euclaise/mathqa_programs huggingface dataset:
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 6 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 56 , e ) 60
Rationale: "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 6 x = 6 * 8 = 48 . hence c ."
Answer: c
Python program:
a = 4 * 2
b = a * 10
c = 4 * 2
d = c * 100
e = b + d 
f = 12 * 1000
g = e + f 
h = g / 230
i = h / 7
j = i * 6
Problem: what is the 23 th digit to the right of the decimal point in the decimal form of 1 / 11 ?
Options: a ) 1 , b ) 6 , c ) 3 , d ) 5 , e ) 0
Rationale: "to solve , we first have to use some long division . long division allows us to get 1 / 11 in decimal form , which is 0.090909 … where “ 09 ” is repeating . we see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 0 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 9 . in other words , each odd - positioned digit is a 0 , and each even - positioned digit is a 9 . then the 23 th digit to the right of the decimal point and we see that 23 is odd , then 23 th digit is a 0 . answer e ."
Answer: e
Python program:
a = 1 / 11
Problem: the present age of the father is 4 years more than 4 times the age of his son . 4 years hence , father ' s age will be 20 years more than twice the age of the son . find the present age of the father ?
Options: a ) 25 , b ) 56 , c ) 45 , d ) 36 , e ) 44
Rationale: let the son ' s present age be x years father ' s present age = ( 4 x + 4 ) 4 x + 4 + 4 = 2 ( x + 4 ) + 10 4 x + 8 = 2 x + 18 x = 5 father ' s present age = 4 x + 4 = 4 * 10 + 4 = 44 years answer is e
Answer: e
Python program:
a = 4 * 2
b = a + 20 
c = b - 4
d = c - 4
e = d / 2
f = e * 4
g = f + 4
Problem: find the slope of the line perpendicular to the line y = ( 1 / 3 ) x - 7
Options: a ) - 1 , b ) - 4 , c ) - 3 , d ) 0 , e ) - 5
Rationale: "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 3 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 3 ) = - 1 solve for m m = - 3 correct answer c ) - 3"
Answer: c
Python program:
a = 1 / 3
Problem: a scuba diver descends at a rate of 60 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3600 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 60 minutes , b ) 72 minutes , c ) 75 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: time taken to reach = 3600 / 60 = 60 minutes answer : a
Answer: a
Python program:
a = 3600 / 60
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 32 . in the company , what is the maximum number of non - managers in a department that has 8 managers ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "8 / 7 * 32 = 36.6 the answer is b ."
Answer: b
Python program:
a = 32 * 8
b = a / 7
c = math.floor(b)
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 30 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 15 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: 3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 30 pints will require 9 / 17 * 30 = 15 pints . . c
Answer: c
Python program:
a = 3 * 2
b = 4 * 3
c = a / b
d = 30 * c
Problem: a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 180 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "lets assume there are 2 x people . half of them have average weight of 180 and other half has 230 . maximum weight is = 2500 so 180 * x + 230 * x = 2500 = > 410 x = 2500 = > x is approximately equal to 6 . so total people is 2 * 6 = 12 answer e ."
Answer: e
Python program:
a = 10 * 180
b = 180 + 230 
c = a / b
d = c * 2
Problem: there are 3 vessels of equal capacity . vessel a contains milk and water in the ratio 4 : 3 ; vessel b contains milk and water in the ratio 2 : 1 and vessel c contains milk and water in the ratio 3 : 2 . if the mixture in all the 3 vessels is mixed up . what will be the ratio of water to milk ?
