euclaise/mathqa_programs huggingface dataset:
Problem: a man covers a certain distance on bike . had he moved 4 kmph faster , he would have taken 72 minutes less . if he moves slow by 4 kmph , he will take hours more to cover the distance . what is the distance travelled by him ?
Options: a ) 48 km , b ) 56 km , c ) 64 km , d ) 96 km , e ) 106 km
Rationale: explanation : let the distance be ' d ' and the speed be ' x ' kmph . d / x + 4 = d / x - 72 / 60 d / x - d / ( x - y ) = 6 / 5 = d ( x + 4 - x ) / x ( x - 4 ) = 6 / 5 ∴ d / x ( x + 4 ) = 3 / 10 . . . . . . ( i ) d / x - 4 - d / x = 2 ∴ dx - dx + 4 d / x ( x - 4 ) = 2 ∴ d / x ( x - 4 ) = 1 / 2 . . . . . ( ii ) from equation ( i ) and ( ii ) : 3 / 10 x ( x + 4 ) = 1 / 2 x ( x - 4 ) ∴ 3 ( x + 4 ) = 5 ( x - 4 ) = 3 x + 12 = 5 x - 20 2 x = 32 ∴ x = 16 kmn - 1 ∴ d = x ( x - 4 ) / 2 = 16 x 12 / 2 = 16 x 6 = 96 km answer : option d
Answer: d
Python program:
a = 4 + 2 
b = const_60 + 4 
c = b / 4
d = c + 4 
e = const_60 + 4 
f = e / 4
g = d * f
h = a * g
i = const_60 + 4 
j = i / 4
k = j + 4 
l = h / k
Problem: if 0.6 : x : : 5 : 8 , then x is equal to :
Options: a ) a ) 0.96 , b ) b ) 1.2 , c ) c ) 1.25 , d ) d ) 1.3 , e ) e ) 0.8
Rationale: "( x * 5 ) = ( 0.6 * 8 ) x = 4.8 / 5 x = 0.96 answer = a"
Answer: a
Python program:
a = 0 * 6
b = a / 5
Problem: excluding stoppages , the speed of a bus is 50 km / hr and including stoppages , it is 36 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 118 min , b ) 10 min , c ) 18 min , d ) 16 min , e ) 15 min
Rationale: "due to stoppages , it covers 14 km less . time taken to cover 14 km = 14 / 50 * 60 = 16 min . answer : d"
Answer: d
Python program:
a = 50 - 36
b = a / 50
c = const_60 * b
Problem: 7 x + y = 19 , and x + 3 y = 1 . find the value of 2 x + y
Options: a ) 20 , b ) 18 , c ) 11 , d ) 5 , e ) 50
Rationale: add these two equations 8 x + 4 y = 20 divide by 2 ( to get 2 x + y ) answer will be d . 10
Answer: d
Python program:
a = 7 - 19
b = 7 * 3
c = b - 1
d = a / c
e = 3 * d
f = 1 - e
g = 2 * f
h = 7 - 19
i = 7 * 3
j = i - 1
k = h / j
l = g + k
Problem: what is the sum of the greatest common factor and the lowest common multiple of 12 and 16 ?
Options: a ) 19 , b ) 22 , c ) 52 , d ) 36 , e ) 38
Rationale: "prime factorization of the given numbers 12 = 2 ^ 2 * 3 48 = 2 ^ 4 * 3 greatest common factor = 4 lowest common multiple = 48 sum = 4 + 48 = 52 answer c"
Answer: c
Python program:
a = 12 * 16
b = a / 4
Problem: the least number which must be subtracted from 909 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 0 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 909 by 9 , we get remainder = 0 therefore , required number to be subtracted = 0 answer : c"
Answer: c
Python program:
a = 4 + 1 
b = a * 10
c = 4 + 2 
d = b + c 
e = d * 9
f = 909 - e
Problem: a person want to give his money of $ 3600 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 2000 , b ) $ 1200 , c ) $ 2500 , d ) $ 1800 , e ) $ 1600
Rationale: "b ' s share = 3600 * 3 / 9 = $ 1200 answer is b"
Answer: b
Python program:
a = 2 + 3 
b = a + 4 
c = 3 / b
d = c * 3600
Problem: each week , harry is paid x dollars per hour for the first 24 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 24 x + 1.5 x ( h - 24 ) = = > 42 = 24 + 1.5 ( h - 24 ) = = > h - 24 = 18 / 1.5 = 12 = > h = 36 answer is b"
Answer: b
Python program:
a = 40 + 2 
b = a - 24
c = b / 1
d = c + 24
Problem: rs . 1600 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 85 . how much was lent at 5.00001 % ?
