euclaise/mathqa_programs huggingface dataset:
Problem: a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 40 - sided polygon have ?
Options: a ) 875 , b ) 740 , c ) 1425 , d ) 2025 , e ) 2500
Rationale: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 40 . plugging it in , we get 740 diagonals ! answer ( b ) ."
Answer: b
Python program:
a = 40 - 3
b = a * 40
c = b / 2
Problem: in covering a distance of 24 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 4 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 7.8 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 24 / x - 24 / 2 x = 3 6 x = 24 x = 4 km / hr . answer : option a"
Answer: a
Python program:
a = 24 / 2
b = 24 - a
c = 1 + 2 
d = b / c
Problem: 20 workers can finish a work in 30 days . after how many days should 5 workers leave the job so the work is completed in 35 days ?
Options: a ) 7 , b ) 6 , c ) 15 , d ) 4 , e ) 3
Rationale: work done by 15 workers in 35 days = 15 * 35 = 525 men days . now , work remaining = 600 – 525 = 75 men days and we have 5 workers . so 5 workers will work for 75 / 5 = 15 days . answer : c
Answer: c
Python program:
a = 20 * 30
b = 20 - 5
c = b * 35
d = a - c
e = d / 5
Problem: a glass was filled with 10 ounces of water , and 0.02 ounce of the water evaporated each day during a 30 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.006 % , b ) 0.06 % , c ) 6 % , d ) 2 % , e ) 60 %
Rationale: "in 30 days 30 * 0.02 = 0.6 ounces of water evaporated , which is 0.6 / 10 â ˆ — 100 = 6 of the original amount of water . answer : c ."
Answer: c
Python program:
a = 0 * 2
b = a / 10
c = b * 100
Problem: a train 284 m in length crosses a telegraph post in 18 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 57 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: "s = 284 / 18 * 18 / 5 = 57 kmph answer : c"
Answer: c
Python program:
a = 284 / 18
b = const_3_6 * a
Problem: roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be 3 times as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108
Rationale: r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d .
Answer: d
Python program:
a = 8 + 2 
b = 3 * 2
c = a - b
d = 3 - 1
e = c / d
f = 8 + 2 
g = e + f 
h = 8 + 2 
i = 3 * 2
j = h - i
k = 3 - 1
l = j / k
m = 8 + 2 
n = l + m 
o = 8 / 2
p = n - o
q = g * p
Problem: a mixture of 120 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 2 liters , b ) 3 liters , c ) 8 liters , d ) 5 liters , e ) 7 liters
Rationale: number of liters of water in 120 liters of the mixture = 20 % of 120 = 20 / 100 * 120 = 24 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 24 + p ) and total volume of mixture is ( 120 + p ) . ( 24 + p ) = 25 / 100 * ( 120 + p ) 96 + 4 p = 120 + p p = 8 liters . answer : c
Answer: c
Python program:
a = 25 / 100
b = a * 120
c = 20 / 100
d = c * 120
e = b - d
f = 25 / 100
g = 1 - f
h = e / g
Problem: 5 friends visited a fruit stall , and everyone decided to contribute equally to the total bill of $ 100 . if one of the friends had a coupon for 6 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) 18 , b ) 18.8 , c ) 19 , d ) 17.8 , e ) 17.9
Rationale: at the non - discounted price , each friend would pay $ 20 , as $ 100 divided by 5 friends is $ 20 per friend . but if the bill is 6 % off , then each friend would pay 6 % less . 6 % of $ 20 is $ 1.2 , so each friend saves $ 1.2 and pays the remaining 18.8 correct option : option b
Answer: b
Python program:
a = 6 * 100
b = a / 100
c = 100 - b
d = c / 5
Problem: a certain country is divided into 5 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 15 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 15 the total number of traditionalists is 5 p / 15 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Python program:
a = 5 / 15
b = 5 / 15
c = b + 1 
d = a / c
e = 1 - d
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22050 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 25 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22050 / - - 17640 / - = rs . 4410 / - rate of interest = ( 4410 / 17640 ) × ( 100 / 1 ) = > 25 % answer : option e"
Answer: e
Python program:
a = 22050 - 17640
b = a / 17640
c = b * 100
Problem: which number can we add to 859722 to get a number exactly divisible by 456 ?
