euclaise/mathqa_programs huggingface dataset:
Problem: a train 100 m long crosses a platform 125 m long in 10 sec ; find the speed of the train ?
Options: a ) 81 , b ) 77 , c ) 54 , d ) 33 , e ) 99
Rationale: "d = 100 + 125 = 225 t = 10 s = 225 / 10 * 18 / 5 = 81 kmph answer : a"
Answer: a
Python program:
a = 125 * const_0_2778
b = 10 * a
c = b - 100
Problem: calculate the largest 3 digit number which is exactly divisible by 89 ?
Options: a ) 911 , b ) 969 , c ) 979 , d ) 977 , e ) 971
Rationale: "largest 4 digit number is 999 after doing 999 ÷ 89 we get remainder 20 hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 c"
Answer: c
Python program:
a = 100 + 2 
b = a * 89
Problem: on dividing 83 by a number , the quotient is 9 and the remainder is 2 . find the divisor ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "d = ( d - r ) / q = ( 83 - 2 ) / 9 = 81 / 9 = 9 c )"
Answer: c
Python program:
a = 83 / 9
b = math.floor(a)
Problem: albert invested rs . 1000 in a scheme for 3 years at compound interest rate 10 % p . a . how much amount will albert get on maturity of the fixed deposit ?
Options: a ) s . 1300 , b ) s . 1005 , c ) s . 1031 , d ) s 1331 , e ) s . 1120
Rationale: "amount = [ 1000 * ( 1 + 10 / 100 ) 3 ] = 1000 * 11 / 10 * 11 / 10 * 11 / 10 = rs . 1331 answer : d"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 3
d = 1000 * c
Problem: if a ' s height is 35 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 53.84 % , d ) 86.66 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 35 / ( 100 - 35 ) ] x 100 % = 53.84 % answer : c )"
Answer: c
Python program:
a = 100 - 35
b = 35 / a
c = b * 100
Problem: what is 5 / 8 as a percent
Options: a ) 62.5 % , b ) 63 % , c ) 63.5 % , d ) 64.5 % , e ) 65 %
Rationale: "5 / 8 as a percent = ( 5 / 8 ) x 100 = 0.625 x 100 = 62.5 % answer : a i . e . 62.5 %"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 5 * n
p = o / 100
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 77.44 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 88 , e ) 97
Rationale: "money collected = ( 77.44 x 100 ) paise = 7744 paise . number of members = square root of 7744 = 88 . answer : option d"
Answer: d
Python program:
a = 77 * 44
b = math.sqrt(a)
Problem: a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 288 , b ) 278 , c ) 267 , d ) 285 , e ) 231
Rationale: "since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d"
Answer: d
Python program:
a = 4 + 1 
b = a * 510
c = 4 + 1 
d = 4 + 1 
e = c * d
f = e * 240
g = b + f 
h = g / 30
Problem: some of the 50 % solution of acid was removed and this was replaced with an equal amount of 10 % solution of acid . as a result , a 20 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.1 ( x ) = 0.2 0.4 x = 0.3 x = 3 / 4 the answer is c ."
Answer: c
Python program:
a = 50 + 10 
b = 20 / a
Problem: in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 30 ducks and in the larger pond there are 50 ducks . if 20 % of the ducks in the smaller pond are green and 12 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12 / 80 * 100 = 15 % answer : c
Answer: c
Python program:
a = 20 / 100
b = 30 * a
c = 12 / 100
d = 50 * c
e = b + d 
f = 30 + 50 
g = e / f
h = g * 100
Problem: the h . c . f of two numbers is 17 and their l . c . m is 5134 . if one of the numbers is 289 , then the other is ?
Options: a ) 302 , b ) 304 , c ) 306 , d ) 308 , e ) 310
Rationale: "other number = ( 17 * 5134 ) / 289 = 302 . answer : a"
Answer: a
Python program:
a = 17 * 289
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 15 percent of the drink is orange juice and 60 percent is watermelon juice . if the drink is made with 35 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "let the total number of ounces in the drink be x . % of orange = 15 % % of watermelon = 60 % % of grape = 100 % - 75 % = 25 % 0.25 x = 35 x = 140 therefore there are a total of 140 ounces in the drink . the answer is b ."