Options: a ) 9 : 6 , b ) 3 : 2 , c ) 118 : 126 , d ) 122 : 193 , e ) 201 : 132
Rationale: 4 : 3 = > 4 x + 3 x = 7 x 2 : 1 = > 2 y + 1 y = 3 y 3 : 2 = > 3 z + 2 z = 5 z 7 x = 3 y = 5 z take lcm of 7 , 3,5 = 105 or simply ; x = 3 * 5 = 15 y = 7 * 5 = 35 z = 3 * 7 = 21 so , ratio of water : milk = ( 3 x + y + 2 z ) / ( 4 x + 2 y + 3 z ) = 122 / 193 ans : d
Answer: d
Python program:
a = 3 + 2 
b = 2 / a
c = 2 + 1 
d = 1 / c
e = b + d 
f = 3 + 2 
g = 2 / f
h = 2 + 1 
i = 1 / h
j = g + i 
k = 4 + 3 
l = 3 / k
m = j + l 
n = e / m
Problem: each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 5625 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
Options: a ) 2304 , b ) 2305 , c ) 2309 , d ) 2310 , e ) 2311
Rationale: "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate b , c , d , e the answer to be a again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 2304 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 2304 = 5625 hence , correct answer = a"
Answer: a
Python program:
a = 1 / 4
b = a + 1 
c = b ** 4
d = 5625 / c
Problem: the time it took car p to travel 800 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 43 , b ) 58 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 800 / x ) - ( 800 / ( x + 10 ) ) = 2 solving for x = 58 miles \ hr . b"
Answer: b
Python program:
a = negate + ( 
b = negate ** (
c = b - 2
d = 800 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
Problem: a flamboyant comic book villain has abducted a bystander ! captain valiant is alerted to the crime and reaches the start of the villain ' s trail 30 minutes later . the villain is in a getaway car going 40 kmph , and captain valiant can fly at 50 kmph . how long will the bystander have to wait for rescue ?
Options: a ) 1 hour , b ) 1 1 / 2 hours , c ) 2 hours , d ) 2 1 / 2 hours , e ) 3 hours
Rationale: distance covered by the villain in 1 / 2 hour = 20 km now , 10 km is compensated in 1 hour therefore 20 km will be compensated in 2 hours added to the half hour head start , the bystander has been kidnapped for 2 1 / 2 hours . correct answer : d
Answer: d
Python program:
a = 50 - 40
Problem: a man can do a piece of work in 5 days , but with the help of his son , he can do it in 4 days . in what time can the son do it alone ?
Options: a ) 15 , b ) 17 , c ) 20 , d ) 8 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 5 ) = 1 / 20 the son alone can do the work in 20 days answer is c"
Answer: c
Python program:
a = 5 * 4
b = 5 - 4
c = a / b
Problem: a train running at the speed of 60 km / hr crosses a pole in 27 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 876 meter , c ) 167 meter , d ) 450 meter , e ) 169 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 27 = 450 meter answer : d"
Answer: d
Python program:
a = 60 * 1000
b = a / 3600
c = b * 27
Problem: find the greatest number that will divide 400 , 435 and 541 leaving 9 , 10 and 14 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 13 , d ) 9 , e ) 8
Rationale: "explanation : answer will be hcf of ( 400 - 9 , 435 - 10 , 541 - 14 ) hcf of ( 391 , 425 , 527 ) = 17 option b"
Answer: b
Python program:
a = 10 * 4
b = 12 + a
Problem: what is the largest 4 digit number exactly divisible by 88
Options: a ) 9900 , b ) 9999 , c ) 9988 , d ) 9944 , e ) 9966
Rationale: "explanation : largest 4 digit number is 9999 after doing 9999 ÷ 88 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer : option d"
Answer: d
Python program:
a = 10 ** 4
b = a / 88
c = math.floor(b)
d = c * 88
Problem: if the cost price of 15 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 40 % loss , e ) 50 % loss
Rationale: "explanation : 15 cp = 25 sp cost price cp = 25 selling price sp = 15 formula = ( sp - cp ) / cp * 100 = ( 15 - 25 ) / 25 * 100 = 40 % loss answer : option d"
Answer: d
Python program:
a = 100 * 25
b = a / 15
c = 100 - b
d = 100 * 25
e = d / 15
f = c / e
g = 100 * f
Problem: a and b complete a work in 16 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.0875 days , b ) 0.1875 days , c ) 0.0675 days , d ) 0.0875 days , e ) 0.0775 days
Rationale: "1 / 16 + 1 / 40 = 0.0875 days answer : d"
Answer: d
Python program:
a = 1/(16)
b = 1/(40)
c = a + b 
d = 1/(c)
Problem: find the area of the quadrilateral of one of its diagonals is 22 cm and its off sets 9 cm and 6 cm ?
