euclaise/mathqa_programs huggingface dataset:
Problem: one fourth of a solution that was 12 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 28 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "instead of using complex calculations and remembering formulae , why dont u directly get to weighted average . 3 parts of 12 % + 1 part of x ( unknown ) % = 4 parts of 16 % = > x % = 64 % - 36 % = 28 % ans b it is ."
Answer: b
Python program:
a = 16 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 12 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
Problem: a palindrome is a number that reads the same forward and backward , such as 144 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 62 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 12 = 62 ways d"
Answer: d
Python program:
a = 4 / 2
b = 10 ** a
c = b / 2
Problem: a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 30 - sided polygon have ?
Options: a ) 875 , b ) 405 , 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 = 30 . plugging it in , we get 405 diagonals ! answer ( b ) ."
Answer: b
Python program:
a = 30 - 3
b = a * 30
c = b / 2
Problem: a batsman makes a score of 66 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 31 , c ) 27 , d ) 29 , e ) 18
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 66 = total runs scored in 17 innings = > 16 ( x - 3 ) + 66 = 17 x = > 16 x - 48 + 66 = 17 x = > x = 18 answer is e ."
Answer: e
Python program:
a = 17 * 3
b = 66 - a
c = b + 3
Problem: find the value of e from ( 14 ) ^ 2 x 5 ^ 3 ã · 568 = e .
Options: a ) 13.1 , b ) 43.1 , c ) 40.1 , d ) 23.1 , e ) 45.1
Rationale: given exp . = ( 14 ) ^ 2 x 5 ^ 3 ã · 568 = e = 196 x 125 ã · 568 43.1 b
Answer: b
Python program:
a = 14 ** 2
b = 5 ** 3
c = a * b
d = c / 568
Problem: a cube of side one meter length is cut into small cubes of side 5 cm each . how many such small cubes can be obtained ?
Options: a ) 2878 , b ) 8000 , c ) 1000 , d ) 2997 , e ) 2701
Rationale: "along one edge , the number of small cubes that can be cut = 100 / 5 = 20 along each edge 5 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : b"
Answer: b
Python program:
a = 5 ** 2
b = a ** 3
c = 5 ** 3
d = b / c
Problem: if 0.75 of a number is equal to 0.025 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 1 : 30 , d ) 20 : 3 , e ) 30 : 7
Rationale: "0.75 a = 0.025 b - > a / b = 0.025 / 0.75 = 25 / 750 = 1 / 30 : . a : b = 1 : 30 answer : c"
Answer: c
Python program:
a = 0 * 25
b = 0 * 75
c = a / b
Problem: a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 60 minutes and a model y computer can complete the same task in 30 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model x computers were used ?
Options: a ) 18 , b ) 16 , c ) 15 , d ) 17 , e ) 20
Rationale: "let ' s say 1 work is processing 60 gb of data . model x : 1 gb per min model y : 2 gb per min working together , 1 x and 1 y = 3 gb per min so , 20 times as many computers would work at 60 gb per min . so no . of x = 20 answer is e"
Answer: e
Python program:
a = 60 * 30
b = 60 + 30 
c = a / b
Problem: a certain number of men can do a work in 40 days . if there were 5 men less it could be finished in 10 days more . how many men are there ?
Options: a ) 15 men , b ) 25 men , c ) 18 men , d ) 12 men , e ) 14 men
Rationale: "explanation : x * 40 = ( x - 5 ) * 50 5 x - 4 x = 25 x = 25 men answer : option b"
Answer: b
Python program:
a = 40 + 10 
b = a * 5
c = b / 10
Problem: mike earns $ 12 per hour and phil earns $ 6 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 50 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 12 is 6 let it be x % less , then = 12 ( 1 - x / 100 ) = 6 1 - x / 100 = 6 / 12 x = 100 / 2 x = 50 % ans a"
Answer: a
Python program:
a = 6 / 12
b = a * 100
Problem: a can do a job in 45 days and b can do it in 30 days . a and b working together will finish four times the amount of work in - - - - - - - days ?
Options: a ) 30 days , b ) 45 days , c ) 80 days , d ) 72 1 / 2 days , e ) 72 days
Rationale: "1 / 45 + 1 / 30 = 5 / 90 = 1 / 18 18 / 1 = 18 * 4 = 72 days answer : e"
Answer: e
Python program:
a = 1 / 45
b = 1 / 30
c = a + b
Problem: a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 982 in total compensation , how many total hours did he work that week ?