Options: a ) 1100 , b ) 1200 , c ) 1300 , d ) 1400 , e ) 1700
Rationale: ( x * 5 * 1 ) / 100 + [ ( 1600 - x ) * 6 * 1 ] / 100 = 85 5 x / 100 + ( 9600 – 6 x ) / 100 = 85 = > x = 1100 answer : a
Answer: a
Python program:
a = 5 + 6 
b = a * 100
Problem: a box contains 10 tablets of medicine a and 16 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 18 , e ) 21
Rationale: "the worst case scenario will be if we remove all 16 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 16 + 2 = 18 tablets . answer : d ."
Answer: d
Python program:
a = 16 + 2
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 171 ?
Options: a ) 2820 , b ) 3440 , c ) 4860 , d ) 5560 , e ) 6720
Rationale: "100 + 102 + . . . + 170 = 100 * 36 + ( 2 + 4 + . . . + 70 ) = 100 * 36 + 2 * ( 1 + 2 + . . . + 35 ) = 100 * 36 + 2 ( 35 ) ( 36 ) / 2 = 100 * 36 + 35 * 36 = 135 ( 36 ) = 4860 the answer is c ."
Answer: c
Python program:
a = 171 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: a train 3000 m long can cross an electric pole in 120 sec and then find the speed of the train ?
Options: a ) 90 , b ) 95 , c ) 100 , d ) 105 , e ) 110
Rationale: "length = speed * time speed = l / t s = 3000 / 120 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : a"
Answer: a
Python program:
a = 3000 / 1000
b = 120 / 3600
c = a / b
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 500 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 4,100 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 500 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 500 x 8 = 4000 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 4100 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 4100 ( answer b )"
Answer: b
Python program:
a = 200 / 22
b = a * 500
Problem: a can give b 60 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 63.83 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 101.12
Rationale: "a runs 1000 m while b runs 940 m and c runs 880 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 880 ) / 940 = 936.17 m . b can give c = 1000 - 936.17 = 63.83 m . answer : a"
Answer: a
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 120
e = b * d
f = 100 * 10
g = f - 60
h = e / g
i = a - h
Problem: you have 59 cubic blocks . what is the minimum number that needs to be taken away in order to construct a solid cube with none left over ?
Options: a ) 27
b ) 43
c ) 11
d ) 32
e ) 45
Rationale: d 32 the next cube number below 64 ( 4 × 4 × 4 ) is 27 ( 3 × 3 × 3 ) . in order to construct a solid cube , therefore , with none left over , 59 – 27 = 32 blocks need to be taken away .
Answer: d
Python program:
a = 3 * 3
b = a * 3
c = 59 - b
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 8 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 1 kilometer per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 12
Rationale: "the distance traveled by ferry p is 24 km . then the distance traveled by ferry q is 72 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 72 / 9 = 8 hours , which is 5 hours more than ferry p . the answer is a ."
Answer: a
Python program:
a = 8 * 3
b = 3 * a
c = 8 + 1 
d = b / c
e = d - 3
Problem: n a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 4 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ?
Options: a ) 62 , b ) 63 , c ) 64 , d ) 66.66 , e ) 65
Rationale: given : - violets - c / 3 carnations - c tulip - c / 12 rose - c / 12 total flowers in terms of c = c / 3 + c + c / 12 + c / 12 = 18 c / 12 percentage of carnations = c / 3 c / 2 * 100 = 66.66 % answer d
Answer: d
Python program:
a = 1 / 3
b = 1 / 3
c = a + b 
d = c * 100
Problem: at a contest with 500 participants , 1 / 2 of the people are aged 28 to 32 . next year , the number of people aged 28 to 32 will increase by 1 / 8 . after this change , what percentage of the total 500 people will the 28 - to 32 - year - olds represent ?