Options: a ) 294 , b ) 306 , c ) 318 , d ) 338 , e ) 362
Rationale: "859722 / 456 = 1885 with a remainder of 162 . we need to add 456 - 162 = 294 the answer is a ."
Answer: a
Python program:
a = 456 - reminder
Problem: find the l . c . m of 12 , 25 , 24 and 20 .
Options: a ) 240 , b ) 600 , c ) 320 , d ) 150 , e ) 250
Rationale: "explanation : 6 x 2 x 2 x 5 x 5 = 600 answer : option b"
Answer: b
Python program:
a = 3 ** 3
b = 2 ** 3
c = 4 + 1 
d = c ** 2
e = b * d
f = a * e
g = 24 / 2
h = g / 2
i = h / 3
j = 4 + 1 
k = i / j
l = 4 + 1 
m = k / l
n = f * m
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 3 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min
Rationale: speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 3 4 - - - - - - - - - ? è 12 answer : e
Answer: e
Python program:
a = 5 / 4
b = 3 / a
c = b * 5
Problem: what is the probability of getting a sum 9 from two throws of a dice ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) none of these
Rationale: "in two throws of a dice , n ( s ) = ( 6 x 6 ) = 36 . let e = event of getting a sum = { ( 3 , 6 ) , ( 4 , 5 ) , ( 5 , 4 ) , ( 6 , 3 ) } . p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 . answer : c"
Answer: c
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: in the hillside summer camp there are 100 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 150 . , b ) 145 . , c ) 100 . , d ) 30 . , e ) 25 .
Rationale: "given there are 100 students , 90 % of 50 = 90 boys and remaining 10 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 1000 to existing 90 then the count will be 190 and the girls number will be 10 as it . now boys are 95 % and girls are 5 % . ( out of 200 students = 190 boys + 10 girls ) . imo option c is correct ."
Answer: c
Python program:
a = 100 - 5
b = a / 100
c = b * 100
d = 5 / 100
e = d * 100
f = c + e
Problem: what is the sum of the integers from - 185 to 195 inclusive ?
Options: a ) 0 , b ) 5 , c ) 375 , d ) 1905 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = - 185 + 195 / 2 = 5 number of items ( n ) = b - a + 1 = 195 - ( - 185 ) + 1 = 195 + 186 = 381 . sum = average * n = 5 * 381 = 1905 . answer is d"
Answer: d
Python program:
a = 185 * 195
b = a / 4
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 2 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 6 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 6 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 6 ) , which indeed is 6 / 22 . e"
Answer: e
Python program:
a = math.comb(5, 2)
b = math.comb(3, 1)
c = a * b
d = 5 + 4 
e = d + 3 
f = math.comb(e, 3)
g = c / f
Problem: 10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is ?
Options: a ) 1 , b ) 7 , c ) 3 , d ) 9 , e ) 2
Rationale: total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be years . then , age of the elder child = years . so , age of younger child = 3 years . answer : c
Answer: c
Python program:
a = 4 + 2 
b = 24 * a
c = 24 * 4
d = 10 * 4
e = c + d 
f = b - e
g = f - 2
h = g / 2
Problem: a certain quantity of 70 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9
Rationale: let ' s say that the total original mixture a is 100 ml the original mixture a thus has 70 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 70 ml and 25 ml is 45 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 45 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 35 % . therefore , 35 out of 45 is 7 / 9 and e is the answer .
