euclaise/mathqa_programs huggingface dataset:
Problem: calculate the average of all the numbers between 11 and 27 which are divisible by 2 .
Options: a ) 11 , b ) 10 , c ) 18 , d ) 19 , e ) 21
Rationale: "explanation : numbers divisible by 2 are 12,14 , 16,18 , 20,22 , 24,26 , average = ( 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 , ) / 8 = 152 / 8 = 19 answer : d"
Answer: d
Python program:
a = 11 / 2
b = math.floor(a)
c = b + 1 
d = 27 / 2
e = math.floor(d)
f = c + e 
g = f / 2
h = g * 2
Problem: we had $ 3500 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 4600 , b ) $ 4800 , c ) $ 5000 , d ) $ 5200 , e ) $ 5400
Rationale: "let x be the amount of money we started with . 0.7 x = 3500 x = 5000 the answer is c ."
Answer: c
Python program:
a = 30 / 100
b = 1 - a
c = 3500 / b
Problem: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 40 million gallons of water . this amount is one fifth of the normal level . if this amount represents 80 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 40 mg = 80 % of total . . total = 40 / . 8 = 50 mg . . normal level = 1 / 5 of 50 = 10 mg . . shortage of normal level = 50 - 10 = 40 mg . . c"
Answer: c
Python program:
a = 40 / 2
b = 80 / 100
c = a / b
Problem: on a certain farm the ratio of horses to cows is 3 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 5 : 3 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "originally , there were 3 k horses and k cows . 3 ( 3 k - 15 ) = 5 ( k + 15 ) 9 k - 5 k = 75 + 45 4 k = 120 k = 30 the difference between horses and cows is ( 3 k - 15 ) - ( k + 15 ) = 2 k - 30 = 30 the answer is b ."
Answer: b
Python program:
a = 15 * 5
b = 15 * 3
c = a + b 
d = 3 * 3
e = d - 5
f = c / e
g = 3 * f
h = g - 15
i = 15 * 5
j = 15 * 3
k = i + j 
l = 3 * 3
m = l - 5
n = k / m
o = n + 15 
p = h - o
Problem: what is the total number of integers between 2 and 38 that are divisible by 4 ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 11
Rationale: "4 , 6 , 8 , . . . , 32,36 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 36 - 4 ) / ( 4 ) + 1 = 32 / 4 + 1 = 8 + 1 = 9 answer is b"
Answer: b
Python program:
a = 38 - 2
b = a / 4
c = b + 1
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 7 rows or 6 rows or 4 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 84 , c ) 28 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 7 , 6,4 ) = 84 . answer : b"
Answer: b
Python program:
a = 4 * 6
b = a * 7
c = b / 2
Problem: the number n is 5 , h 64 , where h represents the 100 ' s digit . if n is divisible by 4 , what is the value of h ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) all the above value
Rationale: if the number is divisible by 4 , the last two digits must be divisible by 4 . all the values yields such a number . answer : e
Answer: e
Python program:
a = 5 - 4
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 22 } + { 20 } ?
Options: a ) 23 , b ) 20 , c ) 11 , d ) 5 , e ) 2
Rationale: "soln : { 22 } + { 20 } = 22 * { 20 } + { 20 } = 23 * { 20 } answer : a"
Answer: a
Python program:
a = 22 + 20 
b = a / 2
c = 1 * 2
d = b + c
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1480 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 400 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 1480 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 1480 3.7 z = 1480 , z = 400 answer : . d"
Answer: d
Python program:
a = 25 / 100
b = 1 + a 
c = 20 / 100
d = 1 + c 
e = b * d
f = 20 / 100
g = 1 + f 
h = e + g 
i = h + 1 
j = 1480 / i
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 70 , b ) 25 , c ) 60 , d ) 80 , e ) 55
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 5 years , their ages will be 45 and 25 . sum of their ages = 45 + 25 = 70 . answer a"
Answer: a
Python program:
a = 60 / 5
b = a * 2
c = b + 5 
d = 60 / 5
e = d + 5 
f = c + e
Problem: if the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 5 : 6 , d ) 1 : 4 , e ) 3 : 4
Rationale: "the ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6 . the ratio of apples to bananas to cucumbers is 5 to 2 to 6 . the ratio of apples to cucumbers is 5 to 6 . the answer is c ."