Options: a ) 57 , b ) 51 , c ) 59 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 982 - 560 = 422 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 422 / 24.5 = 17.2 = 17 approx . total hrs = 40 + 17 = 57 answer a"
Answer: a
Python program:
a = 14 * 40
b = 982 - a
c = 100 + 75 
d = 14 * c
e = d / 100
f = b / e
g = 40 + f
Problem: the least number which when divided by 3 , 4 , 5 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 167 , b ) 243 , c ) 252 , d ) 336 , e ) none of these
Rationale: "explanation : l . c . m of 3 , 4 , 5 , 8 = 120 therefore required number is of the form 120 k + 3 . least value of k for which ( 120 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 120 x 2 + 3 ) = 243 answer : b"
Answer: b
Python program:
a = math.lcm(3, 4)
b = math.lcm(a, 5)
c = math.lcm(b, 8)
d = c * 2
Problem: 70 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 71 , c ) 27 , d ) 61 , e ) 81
Rationale: "explanation : 70 + 5 * 12 / ( 180 / 3 ) = 70 + 5 * 12 / ( 60 ) = 70 + ( 5 * 12 ) / 60 = 70 + 1 = 71 . answer : b"
Answer: b
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 70 + c
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 4 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54 , b ) 32 , c ) 75 , d ) 28 , e ) 16
Rationale: "a / 8 = 4 * 4 = > a = 4 * 4 * 8 x * 2 x = 4 * 4 * 8 x = 8 = > 2 x = 16 answer : e"
Answer: e
Python program:
a = square_area * (
b = a / 8
c = 1/(2)
d = math.sqrt(b)
Problem: 14 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 27.5 days , b ) 15.5 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days
Rationale: "14 * 25 = 20 * x = > x = 17.5 days answer : c"
Answer: c
Python program:
a = 25 * 14
b = a / 20
Problem: a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 50 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 276 , b ) 271 , c ) 200 , d ) 278 , e ) 268
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 50 - 40 ) = 4 hours so , the two trains meet at 2 p . m . the two trains meet 4 * 50 = 200 km away from mumbai . answer : c"
Answer: c
Python program:
a = 40 * 1
b = 50 - 40
c = a / b
d = c * 50
Problem: reduce 368 / 598 to the lowest terms
Options: a ) 30 / 25 , b ) 28 / 13 , c ) 28 / 29 , d ) 8 / 13 , e ) none of these
Rationale: explanation : we can do it easily by in two steps step 1 : we get the hcf of 368 and 598 which is 46 step 2 : divide both by 46 , we will get the answer 8 / 13 answer : option d
Answer: d
Python program:
a = 368 / 598
Problem: a , b and c started a partnership business by investing rs . 5000 , rs . 8000 , rs . 9000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 88000 , d ) 90000 , e ) 50000
Rationale: "a : b : c = 5000 : 8000 : 9000 = 5 : 8 : 9 let total profit = p then p ã — 9 / 22 = 36000 p = ( 36000 ã — 22 ) / 9 = 88000 answer is c ."
Answer: c
Python program:
a = 5000 / 9000
b = a * 36000
c = 8000 / 9000
d = c * 36000
e = b + d 
f = e + 36000
Problem: 5 n + 2 > 12 and 7 n - 5 < 37 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 6
Rationale: "5 n > 10 - - > n > 2 7 n < 42 - - > n < 6 2 < n < 6 answer : e"
Answer: e
Python program:
a = 2 * 10
b = 37 + 5 
c = b / 7
d = a + c
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 5 / 100 x 12000 ) = rs . 600 . answer b"
Answer: b
Python program:
a = 10 * 1000
b = 4 * 1000
c = a + b 
d = 4 * 100
e = c + d 
f = 20 / 100
g = 100 * f
h = 100 + g 
i = e / h
j = 100 * i
k = 5 / 100
l = j * k
Problem: two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 49 . find the ratio of their corresponding heights .
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 4 / 7 , e ) 2 / 3
Rationale: "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 16 / 49 - - > height / height = 4 / 7 . answer : d ."
Answer: d
Python program:
a = math.sqrt(16)
b = math.sqrt(49)
c = a / b
Problem: two numbers are respectively 50 % and 100 % more than a third number . the percentage that is first of the second is ?