Options: a ) 188 cm 2 , b ) 165 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 22 ( 9 + 6 ) = 165 cm 2 answer : b"
Answer: b
Python program:
a = 1 / 2
b = 6 + 9 
c = a * b
d = c * 22
Problem: a work which could be finished in 8 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 30 , c ) 88 , d ) 71 , e ) 11
Rationale: "x - - - - - - - 8 ( x + 10 ) - - - - 6 x * 8 = ( x + 10 ) 6 x = 30 \ answer : b"
Answer: b
Python program:
a = 3 * 2
b = a * 10
c = 3 * 2
d = 8 - c
e = b / d
Problem: a certain protective additive increases from 25 days to 30 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 20 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 30 − 25 / 25 ∗ 100 = 20 answer : b ."
Answer: b
Python program:
a = 30 - 25
b = a / 25
c = b * 100
Problem: the average of 13 numbers is 58 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 72 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 58 = 754 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 754 = 72 . answer : a"
Answer: a
Python program:
a = 8 * 61
b = 13 * 58
c = 57 * 7
d = b - c
e = a - d
Problem: the volumes of two cones are in the ratio 1 : 40 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 8 : 5 , b ) 8 : 9 , c ) 2 : 2 , d ) 8 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 40 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 8 / 5 i . e . h 1 : h 2 = 8 : 5 answer : a"
Answer: a
Python program:
a = 1 / 40
b = 1 / 2
c = b ** 2
d = a / c
Problem: in the new budget the price of milk rose by 10 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
Options: a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 12.6 % , e ) 15 %
Rationale: "reduce in consumption = r / ( 100 + r ) * 100 % = 10 / 110 * 100 = 9.1 % answer is c"
Answer: c
Python program:
a = 10 + 100 
b = 10 / a
c = b * 100
Problem: a copy machine , working at a constant rate , makes 40 copies per minute . a second copy machine , working at a constant rate , makes 55 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,700 , c ) 4,500 , d ) 5,400 , e ) 2,850
Rationale: together the two machines make 40 + 55 = 95 copies per minute . so , in half an hour they will make 95 * 30 = 2,850 copies . answer : e .
Answer: e
Python program:
a = 40 + 55 
b = a * const_60
c = b / 2
Problem: working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 6 days ?
Options: a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 4 days therefore , we need to get to 2 x / 4 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 2 x done in 6 days . 2 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 2 x / 6 y = 2 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 8 . answer choice e"
Answer: e
Python program:
a = 4 * 2
b = 6 / 6
c = a * b
Problem: evaluate : 17 + sqrt ( - 7 + 10 ã — 6 ã · 5 ) = ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "according to order of operations , inner brackets first where 10 x 6 ã · 5 is first calculated since it has a multiplication and a division . 10 x 6 ã · 5 = 60 ã · 5 = 12 hence 17 + sqrt ( - 7 + 10 ã — 6 ã · 5 ) = 17 + sqrt ( - 7 + 12 ) = 17 + sqrt ( 5 ) = 17 + 25 = 42 correct answer b ) 42"
Answer: b
Python program:
a = 10 * 7
b = a / 5
c = b - 7
d = math.sqrt(c)
e = 17 + d
Problem: product of two natural numbers is 19 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 1 / 289 , c ) 290 / 90 , d ) 362 / 361 , e ) none of these
Rationale: explanation : if the numbers are a , b , then ab = 19 , as 17 is a prime number , so a = 1 , b = 19 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 19 ( 2 ) = 362 / 361 option d
Answer: d
Python program:
a = 1 / 1
b = a ** 2
c = 1 / 19
d = c ** 2
e = b + d
Problem: if a ( a + 2 ) = 120 and b ( b + 2 ) = 120 , where a ≠ b , then a + b =
Options: a ) - 4 , b ) - 6 , c ) - 2 , d ) - 10 , e ) - 8
Rationale: "i . e . if a = 10 then b = - 12 or if a = - 12 then b = 10 but in each case a + b = - 12 + 10 = - 2 answer : c"
Answer: c
Python program:
a = 120 / 10
b = 120 / 10
c = 120 / b
d = a + c
Problem: a rectangular block has the dimensions 5 x 6 x 7 cm it is dropped into a cylindrical vessel of radius 6 cm and height 10 cm . if the level of the fluid in the cylinder rises by 4 cm , what portion of the block is immersed in the fluid ?