Answer: c
Python program:
a = 5 / 2
b = a / 3
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,6 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 6 = 12 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 12 = 2 / 3 the answer is d ."
Answer: d
Python program:
a = 0 + 0 
b = 4 / a
Problem: the ratio of the present age of two brothers is 1 : 2 and 5 years back , the ratio was 1 : 3 . what will be the ratio of their ages after 5 years ?
Options: a ) 3 : 9 , b ) 3 : 0 , c ) 3 : 5 , d ) 3 : 2 , e ) 3 : 1
Rationale: let the present ages of the two brothers be x and 2 x years respectively . then , ( x - 5 ) / ( 2 x - 5 ) = 1 / 3 3 ( x - 5 ) = ( 2 x - 5 ) = > x = 10 required ratio = ( x + 5 ) : ( 2 x + 5 ) = 15 : 25 = 3 : 5 answer : c
Answer: c
Python program:
a = 5 * 3
b = a - 5
c = 5 + b 
d = 5 * 3
e = d - 5
f = 2 * e
g = 5 + f 
h = c / g
Problem: find the least number must be subtracted from 724946 so that remaining no . is divisible by 10 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "on dividing 724946 by 10 we get the remainder 6 , so 6 should be subtracted d"
Answer: d
Python program:
a = 724946 / 10
b = math.floor(a)
c = b * 10
d = 724946 - c
Problem: if x is 20 percent more than y and y is 30 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 84 % , e ) 60 %
Rationale: "z = 100 ; y = 70 so x = 84 x as % of z = 84 / 100 * 100 = > 84 % answer will be ( d )"
Answer: d
Python program:
a = 20 / 100
b = 1 + a 
c = 100 - 30
d = b * c
Problem: a truck covers a distance of 240 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 0 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 240 / 8 = 30 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 30 + 18 ) = 48 kmph distance travelled by car = 240 + 0 = 240 km time taken by car = distance / speed = 240 / 48 = 5 hours . answer – b"
Answer: b
Python program:
a = 240 + 0 
b = 240 / 8
c = b + 18 
d = a / c
Problem: evaluate : 57 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 49 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 57 - 12 * 3 * 2 = 57 - 8 = 49 correct answer b"
Answer: b
Python program:
a = 12 * 2
b = a * 2
c = 57 - b
Problem: a mixture of 180 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 ) 4 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 12.5 liters
Rationale: "number of liters of water in 180 liters of the mixture = 20 % of 120 = 20 / 100 * 180 = 36 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 36 + p ) and total volume of mixture is ( 180 + p ) . ( 36 + p ) = 25 / 100 * ( 180 + p ) 96 + 4 p = 180 + p p = 12 liters . answer : d"
Answer: d
Python program:
a = 25 / 100
b = a * 180
c = 20 / 100
d = c * 180
e = b - d
f = 25 / 100
g = 1 - f
h = e / g
Problem: the sum of all the integers k such that – 23 < k < 24 is
Options: a ) 0 , b ) - 43 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "- 22 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 22 - 21 sum of which is - 43 . hence option d . b"
Answer: b
Python program:
a = negate + ( 
b = a + 1
Problem: there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) 10 , b ) 12 , c ) 24 , d ) 60 , e ) 100
Rationale: "there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ? 10 12 24 60 100 soln : total number of patterns is 5 ! since 3 red chips are identical and 2 blue ones are identical thus we have = 5 ! / ( 2 ! * 3 ! ) = 10 such different patterns a"
Answer: a
Python program:
a = math.factorial(3)
b = math.factorial(2)
c = a * b
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 45 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 40 = > v = 40 ( option b ) ."