Options: a ) 33.25 % , b ) 40.25 % , c ) 50.25 % , d ) 55.25 % , e ) 56.25 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 8 , we are multiplying it by 1 + 1 / 8 = 9 / 8 , so the answer here must be ( 1 / 2 ) * ( 9 / 8 ) = 9 / 16 = 56.25 % . answer is e"
Answer: e
Python program:
a = 500 / 2
b = 1 / 8
c = 1 + b 
d = a * c
e = d / 500
f = e * 100
Problem: on a purchase of $ 130 , a store offered a payment plan consisting of a $ 30 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 23.5 % , b ) 24.5 % , c ) 23.1 % , d ) 25.5 % , e ) 26.5 %
Rationale: 12 * 10 + 30 = 150 . ( 30 / 130 ) * 100 = 23.1 answer : c
Answer: c
Python program:
a = 10 * 12
b = a + 30 
c = 10 * 12
d = b - c
e = d / 130
f = e * 100
Problem: ashok secured average of 77 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 38 , b ) 27 , c ) 92 , d ) 17 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 77 therefore total marks in 6 subjects = 77 * 6 = 462 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 462 – 370 = 92 answer : c"
Answer: c
Python program:
a = 77 * 6
b = 74 * 5
c = a - b
Problem: roses can be purchased individually for $ 7.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 316 , d ) 324 , e ) 325
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 7.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c ."
Answer: c
Python program:
a = 680 / 50
b = math.floor(a)
c = 12 * 2
d = b * c
e = 680 / 50
f = math.floor(e)
g = f * 50
h = 680 - g
i = h / 7
j = math.floor(i)
k = d + j
Problem: what is the equation of a circle of radius 5 units centered at ( 3 , 2 ) ?
Options: a ) x ^ 2 + y ^ 2 + 6 x – 4 y = 23
b ) x ^ 2 + y ^ 2 - 6 x + 4 y = 23
c ) x ^ 2 + y ^ 2 + 6 x + 4 y = 23
d ) x ^ 2 + y ^ 2 - 6 x – 4 y = - 12
e ) x ^ 2 + y ^ 2 - 6 x – 4 y = 12
Rationale: the equation of a circle with center at ( a , b ) and radius r is ( x - a ) ^ 2 + ( y - b ) ^ 2 = r ^ 2 = > answer = ( x - 3 ) ^ 2 + ( y - 2 ) ^ 2 = 5 ^ 2 solving , , we get the equation in answer choice e .
Answer: e
Python program:
a = 5 ** 2
b = 3 ** 2
c = a - b
d = 2 ** 2
e = c - d
Problem: if the diameter of circle r is 20 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 14 % , e ) 4 %
Rationale: "let diameter of circle r , dr = 20 and diameter of circle s , ds = 100 radius of circle r , rr = 10 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 10 / 50 ) ^ 2 = ( 2 / 10 ) ^ 2 = 4 % answer : e"
Answer: e
Python program:
a = circle_area * (
b = a / 100
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 9 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "let t = usual time = distance / usual speed t + 9 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 36 the answer is d ."
Answer: d
Python program:
a = 5 / 4
b = a - 1
c = 9 / b
Problem: what will be the length of the mini - train , if it crosses a pole in 3 sec while travelling at a speed of 75 kmph ?
Options: a ) 60 m , b ) 65 m , c ) 63.5 m , d ) 64 m , e ) 62.5 m
Rationale: explanation : d = 75 * 5 / 18 * 3 = 62.5 m answer : option e
Answer: e
Python program:
a = 75 * const_0_2778
b = a * 3
Problem: if 4 x = 8 y = 12 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 58 , c ) 84 , d ) 122 , e ) 180
Rationale: "4 x = 8 y = 12 z x = 2 y = 3 z 3 ( 2 * 3 ) = 2 ( 3 * 1 ) = 3 ( 1 * 2 ) addition = 18 + 6 + 6 = 30 answer would be multiple of 30 which is 180 answer : e"
Answer: e
Python program:
a = 8 * 12
b = a * 4
c = b / 4
Problem: find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 6 . ?