Options: a ) 65 % , b ) 83 % , c ) 27 % , d ) 42 % , e ) 75 %
Rationale: "i ii iii 150 200 100 200 - - - - - - - - - - 150 100 - - - - - - - - - - - ? = > 75 % answer : e"
Answer: e
Python program:
a = 50 + 100 
b = 100 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: if an object travels 300 feet in 5 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 39 , b ) 38 , c ) 40 , d ) 41 , e ) 34
Rationale: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 300 feet in 5 sec then it travels 300 / 5 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 60 feet in 1 hour = 216000 feet in 1 hr = 216000 / 5280 miles in 1 hour = 21600 / 528 miles / hr ~ 41 miles / hr answer - d"
Answer: d
Python program:
a = 300 / 5280
b = 1 / 3600
c = 5 * b
d = a / c
Problem: rs . 875 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 875 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1061 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 875 ) = rs . 81 rate = ( 100 x 81 / 875 x 3 ) = 108 / 35 % new rate = ( 108 / 35 + 4 ) % = 248 / 35 % new s . i . = rs . ( 875 x 248 / 35 x 3 / 100 ) rs . 186 . ∴ new amount = rs . ( 875 + 186 ) = rs . 1061 . answer c"
Answer: c
Python program:
a = 956 - 875
b = a * 100
c = 875 * 3
d = b / c
e = d + 4 
f = 875 * e
g = f * 3
h = g / 100
i = 875 + h
Problem: 0.003 * ? * 0.0003 = 0.00000027
Options: a ) 9 , b ) 3 , c ) 0.3 , d ) 0.03 , e ) none of these
Rationale: "explanation : 0.003 * ? * 0.0003 = 0.00000027 3 / 1000 * ? * 3 / 10000 = 3 / 1000 * 3 / 1000 * 3 / 100 ? = 3 / 10 = 0.3 answer is c"
Answer: c
Python program:
a = 0 * 3
Problem: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3400 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 2040 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 136 so , a ’ s amount = 120 × 15 = rs . 2040 . answer : option c"
Answer: c
Python program:
a = 15 * 2
b = a / 10
c = 15 * 2
d = c / 10
e = 15 * 2
f = e / 15
g = d + f 
h = b / g
i = h * 3400
Problem: what will be the reminder when ( 19 ^ 19 + 19 ) is divided by 20 ?
Options: a ) 18 , b ) 40 , c ) 21 , d ) 43 , e ) 28
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 19 ^ 19 + 1 ) will be divisible by ( 19 + 1 ) ; ( 19 ^ 19 + 1 ) + 18 when divided by 20 will give 18 as remainder . correct option : a"
Answer: a
Python program:
a = 19 ** 19
b = a + 19 
c = 19 ** 19
d = c + 19 
e = d / 20
f = math.floor(e)
g = 20 * f
h = b - g
Problem: a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 12 % . their gross income from sales for one month increases by what percent ?
Options: a ) 0.4 % , b ) 0.8 % , c ) 2 % , d ) 4 % , e ) 8 %
Rationale: "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.12 x = 1.008 * ( p * x ) , an increase of 0.8 % . the answer is b ."
Answer: b
Python program:
a = 12 - 10
b = 12 / 10
c = a - b
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 102 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 102 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 40 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 102 ) / ( 3 / 20 ) = 30 / 54 = 58,5 % it means that 9 / 108 represents only 58,5 % . therefore a decrease of 45 % . answer c"
Answer: c
Python program:
a = 3 / 20
b = a * 100
Problem: the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 55 , then how long is the base of isosceles triangle ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "the base of the isosceles triangle is 55 - 20 - 20 = 15 units the answer is c ."
Answer: c
Python program:
a = 60 / 3
b = 55 - a
c = 60 / 3
d = b - c
Problem: one fourth of one third of two fifth of a number is 10 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 120 , d ) d ) 200 , e ) e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 10 then x = 10 * 30 = 300 40 % of 300 = 120 answer : option c"
Answer: c
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 10 / f
h = g * 40
i = h / 100
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 52 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 22
Rationale: "you should notice that 52 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 22 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . e"
Answer: e
Python program:
a = 11 ** 0
b = a + 1000 
c = b / 52
d = c + 1 
e = d * 52
f = reminder * (
g = f - 10
Problem: find the average of first 8 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 22.5 , e ) 21
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 ) / 8 = 22.5 answer is d"
Answer: d
Python program:
a = 8 + 1 
b = 4 + 0 
c = b + 2 
d = a + c 
e = 5 - 8
f = 5 - 2
g = e + f 
h = d + g 
i = h / 8
Problem: a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 16 heads and 45 legs . how many cats does the ship host ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 8 , e ) 7
Rationale: "a ' s + co + ca + cats = 16 . sa ' s + 1 + 1 + cats = 16 or sa ' s + cats = 14 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 45 sa ' s * 2 + cats * 4 = 42 or sa ' s + cats * 2 = 21 or 14 - cats + cat * 2 = 21 then cats = 7 e"
Answer: e
Python program:
a = 45 - 1
b = 16 - 1
c = b * 2
d = a - c
e = 16 - 1
f = e * 4
g = 16 - 1
h = g * 2
i = f - h
j = d / i
k = 16 - 1
l = j * k
Problem: the lcm of two numbers is 2310 and hcf is 83 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 913 , b ) 825 , c ) 330 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 83 / 210 = 11 * 83 = 913 answer : a"
Answer: a
Python program:
a = 2310 * 83
b = a / 210
Problem: nhai employs 100 men to build a highway of 2 km in 50 days working 8 hours a day . if in 25 days , they completed 1 / 3 part of work . than how many more employees should nhai hire to finish it in time working 10 hours a day ?
