euclaise/mathqa_programs huggingface dataset:
Problem: a sum was put a simple interest at a certain rate for 1 years . had it been put at 6 % higher rate , it would have fetched rs . 30 more . the sum is :
Options: a ) s . 500 , b ) s . 600 , c ) s . 700 , d ) s . 800 , e ) s . 900
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 6 ) ã — 1 / 100 â ˆ ’ x ã — r ã — 1 / 100 = 30 â ‡ ’ x ã — 6 ã — 1 / 100 = 30 â ‡ ’ x ã — 1 / 100 = 5 â ‡ ’ x = 500 answer : option a"
Answer: a
Python program:
a = 30 / 1
b = a / 6
c = b * 100
Problem: of the 19,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 33 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . c"
Answer: c
Python program:
a = 2 / 7
b = a / 2
c = 2 / 7
d = c / 2
e = 2 / 7
f = 1 - e
g = d + f 
h = b / g
i = h * 100
j = i * 3
Problem: two trains are moving in opposite directions @ 60 kmph and 90 kmph . their length are 1.10 km and 0.9 km . the time taken by the slower train to cross faster train in second is ?
Options: a ) 25 sec , b ) 30 sec , c ) 48 sec , d ) 36 sec , e ) 40 sec
Rationale: "relative speed = 60 + 90 = 150 * 5 / 18 = 125 / 3 m / s distance covered = 1.10 + 0.9 = 2 km = 2000 m required time = 2000 * 3 / 125 = 48 sec answer is c"
Answer: c
Python program:
a = 1 + 10 
b = 100 + 0 
c = b * const_0_2778
d = a / c
Problem: how many integers are between 9 and 67 / 5 , inclusive ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: "67 / 5 = 13 . xx we are not concerned about the exact value of 67 / 5 as we just need the integers . since the values are small , we can write down the integers . the different integers between 9 and 67 / 5 would be 9 , 10 , 11 , 12,13 total number of integers = 5 option a"
Answer: a
Python program:
a = 67 / 5
b = a - 9
c = b + 1
Problem: total 36 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 35 , b ) 36 , c ) 21 , d ) 32 , e ) 26
Rationale: "35 players answer : a"
Answer: a
Python program:
a = 36 + 1
Problem: a pipe can empty 3 / 4 th of a cistern in 12 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 1 / 2 , b ) 3 / 7 , c ) 4 / 9 , d ) 3 / 8 , e ) 4 / 7
Rationale: 3 / 4 - - - - 12 ? - - - - - 8 = = > 1 / 2 a
Answer: a
Python program:
a = 3 / 4
b = a * 8
c = b / 12
Problem: benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 2 dollars . how many apples does she buy to share them equally between her 6 kids ?
Options: a ) 8 , b ) 30 , c ) 3 , d ) 7 , e ) 10
Rationale: cost of each apple = 2 dollars apples that benny can buy with the amount she has = 360 / 2 = 180 . apples that each kid gets evenly = 180 / 6 = 30 apples . so the answer is b = 30
Answer: b
Python program:
a = 360 / 2
b = a / 6
Problem: in one year , the population , of a village increased by 12 % and in the next year , it decreased by 12 % . if at the end of 2 nd year , the population was 14784 , what was it in the beginning ?
Options: a ) 7787 , b ) 8000 , c ) 15000 , d ) 1277 , e ) 2081
Rationale: "x * 112 / 100 * 88 / 100 = 14784 x * 0.9856 = 14784 x = 14784 / 0.9856 = > 15000 answer : c"
Answer: c
Python program:
a = 12 / 100
b = 1 - a
c = 14784 / b
d = 12 / 100
e = 1 + d 
f = c / e
Problem: a grocer has a sale of rs . 5266 , rs . 5744 , rs . 5864 , rs . 6122 and rs . 6588 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5750 ?
Options: a ) 4016 , b ) 4076 , c ) 4816 , d ) 4916 , e ) 5916
Rationale: "total sale for 5 months = rs . ( 5266 + 5744 + 5864 + 6122 + 6588 ) = rs . 29584 . required sale = rs . [ ( 5750 x 6 ) - 34500 ] = rs . ( 34500 - 29584 ) = rs . 4916 . answer : d"
Answer: d
Python program:
a = 5 + 1 
b = a * 5750
c = 5266 + 5744 
d = c + 5864 
e = d + 6122 
f = e + 6588 
g = b - f
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 20 per square m ?