Answer: b
Python program:
a = 35 * 15
b = 60 + 15 
c = 100 - b
d = a / c
e = 35 + d 
f = 35 * 60
g = 60 + 15 
h = 100 - g
i = f / h
j = e + i
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4529
b ) s . 4586
c ) s . 7248
d ) s . 4530
e ) s . 4528
Rationale: area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 8 = rs . 7248 answer : c
Answer: c
Python program:
a = 2 * 12
b = 15 + 25 
c = a * b
d = 6 * 3
e = c - d
f = 4 * 3
g = 3 * f
h = e - g
i = h * 8
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 61.50 , his capital is ?
Options: a ) 24,607 , b ) 24,609 , c ) 24,600 , d ) 24,602 , e ) 24,604
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 61.50 32 x - 31 x = 6150 * 4 x = 24,600 . answer : c"
Answer: c
Python program:
a = 4 / 4
b = 61 / 50
Problem: a 210 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 290 , b ) 280 , c ) 270 , d ) 260 , e ) 250
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 210 ) / 9 = 500 / 9 = > x = 290 . answer : option a"
Answer: a
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 210
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 6 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 24 min , e ) 12 min
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 5 1 - - - - - - - - 6 4 - - - - - - - - - ? è 24 answer : d"
Answer: d
Python program:
a = 5 / 4
b = 6 / a
c = b * 5
Problem: the age of father 8 years ago was thrice the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
Options: a ) 47 : 11 , b ) 37 : 21 , c ) 27 : 21 , d ) 47 : 21 , e ) 47 : 31
Rationale: let the ages of father and son 8 years ago be 3 x and x years respectively . then , ( 3 x + 8 ) + 5 = 2 [ ( x + 8 ) + 5 ] 3 x + 13 = 2 x + 26 x = 13 . required ratio = ( 3 x + 8 ) : ( x + 8 ) = 47 : 21 . answer : option d
Answer: d
Python program:
a = 8 + 5 
b = 2 * a
c = 8 + 5 
d = b - c
e = d * 3
f = e + 8 
g = 8 + 5 
h = 2 * g
i = 8 + 5 
j = h - i
k = j + 8 
l = f / k
Problem: if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 69 , what is the value of a ?
Options: a ) 26 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: ( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 69 a = 26 the answer is a .
Answer: a
Python program:
a = 69 * 2
b = 16 - 8
c = a - b
d = 2 + 3 
e = c / d
Problem: what is the remainder when 43 ^ 89 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 89 has the form 4 k + 1 so the units digit of 43 ^ 89 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Python program:
a = 5 / 2
b = 43 * 43
c = a - b
Problem: the value of 99 ^ ( 91 / 99 ) x 99 is :
Options: a ) 9989 , b ) 9896 , c ) 9892 , d ) 9809 , e ) 9810
Rationale: ( 100 â € “ 8 / 99 ) x 99 = 9900 â € “ 8 = 9892 . answer : c
Answer: c
Python program:
a = 91 / 99
b = 99 ** a
c = b * 99
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 3 * / 5 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 5 / 3 b"
Answer: b
Python program:
a = 1 / 3
b = a / 3
c = 1 + 4 
d = b / c
Problem: if the average of 55 , 48 , 507 , 2 , 684 and y is 223 , then what is y ?
Options: a ) 701 , b ) 120 , c ) 42 , d ) 868 , e ) 1
Rationale: y = 42 , because : ( 55 + 48 + 507 + 2 + 684 + y ) / 6 = 223 ( 55 + 48 + 507 + 2 + 684 + y ) / 6 * 6 = 223 * 6 ( 55 + 48 + 507 + 2 + 684 + y ) - 1296 = 1338 - 1296 y = 42 so the correct answer is c , 42 .
Answer: c
Python program:
a = 2 + 4 
b = 223 * a
c = 55 + 48 
d = 507 + c 
e = 2 + d 
f = 684 + e 
g = b - f
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 5 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 5 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k - - - > 5 = 2 k - - - > k = 5 / 2 . the answer is , therefore , ( d ) ."
Answer: d
Python program:
a = 5 + 5 
b = a - 5
c = b / 2
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area r of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Python program:
a = 4 * math.pi
b = 3 / math.pi
c = a * b
d = c / 2
e = 3 / math.pi
f = math.pi * e
g = d + f
Problem: the sum of the first 70 positive even integers is 4970 . what is the sum of the first 70 odd integers ?