Options: a ) 22 / 7 x 24 / 35
b ) 22 / 7 x 36 x 4
c ) 22 / 7 x 36 / 5
d ) 22 / 7 x 37 / 21
e ) 22 / 7 x 32 / 21
Rationale: explanation : since level of water increased in cylinder by height 4 . this is because of the rectangular block . therefore , area of rectangular block immersed in water is = 22 / 7 x ( 6 ) ^ 2 x 4 thats why portion of block immersed in water is = ( 22 / 7 x 36 x 4 ) / total vol . of rectangle = ( 22 / 7 x 36 x 4 ) / ( 7 x 5 x 6 ) = 22 / 7 x 24 / 35 . answer is a
Answer: a
Python program:
a = 10 + 4 
b = volume_cylinder - (
c = b / volume_cylinder
Problem: a train 630 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 630 * 2 / 35 = 36 sec answer : option b"
Answer: b
Python program:
a = 63 * 1000
b = 630 / a
c = b * 3600
Problem: of the female students at barkely university , 1 / 6 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 3 / 5 of the students are female , what fraction of all the students are on the honor roll ?
Options: a ) 5 / 9 , b ) 3 / 15 , c ) 26 / 100 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 100 given 3 / 5 of the students are females = 60 then males = 2 / 5 = 40 1 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 5 = 16 total students on honor roll = 10 + 16 = 26 fraction = 26 / 100 c"
Answer: c
Python program:
a = 1 * 3
b = a * 3
c = b + 2 
d = 5 * 1
e = 2 * d
f = c / e
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many u apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons u = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Python program:
a = 10 + 10 
b = a + 2 
c = 1430 / b
d = c + 45 
e = 1430 / d
f = e + 9
Problem: what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 21 ?
Options: a ) 5037 , b ) 5447 , c ) 5867 , d ) 6297 , e ) 6617
Rationale: "when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d ."
Answer: d
Python program:
a = math.lcm(18, 70)
b = math.lcm(100, 21)
c = math.lcm(a, b)
d = c + 3
Problem: if a ( k ) = ( 2 k + 1 ) ^ k , and k = 0 , what is the value of a ( a ( a ( k ) ) ) ?
Options: a ) 343 , b ) 199 , c ) 121 , d ) 69 , e ) 249
Rationale: a ( a ( a ( 0 ) ) ) = a ( a ( 1 ) ) = a ( 3 ) = ( 6 + 1 ) ^ 3 = 343 . thus , the answer is a .
Answer: a
Python program:
a = 2 * 0
b = 1 + a 
c = b ** 0
d = 2 * c
e = d + 1 
f = e ** 1
g = 2 * f
h = g + 1 
i = 2 * 0
j = 1 + i 
k = j ** 0
l = 2 * k
m = l + 1 
n = m ** 1
o = h ** n
Problem: the cricket team of 11 members is 27 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 24
Rationale: "let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) = > 11 x - 9 x = 48 = > 2 x = 48 = > x = 24 . so , average age of the team is 24 years . e"
Answer: e
Python program:
a = 27 + 3 
b = a + 27 
c = 11 - 2
d = b - c
e = 11 - 2
f = 11 - e
g = d / f
Problem: how many multiples of 5 are there between 1 and 89 ?