Options: a ) s . 43000 , b ) s . 19000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 20 * 950 = rs . 19000 b"
Answer: b
Python program:
a = 20 * 15
b = a * 2
c = b * 20
d = 20 * 5
e = d * 2
f = e * 20
g = c + f 
h = 15 * 5
i = h * 2
j = i * 20
k = g + j
Problem: a shipment of 220 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 11 / 76 , d ) 1 / 9 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 220 which ontains 84 defective phones is = ( 84 / 220 ) probability of chosing one defective phone from a lot of 219 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 219 ) combined probability of series of events = product of the probabilities = ( 84 / 220 ) * ( 83 / 219 ) 84 / 220 is close to ( 21 / 55 ) and ( 83 / 219 ) = ( 36 / 95 ) so answer is ( 21 / 55 ) * ( 36 / 95 ) = ( 11 / 76 ) so , answer will be c"
Answer: c
Python program:
a = 84 - 1
b = 84 * a
c = 220 - 1
d = 220 * c
e = b / d
Problem: after decreasing 20 % in the price of an article costs rs . 600 . find the actual cost of an article ?
Options: a ) 775 , b ) 620 , c ) 53 , d ) 530 , e ) 220
Rationale: "cp * ( 80 / 100 ) = 600 cp = 7.75 * 100 = > cp = 775 answer : a"
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 600 / b
Problem: the average score of a cricketer in 2 matches is 27 and in other 3 matches is 32 . then find the average score in all the 5 matches ?
Options: a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 27 + 3 * 32 ) / 2 + 3 = 54 + 96 / 5 = 30 answer is c"
Answer: c
Python program:
a = 2 * 27
b = 3 * 32
c = a + b 
d = c / 5
Problem: the number of singles that a baseball player hit increased 18 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 6 percent . if the total number of singles and doubles that she hit increased 3 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 1 : 3 , b ) 4 : 5 , c ) 1 : 5 , d ) 2 : 5 , e ) 3 : 5
Rationale: "soln : - 1.18 s + 0.94 d = 1.03 [ s + d ] 0.15 s = 0.09 d s / d = 3 / 5 answer : e"
Answer: e
Python program:
a = 100 - 6
b = 100 + 18 
c = a / b
Problem: if a and d are both integers , a > d , and - 3 c > 19 , then the largest value of d would be ?
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10
Rationale: no , your thinking is incorrect . when we know that a > d and a < - 6.33 , the largest value of a can be - 7 while if a = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < a and a = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d
Answer: d
Python program:
a = 19 / 3
b = math.floor(a)
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 6 inches on a side and costs $ 10 , and a large pizza that measures 9 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 9 square inches , b ) 10 square inches , c ) 15 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 6 * 6 = 36 ) for the small pizza and ( 9 * 9 = 81 ) for the large pizza . in total sq inches that would be ( 36 + 81 ) * 2 = 234 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 81 = 243 sq inches . hence , the difference is 9 square inches more ( 243 - 234 ) . the correct answer is a"
Answer: a
Python program:
a = 9 ** 2
b = a * 3
c = 6 ** 2
d = 9 ** 2
e = c + d 
f = 6 ** 2
g = 9 ** 2
h = f + g 
i = e + h 
j = b - i
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 20 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 12.6 , b ) 1.21 , c ) 1.25 , d ) 12.4 , e ) 12.7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 20 ? - - - 1 = > rs . 1 100 - - - 80 ? - - - 1 = > rs . 1.25 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 100
c = b / 20
d = 20 / 100
e = d * 100
f = c / e
g = f * 100
Problem: john found that the average of 15 numbers is 40 . if 12 is added to each number then the mean of number is ?