Options: a ) 4500 , b ) 4600 , c ) 4300 , d ) 4900 , e ) 5000
Rationale: sum of first n even numbers = n ( n + 1 ) = 4970 sum of first n odd numbers = n ^ 2 = 70 * 70 = 4900 ( here n = 70 ) answer : d
Answer: d
Python program:
a = 4970 + 1
Problem: a train crosses a platform of 150 m in 10 sec , same train crosses another platform of length 250 m in 15 sec . then find the length of the train ?
Options: a ) 150 m , b ) 180 m , c ) 159 m , d ) 250 m , e ) 50 m
Rationale: "length of the train be ‘ x ’ x + 150 / 10 = x + 250 / 15 3 x + 450 = 2 x + 500 x = 50 m answer : e"
Answer: e
Python program:
a = 10 / 3
b = 10 / a
c = 250 * b
d = 10 / 3
e = 15 / d
f = 150 * e
g = c - f
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 5 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 7 th year ?
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 7 th year : 6 - 7 ( age ) , we take age = 6 thus for the 5 th year = 50 , 6 th year = 50 - 5 = 45 7 th year = 45 - 6 = 39 the correct answer is d ."
Answer: d
Python program:
a = 5 - 1
b = a - 1
c = 5 - 1
d = 50 + c 
e = b + d 
f = e / 3
g = f + 3
Problem: two trains 170 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 sec , b ) 18.8 sec , c ) 14.8 sec , d ) 10.88 sec , e ) 11.88 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 170 + 160 = 330 m . required time = 330 * 9 / 250 = 297 / 25 = 11.88 sec . answer : e"
Answer: e
Python program:
a = 170 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: on a certain road 12 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 12 % + 0,2 x id est x = 15 %"
Answer: c
Python program:
a = 12 / 100
b = 20 / 100
c = a * b
d = c * 100
e = 100 / d
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 2.5 liters of alcohol and 7.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 9 % , b ) 12 % , c ) 15 % , d ) 18 % , e ) 21 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 2.5 ) / 50 = 4.5 / 50 = 9 % the answer is a ."
Answer: a
Python program:
a = 5 / 100
b = 40 * a
c = b + 2 
d = 2 + 5 
e = 40 + d 
f = c / e
g = f * 100
Problem: in a consumer survey , 80 % of those surveyed liked at least one of 3 products : 1 , 2 , and 3 . 50 % of those asked liked product 1 , 30 % liked product 2 , and 20 % liked product 3 . if 5 % of the people in the survey liked all 3 of the products , what percentage of the survey participants liked more than one of the 3 products ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: pick 100 and x = all set with exactly two items 80 = 30 + 50 + 20 - ( x ) - 10 x = 10 so the answer is 10 + 5 / 100 = 15 % answer c
Answer: c
Python program:
a = 50 + 30 
b = a + 20 
c = b - 80
d = c - 5
Problem: in township k each property is taxed at 8 percent of its assessed value . if the assessed value of a property in township k is increased from $ 180,000 to $ 24,000 , by how much will the property tax increase ?
Options: a ) $ 32 , b ) $ 50 , c ) $ 480 , d ) $ 400 , e ) $ 500
Rationale: "increase in house value = $ 24,000 - $ 18,000 = $ 8000 so , tax increase = 8 % of $ 6000 = $ 480 answer : c"
Answer: c
Python program:
a = 3 + 4 
b = a * 4
c = b * 1000
d = 4 + 1 
e = d * 4
f = e * 1000
g = c - f
h = g * 8
i = h / 100
Problem: find the greatest number which on dividing 1255 and 1490 , leaves a reminder of 8 and 11 respectively
Options: a ) 27 , b ) 29 , c ) 33 , d ) 39 , e ) 41
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1255 - 8 ) and ( 1490 - 11 ) = hcf ( 1247 , 1479 ) = 29 option b"
Answer: b
Python program:
a = 1255 - 8
b = 1490 - 11
c = math.gcd(a, b)
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2.5 % more . she would get how much ?