Options: a ) 55 , b ) 60 , c ) 70 , d ) 50 , e ) 65
Rationale: explanation : the given problem can be written in a tabular form like below : - men days hour work planned 100 50 8 1 actual 100 25 8 1 / 3 remaining ? 25 10 2 / 3 we can apply chain rule now . total men required to complete the remaining work = 100 × ( 25 / 25 ) × ( 8 / 10 ) × ( 2 / 3 ) / ( 1 / 3 ) = 160 . so additional men required = 160 - 100 = 60 . answer is b
Answer: b
Python program:
a = 100 * 25
b = a * 8
c = 2 * b
d = 25 * 10
e = c / d
f = e - 100
Problem: what least number must be subtracted from 9671 so that the remaining number is divisible by 2 ?
Options: a ) 3 , b ) 1 , c ) 16 , d ) 11 , e ) 15
Rationale: "on dividing 9671 by 2 , we get remainder = 1 . required number be subtracted = 1 answer : b"
Answer: b
Python program:
a = 9671 / 2
b = math.floor(a)
c = b * 2
d = 9671 - c
Problem: find the value of ( 200 + 200 / 90 ) × 90
Options: a ) 18500 , b ) 18200 , c ) 17500 , d ) 16500 , e ) 13500
Rationale: "( 18000 + 200 ) / 90 * 90 = 18200 answer : b"
Answer: b
Python program:
a = 200 / 90
b = a + 200 
c = b * 90
Problem: mr . loyd wants to fence his square shaped land of 130 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 52
Rationale: "if each side is 120 feet . . then total perimeter is 130 * 4 = 520 poles every 10 feet hence no of poles = 520 / 10 = 52 answer : e"
Answer: e
Python program:
a = 130 * 4
b = a / 10
c = b / 2
Problem: a beekeeper has 600000 bees living in 4 beehives . among these beehives , the sizes of the beehives are proportional to the numbers of bees living in them . no beehive has less than 80 % the number of bees of any other beehive . what is the maximum possible number of bees that the greatest beehive could have ?
Options: a ) 20,000 , b ) 176470 , c ) 10000 , d ) 13000 , e ) 56600
Rationale: x be the # of bees in the hive with the max # of bees . let other hives have same # of bees . so , x + 3 * ( 0.8 ) * x = 600,000 = > 3.4 x = 600,000 = > x = 176470 . b is the answer .
Answer: b
Python program:
a = 80 - 10
b = 600000 / 100
c = 1000 * 10
d = 600000 / 4
e = c + d 
f = 1000 * 10
g = e + f 
h = b + g 
i = 100 * 4
j = h + i 
k = a + j
Problem: if 36 men can do a piece of work in 25 hours , in how many hours will 10 men do it ?
Options: a ) 22 , b ) 38 , c ) 60 , d ) 88 , e ) 90
Rationale: explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 10 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 10 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 10 } = 90 hence , 10 men can do it in 90 hours . answer : e ) 90
Answer: e
Python program:
a = 36 * 25
b = a / 10
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 10 percent on food , and 40 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 10 , others = 40 tax on clothing = 2 tax on others = 3.2 percentage = 5.2 / 100 = 5.2 % answer : d"
Answer: d
Python program:
a = 4 / 100
b = 50 * a
c = 8 / 100
d = 40 * c
e = b + d 
f = e / 100
g = f * 100
Problem: if the average ( arithmetic mean ) of 4 x - 5 , 8 x - 6 , and 9 x + 5 is 279 , what is the value of x ?
Options: a ) 18 , b ) 25 , c ) 27 , d ) 29 , e ) 31
Rationale: "am of 4 x - 5 , 8 x - 6 , and 9 x + 5 = 4 x - 5 + 8 x - 6 + 9 x + 5 / 3 = 31 x / 3 given that 31 x / 3 = 279 x = 837 / 31 = 27 x = 27 answer is c"
Answer: c
Python program:
a = 5 - 4
b = a + 1
Problem: a retailer bought a hat at wholesale and marked it up 70 % to its initial price of $ 34 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.7 x = 34 and x = 34 / 1.7 = 20 . to achieve a 100 % markup , the price needs to be $ 40 . the retailer needs to increase the price by $ 6 more . the answer is c .
Answer: c
Python program:
a = 100 + 70 
b = a / 100
c = 34 / b
d = c * 2
e = d - 34