Answer: b
Python program:
a = 100 - 80
b = 100 / 45
c = 80 / 80
d = b - c
e = a * d
Problem: what is the sum between the place values of three 7 ' s in the numeral 87953.0727
Options: a ) 21 , b ) 7000.0707 , c ) 7777 , d ) 7014 , e ) 7000.0077
Rationale: "required sum = 7000 + 0.0700 + 0.0007 = 7000.0707 answer is b"
Answer: b
Python program:
a = 7 * 10
b = 7 * 1000
c = a + b
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 18 , d ) d ) 56 , e ) e ) 12
Rationale: "let the total number of workers be x . then , 8000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 2000 x = 36000 = x = 18 . answer : c"
Answer: c
Python program:
a = 12000 - 8000
b = 6 * a
c = 8000 - 6000
d = b / c
e = 6 + d
Problem: two good train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none
Rationale: sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 500 + 500 ) m = 1000 m . required time = ( 1000 x 6 / 125 ) sec = 48 sec . answer c
Answer: c
Python program:
a = 45 + 30 
b = a * const_0_2778
c = 1/(b)
d = 500 * c
e = d * 2
Problem: in a tree , 2 / 5 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 2 / 3 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 3 / 5 , b ) 4 / 15 , c ) 7 / 15 , d ) 8 / 15 , e ) 17 / 30
Rationale: the fraction of birds that are male robins is ( 2 / 3 ) ( 2 / 5 ) = 4 / 15 . the fraction of birds that are male bluejays is ( 1 / 3 ) ( 3 / 5 ) = 1 / 5 . the total fraction of male birds is 4 / 15 + 1 / 5 = 7 / 15 . the answer is c .
Answer: c
Python program:
a = 2 / 5
b = 2 / 3
c = a * b
d = 3 / 5
e = 1 / 3
f = d * e
g = c + f
Problem: what distance will be covered by a bus moving at 90 kmph in 20 seconds ?
Options: a ) 500 , b ) 600 , c ) 289 , d ) 276 , e ) 207
Rationale: "90 kmph = 90 * 5 / 18 = 25 mps d = speed * time = 25 * 20 = 500 m . answer : a"
Answer: a
Python program:
a = 90 * const_0_2778
b = a * 20
Problem: in traveling from a dormitory to a certain city , a student went 1 / 2 of the way by foot , 1 / 4 of the way by bus , and the remaining 6 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 35 , b ) 24 , c ) 14 , d ) 24 , e ) 12
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 1 / 4 x + 6 x - 1 / 2 x - 1 / 4 x = 6 x = 24 km option : d"
Answer: d
Python program:
a = 1 / 2
b = 1 / 4
c = a + b 
d = 1 - c
e = 1/(d)
f = 6 * e
Problem: the speed of a car is 80 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 70 kmph , c ) 87 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 80 + 60 ) / 2 = 70 kmph answer : b"
Answer: b
Python program:
a = 80 + 60 
b = a / 2
Problem: if a town of 15,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 16000 , b ) b . 17000 , c ) c . 18000 , d ) d . 19000 , e ) e . 20000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Python program:
a = 3 + 4 
b = 5 * a
c = b * 100
d = 3 + 4 
e = d + 3 
f = c * e
Problem: the ratio , by volume , of bleach ( b ) to detergent ( d ) to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 60
b ) 50
c ) 40
d ) 80
e ) 70
Rationale: b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be a
Answer: a
Python program:
a = 40 / 100
b = a / 2
c = 300 * b
Problem: in a garden , 26 trees are planted at equal distances along a yard 400 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 12 , d ) 14 , e ) 16
Rationale: 26 trees have 25 gaps between them . length of each gap = 400 / 25 = 16 i . e . , distance between two consecutive trees = 16 answer is e .
Answer: e
Python program:
a = 26 - 1
b = 400 / a
Problem: 36 men can complete a piece of work in 18 days . in how many days will 108 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 6 , d ) 29 , e ) 21
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 108 : 36 : : 18 : x x = 6 answer : c ) 6 days"
Answer: c
Python program:
a = 18 * 36
b = a / 108
Problem: the simple interest on a sum of money will be rs . 700 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 2261 , b ) 2888 , c ) 1400 , d ) 2699 , e ) 2771
Rationale: "p - - - 10 - - - - 700 p - - - 5 - - - - - 350 3 p - - - 5 - - - - - 1050 - - - - - - = > 1400 answer : c"
Answer: c
Python program:
a = 700 / 10
b = a * 5
c = b * 3
d = 700 / 10
e = d * 5
f = c + e
Problem: barbata invests $ 2000 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2000 + 0.05 * 2000 + x + 0.08 x = 2000 + x + 0.06 ( 2000 + x ) 0.05 * 2000 + 0.08 x = 0.06 x + 0.06 * 2000 0.02 x = 2000 ( 0.06 - 0.05 ) x = 2000 * 0.01 / 0.02 = 1000 ans : ` ` c ' '"
Answer: c
Python program:
a = 6 / 100
b = a * 2000
c = 5 / 100
d = 2000 * c
e = b - d
f = 8 / 100
g = 6 / 100
h = f - g
i = e / h
Problem: what is the greatest positive integer x such that 5 ^ x is a factor of 125 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "125 ^ 10 = ( 5 ^ 3 ) ^ 10 = 5 ^ 30 answer : e"
Answer: e
Python program:
a = 125 - 10
b = a * 10
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 35 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 40 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.35 m = = > revenue = price x quantity = 0.40 ( m + w ) = = > profit = 0.40 ( m + w ) - 0.35 m = 0.2 * ( 0.35 m ) [ 20 % of cost ] = = > 0.40 m + 0.40 w - 0.35 m = 0.07 m = = > 0.02 m = 0.40 w = = > m / w = 0.40 / 0.02 = 20 - - or - - w / m = 1 / 20 a is correct ."