Options: a ) 9800 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 2.5 ) / 100 = 600 9200 - - - - - - - - 9800 answer : a"
Answer: a
Python program:
a = 2 / 5
b = 9200 - 8000
c = b / 3
d = c / 8000
e = a + d 
f = e * 8000
g = f * 3
h = g + 8000
Problem: 8 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 84 , e ) 45
Rationale: "there are 8 business exec and in each handshake 2 business execs are involved . hence 8 c 2 = 28 also , each of 8 exec will shake hand with every 7 other chairmen for total of 56 handshake . total = 28 + 56 = 84 ans : d"
Answer: d
Python program:
a = 8 - 1
b = 8 * a
c = b / 2
d = 8 * 7
e = c + d
Problem: there are 2 positive integers x and y . what is the probability that x + y is odd ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 5 , e ) 1 / 9
Rationale: explanation : the addition of two integer results in an odd number only if any one of the integers is an odd number . the probability of an odd among the two integer is 1 / 2 . hence , the required probability is 1 / 2 . answer : b
Answer: b
Python program:
a = 2 / 4
Problem: solution x contains 20 % of material a and 80 % of material b . solution y contains 30 % of material a and 70 % of material b . a mixture of both these solutions contains 22 % of material a in the final product . how much solution x is present in the mixture ?
Options: a ) 40 % , b ) 60 % , c ) 80 % , d ) 100 % , e ) 110 %
Rationale: we can assume the total weight of the mixture = 100 conc of a in the final mixture = 22 let weight of a in the mixture be x . conc given = 20 % = . 2 therefore , weight of b = 100 - x . conc given = 30 % = . 3 now , acc to the problem , . 2 x + . 3 ( 100 - x ) = 22 solving , we get x = 80 . since we assumed the weight of the mixture = 100 , therefore presence of a in the mixture = 80 % . answer : c
Answer: c
Python program:
a = 80 * 1000
b = a / 100
c = b / 100
d = c * 10
Problem: set a consists of the integers from 4 to 17 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "a = { 4 , 5,6 , 7,8 , 9,10 , 11,12 , . . . 17 } b = { 6 , 7,8 , 9,10 , 11,12 . . . , 20 } thus we see that there are 12 distinct integers that are common to both . e is the correct answer ."
Answer: e
Python program:
a = 6 + 4
Problem: a student travels from his house to school at 10 km / hr and reaches school 2 hours late . the next day he travels 16 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
Options: a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "let x be the distance from his house to the school . x / 10 = x / 16 + 3 8 x = 5 x + 240 3 x = 240 x = 80 km the answer is c ."
Answer: c
Python program:
a = 10 * 16
b = 16 - 10
c = 2 + 2 
d = b / c
e = a * d
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 1 / 2 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 8 / 11 , d ) 7 / 12 , e ) 11 / 15
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( x / 2 ) ( 3 y / 4 ) = 3 xy / 8 the total number of boxes is xy + 3 xy / 8 = 11 xy / 8 the fraction loaded by the day crew is xy / ( 11 xy / 8 ) = 8 / 11 the answer is c ."
Answer: c
Python program:
a = 2 * 4
b = 2 * 4
c = 3 * 1
d = b + c 
e = a / d
Problem: of the 200 employees at company x , 80 are full - time , and 150 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "200 employees 80 are full - time 150 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 200 - 80 = 120 employees not full time 120 - 20 = 100 employees not full time who worked over a year 150 employees have worked at company x for at least a year - 100 employees not full time who worked over a year = 50 full - time employees of company x have worked at the company for at least a year c . 50"
Answer: c
Python program:
a = 200 - 80
b = a - 20
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 1 / 2 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 62.5 , e ) 50
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 1 x / 2 hence , number of buckets needed = 25 x / ( 1 x / 2 ) = ( 25 × 2 ) / 1 = 50 answer is e ."
Answer: e
Python program:
a = 4 + 1 
b = 25 * a
c = b / 2
Problem: how many of the positive divisors of 480 are also multiples of 4 not including 480 ?
Options: a ) 15 , b ) 16 , c ) 19 , d ) 20 , e ) 24
Rationale: "480 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 ^ 3 * 3 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 3 , 1 , and 1 . there are ( 3 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 480 . the answer is a ."
Answer: a
Python program:
a = 480 / 4
b = a / 2
c = b / 3
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 45 % on his income , while mindy pays a rate of only 20 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 22 % , b ) 25 % , c ) 28 % , d ) 31 % , e ) 34 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 0.8 x = 1.25 x 1.25 x / 5 x = 0.25 the answer is b ."
Answer: b
Python program:
a = 45 / 100
b = 20 / 100
c = 4 * b
d = a + c 
e = 1 + 4 
f = d / e
g = 100 * f