Options: a ) 41 , b ) 46 , c ) 42 , d ) 46 , e ) 47
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 41 meets this description sum of digits - - - 4 + 1 = 5 difference of digits - - - 4 - 1 = 3 answer a ."
Answer: a
Python program:
a = 6 * 6
b = 6 + 4 
c = a * b
Problem: it takes joey the postman 1 hours to run a 3 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 18
Rationale: "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 6 mile an hour 2 * 3 * x / 3 + x = 6 6 x = 6 x + 18 = > x = 18 e"
Answer: e
Python program:
a = 2 * 3
b = a / 6
c = b - 1
d = 3 / c
Problem: 2056 x 987 = ?
Options: a ) 1936372 , b ) 2029272 , c ) 1896172 , d ) 1923472 , e ) none of them
Rationale: "= 2056 x 987 = 2056 x ( 1000 - 13 ) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272 answer is b"
Answer: b
Python program:
a = 2056 / 987
b = a * 100
Problem: a train is moving at 6 / 7 of its usual speed . the train is 30 minutes too late . what is the usual time for the train to complete the journey ?
Options: a ) 1 hour , b ) 30 minutes , c ) 3 hours , d ) 2 hours 30 min , e ) 2 hours
Rationale: "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 30 minutes represents 1 / 6 of the usual time . the usual time is 3 hours . the answer is c ."
Answer: c
Python program:
a = 6 / 7
b = 30 * a
c = 6 / 7
d = 1 - c
e = 1/(d)
f = b * e
g = f / const_60
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 530 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 20 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 530 . 6 ( 85 - g ) + 7 g = 530 . 510 - 6 g + 7 g = 530 . g = 530 - 510 = 20 . the answer is b .
Answer: b
Python program:
a = 85 * 6
b = 530 - a
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 5 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.15 % , c ) 14.95 % , d ) 13.33 % , e ) 12.52 %
Rationale: "( 100 % + 5 % ) * ( 100 % - 19 % ) = 1.05 * . 81 = 0.8505 . 1 - 0.8505 = 14.95 % lost = - 14.95 % the answer is c the organization has lost 14.95 % of its total volunteers from fall to spring ."
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = 19 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: two cars are driving toward each other . the first car is traveling at a speed of 90 km / h , which is 50 % faster than the second car ' s speed . if the distance between the cars is 975 km , how many hours will it take until the two cars meet ?
Options: a ) 6 , b ) 6.5 , c ) 7 , d ) 7.5 , e ) 8
Rationale: "the speed of the first car is 90 km / h . the speed of the second car is 90 / 1.5 = 60 km / h . the two cars complete a total of 150 km each hour . the time it takes the cars to meet is 975 / 150 = 6.5 hours . the answer is b ."
Answer: b
Python program:
a = 90 * 4
b = 4 * 90
c = 1 + 4 
d = b / c
e = d * 4
f = a + e 
g = 4 * 90
h = 1 + 4 
i = g / h
j = 90 + i 
k = f / j
Problem: find the annual income derived by investing $ 6800 in 40 % stock at 136 .
Options: a ) 550 , b ) 2000 , c ) 250 , d ) 3000 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 40 . by investing $ 6800 , income obtained = $ [ ( 40 / 136 ) * 6800 ] = $ 2000 . answer b ."
Answer: b
Python program:
a = 6800 * 40
b = a / 136
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 14.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 16 2 / 3 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 12.0 = 3.6 profit in 1983 = 18.8 - 14.0 = 4.8 increase in profit = 4.8 - 3.6 = 1.2 percentage increase 12 * 100 / 36 = 33.33 ; answer : d"
Answer: d
Python program:
a = 14 - 0
b = a * 100
c = 18 - 8
d = b / c
e = 100 - d
Problem: what is the difference between local value & face value of 7 in the numeral 65793 ?