Options: a ) 15 , b ) 20 , c ) 13 , d ) 17 , e ) 22
Rationale: "5 multiples are 5 , 10,15 , - - - - - - - - - , 80,85 it should be mentioned whether 1 and 89 are inclusive . the answer is ( 85 - 5 ) / 5 + 1 = 17 answer is d"
Answer: d
Python program:
a = 89 - 1
b = a / 5
c = b + 1
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 12 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 40 points as end of season we need another 28 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 hence option b - 7"
Answer: b
Python program:
a = 40 - 12
b = 20 - 5
c = a - b
d = c / 2
e = math.floor(d)
f = e + 1
Problem: if x is an integer and 3.134 × 10 ^ x is less than 31,000 what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "if x = 4 3.134 × 10 ^ 4 = 31340 > 31000 so , x = 3 answer : e"
Answer: e
Python program:
a = 31 / 0
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
Problem: in a river flowing at 2 km / hr , a boat travels 40 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 15 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 40 km total time taken = time taken downstream + time taken upstream = ( 40 / 8 ) + ( 40 / 4 ) = 15 d"
Answer: d
Python program:
a = 6 - 2
b = 40 / a
c = 6 + 2 
d = 40 / c
e = b + d
Problem: a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be
Options: a ) 45 min , b ) 60 min , c ) 55 min , d ) 70 min , e ) 80 min
Rationale: "time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer : b ."
Answer: b
Python program:
a = 50 / const_60
b = 48 * a
c = 40 / const_60
d = b / c
Problem: ifaequals the sum of the even integers from 2 to 100 , inclusive , andbequals the sum of the odd integers from 1 to 99 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 50 , c ) 19 , d ) 20 , e ) 21
Rationale: "this is a solution from beatthegmat : even numbers : ( 100 - 2 ) / 2 + 1 = 50 even integers . ( 100 + 2 ) / 2 = 51 is the average of the even set . sum = avg * ( # of elements ) = 51 * 50 = 2550 = a odd numbers : ( 99 - 1 ) / 2 + 1 = 50 odd integers . ( 99 + 1 ) / 2 = 50 is the average of the odd set . sum = avg * ( # of elements ) = 50 * 50 = 2500 = b a - b = 2550 - 2500 = 50 . ( b )"
Answer: b
Python program:
a = 100 / 2
b = 100 / 2
c = b + 1 
d = a * c
e = 99 + 1 
f = e / 2
g = 99 - 1
h = g / 2
i = h + 1 
j = f * i
k = d - j
Problem: the sum of 4 consecutive numbers is 102 . the greatest among these 3 number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 27
Rationale: let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e
Answer: e
Python program:
a = 1 + 2 
b = a + 3 
c = 102 - b
d = c / 4
e = d + 3
Problem: the sum of all possible two digit numbers formed from 3 different one digit natural numbers when divided by the sum of the original 3 numbers is equal to ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: let the one digit numbers x , y , z sum of all possible two digit numbers = ( 10 x + y ) + ( 10 x + z ) + ( 10 y + x ) + ( 10 y + z ) + ( 10 z + x ) + ( 10 z + y ) = 22 ( x + y + z ) therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22 . answer e
Answer: e
Python program:
a = 3 * 10
b = a + 3 
c = b / 3
d = c * 2
Problem: if a man lost 10 % by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 32 % ?
Options: a ) 13.25 , b ) 14.36 , c ) 15.85 , d ) 12.27 , e ) 11.25
Rationale: "90 % - - - - 18 132 % - - - - ? 90 / 132 * 18 = 12.27 answer : d"
Answer: d
Python program:
a = 100 - 10
b = a * 18
c = 100 + 32 
d = b / c