: if 3 : 12 : : x : 16 , then find the value of x
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : treat 3 : 12 as 3 / 12 and x : 16 as x / 16 , treat : : as = so we get 3 / 12 = x / 16 = > 12 x = 48 = > x = 4 option b
Answer: b
Python program:
a = 12 * 3
b = a + 12 
c = b / 16
Problem: bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 8 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 10 left in his pocket . what was the value of n ?
Options: a ) $ 32 , b ) $ 36 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer b if he had 36 , then he spent 9 at hardware store now he was left with 27 $ he spent 8 dollars on cleaning , thus he remained with 19 $ he then spent 1 / 2 of 19 , or 9.50 , hence , the only option that can be right is a . ans a"
Answer: a
Python program:
a = 1 / 4
b = 1 - a
c = 1/(b)
d = 8 / 2
e = d + 10 
f = c * e
g = f * 2
Problem: john can complete a given task in 20 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 4 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 6 , b ) 10 , c ) 8 , d ) 7.5 , e ) 3.5
Rationale: "john 6 * 20 = 120 jane 10 * 12 = 120 in 4 days working alone john did : 4 days * rate = 4 * 6 = 24 , so working together they did 120 - 24 = 96 - - > rate ( a + b ) * t = 96 - > 16 * t = 96 , t = 6 . hence the answer is b ( john worked 4 days + 6 days they worked together = 10 days )"
Answer: b
Python program:
a = 20 * 12
b = 12 * 4
c = a - b
d = 12 + 20 
e = c / d
f = 4 + e
Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 1 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 45 , c ) 270 , d ) 90 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 1 / 3 ) of total igneous rocks . ( 1 / 3 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 3 ) = 90 total sedimentary rocks = 2 * total igneous rocks = 2 * 90 = 180 total number of rocks = 90 + 180 = 270 answer ( c )"
Answer: c
Python program:
a = 1 * 3
b = a * 30
c = b / 1
d = c * 3
e = d / 1
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 5 / 6 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 4 / 7 , b ) 5 / 9 , c ) 6 / 11 , d ) 7 / 12 , e ) 8 / 13
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 5 x / 6 ) ( 3 y / 4 ) = 5 xy / 8 the total number of boxes is xy + 5 xy / 8 = 13 xy / 8 the fraction loaded by the day crew is xy / ( 13 xy / 8 ) = 8 / 13 the answer is e ."
Answer: e
Python program:
a = 6 * 4
b = 6 * 4
c = 3 * 5
d = b + c 
e = a / d
Problem: a man has some hens and cows . if the number of heads be 50 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 30 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 50 implies , 2 x + 4 y = 140 and x + y = 50 solving these two equations , we get x = 30 and y = 20 therefore , hens are 26 . answer : d"
Answer: d
Python program:
a = 50 * 4
b = a - 140
c = b / 2
Problem: the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 4.4 miles in the fifth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 45 , b ) 48 , c ) 51 , d ) 54 , e ) 57
Rationale: "( 4.4 miles / 8 minutes ) * 60 minutes / hour = 33 mph let x be the original speed . x - 4 ( 3 ) = 33 x = 45 mph the answer is a ."
Answer: a
Python program:
a = 8 / const_60
b = 4 / 4
c = b + 3 
d = c + 3 
e = d + 3 
f = e + 3
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 9 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 36.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.91 * 150 x = 136.5 x hence total profit = 36.5 % option d"
Answer: d
Python program:
a = 100 - 9
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100
Problem: if p / q = 6 / 7 , then 2 p + q = ?
Options: a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 19
Rationale: "let p = 6 , q = 7 then 2 * 6 + 7 = 19 so 2 p + q = 19 . answer : e"
Answer: e
Python program:
a = 6 * 2
b = a + 7
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.08 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fourth day it is overdue ?
Options: a ) $ 0.62 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.08 2 nd day fine - 0.08 * 2 = 0.16 ( as doubling gives lower value ) 3 rd day fine - 0.16 * 2 = 0.32 ( as doubling gives lower value ) 4 th day fine - 0.32 + 0.3 = 0.62 ( as doubling gives higher value we add 0.3 this time ) answer : a ."
Answer: a
Python program:
a = 0 * 8
b = a * 2
c = b * 2
d = c + 0