Options: a ) 693 , b ) 656 , c ) 691 , d ) 9890 , e ) 10000
Rationale: ( local value of 7 ) - ( face value of 7 ) = ( 700 - 7 ) = 693 a
Answer: a
Python program:
a = 7 * 100
b = a - 7
Problem: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 14 miles , how many miles was mike ' s ride ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 14 ) = $ 11 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 11 0.25 * x = 8.5 x = 34 miles the answer is d .
Answer: d
Python program:
a = 2 + 5 
b = 0 * 25
c = a + b 
d = c - 2
e = d / 0
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 35 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 335 km , at what time will the truck and the car meet each other ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: "at 2 : 00 pm , the truck and the car are 300 km apart . the truck and the car complete a distance of 75 km each hour . the time it takes to meet is 300 / 75 = 4 hours . they will meet at 6 : 00 pm . the answer is c ."
Answer: c
Python program:
a = 335 / 35
b = a - 1
c = 40 / 35
d = 1 + c 
e = b / d
Problem: a license plate in the country kerrania consists of 4 digits followed by two letters . the letters a , b , and c are used only by government vehicles while the letters d through z are used by non - government vehicles . kerrania ' s intelligence agency has recently captured a message from the country gonzalia indicating that an electronic transmitter has been installed in a kerrania government vehicle with a license plate starting with 79 . if it takes the police 10 minutes to inspect each vehicle , what is the probability that the police will find the transmitter within 3 hours ?
Options: a ) 18 / 79 , b ) 1 / 6 , c ) 1 / 25 , d ) 1 / 50 , e ) 1 / 900
Rationale: if it takes 10 minutes to inspect one vehicle , the # of vehicles that can be inspected in 3 hours ( 180 minutes ) = 180 / 10 = 18 . hence , for calculating the probability that the police will find the transmitter within three hours , the favorable cases = 18 . now , we need to figure out the total # of cases . the total # of cases = total # of such cars possible . the details given about the car is that it starts with 79 , which leaves 2 more digits , both of which can be filled by all 10 numbers ( 0 - 9 ) . in addition , we have 3 letters , each of which can be filled by any from the set { a , b , c } . hence the total # of such cars possible = 10 * 10 * 3 * 3 = 900 so , the probability that the police will find the transmitter within three hours = 18 / 900 = 1 / 50 . option d
Answer: d
Python program:
a = 3 * const_60
b = a / 10
c = 4 - 2
d = 10 ** c
e = 3 ** 2
f = d * e
g = b / f
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 61 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "the total number of books is 75 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 61 books , thus the number of un - returned books is 75 - 61 = 14 books . 0.35 x = 14 x = 40 the answer is d ."
Answer: d
Python program:
a = 75 - 61
b = 65 / 100
c = 1 - b
d = a / c
Problem: one - sixth of the light switches produced by a certain factory are defective . 4 - fifths of the defective switches are rejected and 1 / 15 of the non defective switches are rejected by mistake . if all the switches not rejected are sold , what percent of the switches sold by the factory are defective ?
Options: a ) 1.8 % , b ) 2.9 % , c ) 4.1 % , d ) 5.6 % , e ) 6.4 %
Rationale: 1 / 6 of the switches are defective . the defective switches that are not rejected are 1 / 5 * 1 / 6 = 1 / 30 = 3 / 90 of all switches . the non defective switches that are sold are 5 / 6 * 14 / 15 = 70 / 90 of all switches . the percent of switches sold that are defective is 3 / 73 which is about 4.1 % . the answer is c .
Answer: c
Python program:
a = 4 + 1 
b = 1 / a
c = b * 100
d = 4 + 1 
e = 4 / d
f = 4 + 1 
g = 1 / f
h = g * 100
i = e * h
j = c - i
Problem: a man buys a cycle for rs . 1600 and sells it at a loss of 12 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1420 , c ) 1430 , d ) 1408 , e ) 1540
Rationale: s . p . = 88 % of rs . 1600 = 88 / 100 x 1600 = rs . 1408 answer : d
Answer: d
Python program:
a = 100 - 12
b = a * 1600
c = b / 100