Options: a ) 52 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 52 option a"
Answer: a
Python program:
a = 40 + 12
Problem: a and b together can do a piece of work in 2 days . if a alone can do the same work in 22 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
Rationale: "b = 1 / 2 – 1 / 22 = 0.45 days answer : b"
Answer: b
Python program:
a = 1/(2)
b = 1/(22)
c = a - b
d = 1/(c)
Problem: if 1 / ( x + 3 ) + 1 / ( x - 3 ) = 1 / ( x + 3 ) , what is the value of x ?
Options: a ) 2 , b ) 3 , c ) - 1 , d ) - 2 , e ) - 3
Rationale: "if we solve the question , we get x = - 3 . option : e"
Answer: e
Python program:
a = 1 + 1 
b = a - 1
Problem: the area of a square field is 1600 km 2 . how long will it take for a horse to run around at the speed of 16 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 1600 km 2 . then , each side of field = √ 1600 = 40 km distance covered by the horse = perimeter of square field = 40 × 4 = 160 km ∴ time taken by horse = distances / peed = 160 / 16 = 10 h answer b
Answer: b
Python program:
a = math.sqrt(1600)
b = 4 * a
c = b / 16
Problem: how many 4 - digit positive integers can be formed by using the digits from 1 to 9 so that two digits are equal to each other and the remaining two are also equal to each other but different from the other two ? .
Options: a ) 400 , b ) 1728 , c ) 108 , d ) 216 , e ) 432
Rationale: the number of ways u can chose two digits from 9 digits is 9 c 2 = ( 9 * 8 ) / 2 . and the no of ways u can arrange two digits like asked is 4 c 2 = ( 4 * 3 ) / 2 . total ways is 36 * 6 = 216 . answer : d
Answer: d
Python program:
a = 9 - 1
b = 9 * a
c = b / 2
d = 4 * 3
e = d / 2
f = c * e
Problem: the charge for a single room at hotel p is 50 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 45 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: p = 0.5 r = 0.9 g r = 0.9 g / 0.5 = 1.8 * g thus r is 80 % greater than g . the answer is d .
Answer: d
Python program:
a = 100 - 50
b = 100 - 10
c = a / b
d = c * 100
e = 100 - d
f = 100 - 50
g = 100 - 10
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: 0.009 / x = 0.03 . find the value of x
Options: a ) 0.0003 , b ) 0.03 , c ) 0.3 , d ) 3 , e ) 30
Rationale: "x = 0.009 / 0.03 = 0.3 answer : c"
Answer: c
Python program:
a = 0 / 9
Problem: a man rows his boat 90 km downstream and 70 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 3.5 kmph , d ) 4.5 kmph , e ) 4 kmph
Rationale: "speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 70 / ( 3 ) = 23 kmph the speed of the stream = ( 30 - 23 ) / 2 = 3.5 kmph answer : c"
Answer: c
Python program:
a = 90 / 3
b = 70 / 3
c = a - b
d = c / 2
Problem: one night 18 percent of the female officers on a police force were on duty . if 180 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 180 number of female officers on duty on that night = 180 / 2 = 90 ( 18 / 100 ) * f = 90 = > f = 500 answer d"
Answer: d
Python program:
a = 180 / 2
b = 18 / 100
c = a / b
Problem: there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 24 plants . how many birches and roses were planted ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of roses . then the number of birches is 24 − x , and the number of boys is 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 216 − 72 = 8 x 1448 = x x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . so answer is d ."
Answer: d
Python program:
a = 3 * 24
b = a - 24
c = 3 * 3
d = c - 1
e = b / d
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,900 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,900 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.9 so , answer is d ."
Answer: d
Python program:
a = 100 * 100
b = a * 4
Problem: if shares of two persons in profits are rs . 400 and rs . 1200 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: profit = time * capital so 400 : 1200 = 1 : 3 answer : d
Answer: d
Python program:
a = 400 / 1200
Problem: rectangular tile each of size 60 cm by 56 cm must be laid horizontally on a rectangular floor of size 560 cm by 240 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 54 , c ) 47 , d ) 40 , e ) 45
Rationale: "area of tile = 60 * 56 = 3360 area of floor = 560 * 240 = 134400 no of tiles = 134400 / 3360 = 40 so , the no of tile = 40 answer : d"
Answer: d
Python program:
a = 560 * 240
b = 60 * 56
c = a / b
Problem: the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 10 , then their difference is
Options: a ) 10 , b ) 46 , c ) 70 , d ) 90 , e ) none
Rationale: "solution let the numbers be x and ( 100 - x ) . then , x ( 100 - x ) = 5 × 495 ‹ = › x 2 - 100 x + 2475 = 0 . ‹ = › ( x - 55 ) ( x - 45 ) = 0 . x = 55 or x = 45 . therefore , the numbers are 45 and 55 . required difference = ( 55 - 45 ) = 10 . answer a"
Answer: a
Python program:
a = 5 * 495
b = a / 10
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 9 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 304 , e ) 320
Rationale: 4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with two 9 - s , 9 x 9 x 4 * 1 * 4 * 1 = 16 . thus there are 320 - 16 = 304 such numbers . answer : d .