Answer: e
Python program:
a = 35 - 25
b = 70 - 35
c = a / b
d = c + 1 
e = 1/(d)
Problem: f 1 ( x ) f 1 ( x ) = 2 x - 1 and fn ( x ) = f 1 ( fn − 1 ( x ) ) fn ( x ) = f 1 ( fn − 1 ( x ) ) for n ≥ ≥ 2 . find f 5 ( 2 )
Options: a ) 7 , b ) 6 , c ) 78 , d ) 9 , e ) 1
Rationale: answer : a
Answer: a
Python program:
a = 2 + 5
Problem: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 22 boys and 38 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 22 boys . so 22 - 6 - 6 = 10 boys must be neither happy nor sad . answer ( e )"
Answer: e
Python program:
a = 10 - 4
b = 22 - a
c = b - 6
Problem: real - estate salesman z is selling a house at a 10 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 10 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 10 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 38 / 6 , b ) 38 / 5 , c ) 77 / 81 , d ) 38 / 7 , e ) 38 / 10
Rationale: "let the retail price be = x selling price of z = 0.90 x selling price of x = 0.90 * 0.90 x = 0.81 x selling price of y = ( ( 0.90 x + 0.81 x ) / 2 ) * 0.90 = 0.86 x * 0.90 = 0.77 x 0.77 x = k * 0.81 x k = 0.77 / 0.81 = 77 / 81 answer : c"
Answer: c
Python program:
a = 100 - 10
b = 100 - 10
c = 100 - 10
d = c / 100
e = b * d
f = a + e 
g = f / 2
h = 100 - 10
i = g * h
j = i / 100
k = 100 - 10
l = 100 - 10
m = l / 100
n = k * m
o = j / n
p = o * 10
Problem: find the distance covered by a man walking for 42 min at a speed of 10 km / hr ?
Options: a ) 7 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 42 / 60 = 7 km answer is a"
Answer: a
Python program:
a = 10 * 1000
b = a / const_60
c = 42 * b
d = c / 1000
Problem: the output of a factory was increased by 15 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 27 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: the original output increases by 15 % and then 20 % . total % change = a + b + ab / 100 total % change = 15 + 20 + 15 * 20 / 100 = 38 % now , you want to change it to 0 , so , 0 = 38 + x + 38 x / 100 x = - 38 ( 100 ) / 138 = 27 % approximately answer is b
Answer: b
Python program:
a = 100 + 15 
b = 100 + 15 
c = 20 / 100
d = b * c
e = a + d 
f = e - 100
g = f * 100
h = 100 + 15 
i = 100 + 15 
j = 20 / 100
k = i * j
l = h + k 
m = g / l
Problem: in a sample of associates at a law firm , 30 percent are second - year associates , and 60 percent are not first - year associates . what percentage of the associates at the law firm have been there for more than two years ?
Options: a ) 10 , b ) 20 , c ) 30 % , d ) 40 , e ) 50
Rationale: let the sample be 100 . given 60 % are not first year i . e . there could be second year ( x ) and more than 2 years ( y ) possibility . 60 % = ( x ) + y given 30 % = second year ( x ) club both , we get y = 30 % . answer : option c is correct answer .
Answer: c
Python program:
a = 60 - 30
Problem: in a company of 160 employees , 90 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with college degree only , how many employees are females with advanced degrees ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "the number of males is 160 - 90 = 70 . the number of males with advanced degrees is 70 - 40 = 30 . the number of females with advanced degrees is 80 - 30 = 50 . the answer is c ."
Answer: c
Python program:
a = 160 - 90
b = a - 40
c = 80 - b
Problem: in business , a and c invested amounts in the ratio 3 : 2 , whereas the ratio between amounts invested by a and b was 3 : 1 , if rs 60000 was their profit , how much amount did c receive .
Options: a ) 10000 , b ) 20000 , c ) 15000 , d ) 61000 , e ) 26000
Rationale: "explanation : a : b = 3 : 1 = 3 : 1 = > a : c = 3 : 2 = 3 : 2 = > a : b : c = 3 : 1 : 2 c share = ( 2 / 6 ) * 60000 = 20000 option b"
Answer: b
Python program:
a = 1 + 3 
b = a * 1
c = b * 100
d = c * 100
e = 2 + 2 
f = e + 1 
g = 3 / 0
h = d * g
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 50 , and what number ?
Options: a ) 40 , b ) 45 , c ) 55 , d ) 45 , e ) 50
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 60 = 45 d"
Answer: d
Python program:
a = 20 + 40 
b = a + 60 
c = 5 * 3
d = c + 10 
e = d + 50 
f = b - e
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 49 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 49 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 49 ( x - y ) - - > x + y = 49 . answer : d ."
Answer: d
Python program:
a = math.floor(49)
Problem: how many times will the digit 4 be written when listing the integers from 1 to 1000 ?
Options: a ) 512 , b ) 300 , c ) 294 , d ) 264 , e ) 385
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 4 ) 3000 / 10 = 300 times . answer : b ."