Answer: a
Python program:
a = 20 / 2
b = 1 / a
Problem: two trains start simultaneously from opposite ends of a 150 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 150 - km trip in 4 hours . train y , travelling at a constant rate , completes the 150 - km trip in 3.5 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 68 , b ) 70 , c ) 72 , d ) 74 , e ) 76
Rationale: if the two trains cover a total distance d , then train x travels ( 7 / 15 ) * d while train y travels ( 8 / 15 ) * d . if the trains travel 150 km to the meeting point , then train x travels ( 7 / 15 ) * 150 = 70 km . the answer is b .
Answer: b
Python program:
a = 150 / 4
b = 150 / 4
c = 150 / 3
d = b + c 
e = 150 / d
f = a * e
Problem: ( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: ( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ ( m + 1 ) = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 34 answer c
Answer: c
Python program:
a = 18 * 2
b = a - 1
c = b - 1
Problem: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 106 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 277 , d ) 122 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 106 x = 122 answer : d"
Answer: d
Python program:
a = 106 + 138 
b = a / 2
Problem: a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 1.4 , b ) 1.5 , c ) 1.6 , d ) 1.8 , e ) 1.0
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 18 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 1.8 m / s d"
Answer: d
Python program:
a = 6 * 3
b = a + 18 
c = b / 10
Problem: if the cost price is 98 % of sp then what is the profit %
Options: a ) 4.07 % , b ) 4 % , c ) 2.7 % , d ) 2.04 % , e ) 2.08 %
Rationale: "sol . sp = rs 100 : then cp = rs 98 : profit = rs 2 . profit = { ( 2 / 98 ) * 100 } % = 2.04 % answer is d ."
Answer: d
Python program:
a = 100 - 98
b = a / 98
c = b * 100
Problem: mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 3 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 1.5 , b ) 1.3 , c ) 1.25 , d ) 1.6 , e ) 2
Rationale: "d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 50 t + 50 / 4 = 60 t 10 t = 50 / 4 t = 1.25 or 1 hr , 15 min c"
Answer: c
Python program:
a = 15 / const_60
b = 50 * a
c = 60 - 50
d = b / c
e = const_60 * d
Problem: the banker â € ™ s discount of a certain sum of money is rs . 78 and the true discount on the same sum for the same time is rs . 66 . the sum due is
Options: a ) 429 , b ) 280 , c ) 360 , d ) 450 , e ) none
Rationale: sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 78 * 66 / 78 - 66 ] = rs . [ 78 * 66 / 12 ] = rs . 429 answer a
Answer: a
Python program:
a = 78 * 66
b = 78 - 66
c = a / b
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 10 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 152.3 , c ) $ 180 , d ) $ 220 , e ) $ 260
Rationale: "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 10 * ( a + e ) = = > 9 a = 11 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.2 e = = > 11 a = 220 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 11 e / 9 * 11 = 220 + 12 e or ( 121 / 9 - 12 ) e = 220 or 13 / 9 e = 220 e = 220 * 9 / 13 = 152.3 b"
Answer: b
Python program:
a = 22 * 100
b = 10 + 1 
c = b * 10
d = 100 + 20 
e = c - d
f = a / e
Problem: a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number q of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average q sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Python program:
a = 1 + 2 
b = 66 * a
c = 70 * 2
d = b - c
Problem: subtract the absolute value from the local value of 4 in 564823
Options: a ) 196 , b ) 1996 , c ) 2996 , d ) 3996 , e ) 6000
Rationale: explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 - 4 = 3996 answer : option d
Answer: d
Python program:
a = 4 * 100
b = a * 10