Answer: d
Python program:
a = 4 + 1 
b = 4 + 1 
c = a * b
d = 4 * 4
e = c * d
f = 4 + 1 
g = 4 + 1 
h = f * g
i = h * 4
j = e - i
Problem: there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 45 , then find the smaller number ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 88 , e ) 75
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 45 3 x = 45 = > x = 15 = > smaller number = 5 x = 75 . answer : e"
Answer: e
Python program:
a = 45 * 5
b = a / 4
Problem: the sum of ages of 4 children born 2 years different each is 36 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 17
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 36 4 x = 24 x = 6 . x + 6 = 6 + 6 = 12 answer : d"
Answer: d
Python program:
a = 2 + 4 
b = 2 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 36 
g = f / 4
Problem: if ajay completes a certain work in 8 days and vijay can complete the same work in 24 days , find the time in which the work will be completed if both ajay and vijay work together .
Options: a ) 6 days , b ) 9 days , c ) 2 days , d ) 7 days , e ) 1 days
Rationale: explanation : on working together ajay and vijay can complete the work in ( 8 * 24 ) / ( 8 + 24 ) = 192 / 32 = 6 days answer : a
Answer: a
Python program:
a = 1/(8)
b = 1/(24)
c = a + b 
d = 1/(c)
Problem: a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 14 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 12.05 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 14 = 12.05 cm answer is b"
Answer: b
Python program:
a = volume_cube / (
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 9 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 144 , c ) 104 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 9 ) * 360 = 40 gallons . remaning paint = 320 gallons paint used in the second week = ( 1 / 5 ) * 320 = 64 gallons total paint used = 104 gallons . option c"
Answer: c
Python program:
a = 360 / 9
b = a * 1
c = 360 / 9
d = c * 1
e = 360 - d
f = e / 5
g = b + f
Problem: what is the sum of 59 consecutive integers from - 29 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 29 , c ) - 30 , d ) 0 , e ) 60
Rationale: "from - 29 to - 1 - - > 29 nos . zero - - > 1 number from + 1 to + 29 - - > 29 nos . when we add up nos . from - 29 to + 29 sum will be zero for total 59 nos . sum of these 59 nos . = 0 . d is the answer ."
Answer: d
Python program:
a = 29 + 1
Problem: if an integer n is to be selected at random from 1 to 400 , inclusive , what is probability n ( n + 1 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 8 , either n or n + 1 has to be a multiple of 8 . thus n must be of the form 8 k or 8 k - 1 . the probability is 2 / 8 = 1 / 4 . the answer is a ."
Answer: a
Python program:
a = 2 / 8
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 185 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 2 : 1 , e ) 3 : 1
Rationale: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 185 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 185 m ) / ( w + m ) = 180 170 w + 185 m = 180 w + 180 m 5 m = 10 w m = 2 w m / w = 2 / 1 the ratio of men to women is 2 to 1 . d"
Answer: d
Python program:
a = 180 - 170
b = 185 - 180
c = a / b
Problem: a and b start walking towards each other at 6 pm at speed of 4 kmph and 6 kmph . they were initially 18 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 pm , c ) 7 pm , d ) 10 pm , e ) 5 pm
Rationale: "time of meeting = distance / relative speed = 18 / 6 + 3 = 18 / 9 = 2 hrs after 6 pm = 8 pm answer is a"
Answer: a
Python program:
a = 4 + 6 
b = 18 / a
c = 6 + b