Answer: b
Python program:
a = 1 * 10
b = a * 10
c = b * 3
Problem: jonathan can type a 20 page document in 50 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 11 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 20 / 50 + 20 / 30 + 20 / 24 = 20 / x if you solve this equation , you get the same answer b ( 11 )
Answer: b
Python program:
a = 20 / 24
b = 20 / 50
c = 20 / 30
d = b + c 
e = a + d 
f = 20 / e
Problem: in a certain village , 150 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 6000 litres of water last ?
Options: a ) 8 , b ) 10 , c ) 6 , d ) 2 , e ) 4
Rationale: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 150 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 150 * 10 = 1500 ( m * n ) water available is 6000 ( p ) it will last 4 months ( p / m * n ) ans : e"
Answer: e
Python program:
a = 150 * 10
b = 6000 / a
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 20 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 11 and 8 , d ) 3 and 10 , e ) 10 and 10
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 20 cm 2 more than the first area . therefore a 1 + 20 = a 2 x ( x − 3 ) + 20 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 20 = x 2 + x − 2 x − 2 2 x = 22 x = 11 . so , the sides of the rectangle are 11 cm and ( 11 − 3 ) = 8 cm long . so answer is c ."
Answer: c
Python program:
a = 20 / 2
b = a + 1 
c = b - 3
Problem: a rope of which a calf is tied is increased from 12 m to 18 m , how much additional grassy ground shall it graze ?
Options: a ) 1217 , b ) 1219 , c ) 1210 , d ) 565.7 , e ) 1312
Rationale: "π ( 182 – 122 ) = 565.7 answer : d"
Answer: d
Python program:
a = 18 ** 2
b = 10 ** 2
c = a - b
d = 12 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 2 . ?
Options: a ) 66 , b ) 87 , c ) 75 , d ) 88 , e ) 90
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 75 meets this description sum of digits - - - 7 + 5 = 12 difference of digits - - - 7 - 5 = 2 answer c ."
Answer: c
Python program:
a = 2 * 2
b = 2 + 4 
c = a * b
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 24 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: l = r l = 3 c r = c + 24 3 c = c + 24 c = 12 the answer is d .
Answer: d
Python program:
a = 3 - 1
b = 24 / a
Problem: what is 25 % of 4 / 12 of 520 ?
Options: a ) 49 , b ) 56 , c ) 60 , d ) 43 , e ) 70
Rationale: 25 % = 25 / 100 = 1 / 4 of 4 / 12 = 1 / 4 * 4 / 12 = 1 / 12 of 520 = 1 / 12 * 520 = 43.33 = = 43 ans - d
Answer: d
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 25 * n
p = o / 100
Problem: 42 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 16 , c ) 13 , d ) 14 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 42 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 42 x 5 x 12 x = ( 42 x 5 x 12 ) / ( 30 x 6 ) x = 14 answer d"
Answer: d
Python program:
a = 42 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 30 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 27 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 30 % of 200 seeds germinated , so 0.30 x 200 = 60 seeds germinated . since 75 + 60 = 135 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 135 / 500 ) x 100 % , or 27 % . answer : a ."
Answer: a
Python program:
a = 25 / 100
b = a * 300
c = 30 / 100
d = c * 200
e = b + d 
f = 300 + 200 
g = e / f
h = g * 100
Problem: if x : y = 1 : 4 , then find the value of ( 7 x + 3 y ) : ( 2 x + y )
Options: a ) 14 : 5 , b ) 15 : 5 , c ) 16 : 5 , d ) 19 : 6 , e ) none of these
Rationale: explanation : let x = 1 k and y = 4 k , so = 7 ( k ) + 3 ( 4 k ) / 2 ( k ) + 1 ( 4 k ) = 19 k / 6 k = 19 : 6 option d
Answer: d
Python program:
a = 3 * 4
b = a + 7 
c = 2 + 4 
d = b / c
Problem: ages of two persons differ by 24 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 16,32 , d ) 18,42 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 24 ) = > 3 ( x - 6 ) = ( x + 24 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 18 = > x = 18 . so other person age is x + 24 = 42 answer : option d"
Answer: d
Python program:
a = 6 * 6
b = a + 24 
c = b - 6
d = 6 - 1
e = c / d
f = e - 1
Problem: john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 55 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 45 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 55 = 45 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 45 / 100 ) * 100 = ( 0.45 ) * 100 = 45 % . e"
Answer: e
Python program:
a = 100 - 55