euclaise/mathqa_programs huggingface dataset:
Problem: in a company , 50 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 50 % of all employees are women , so non - union women are 50 % - 18 % = 32 % 40 % of all employees are non - union . the percent of non - union employees who are women is 32 % / 40 % = 80 % the answer is b ."
Answer: b
Python program:
a = 100 - 50
b = 70 / 100
c = 60 * b
d = 60 - c
e = a - d
f = 100 - 60
g = e / f
h = 100 * g
Problem: 9 log 9 ( 4 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 4 ) = 4 correct answer d"
Answer: d
Python program:
a = 9 * 9
b = math.log(a)
c = math.log(10)
d = b / c
Problem: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?
Options: a ) 96 , b ) 106 , c ) 128 , d ) 137 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 5 = 37 runs total runs = new avg x new no . of innings = 37 * 21 = 777 runs made in the 11 th inning = 777 - 640 = 137 answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 5 + 32 
c = a * b
d = 20 * 32
e = c - d
Problem: yearly subscription to professional magazines cost a company $ 840.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 656 , d ) 588 , e ) 658
Rationale: "total cost 840 840 * 30 / 100 = 252 so the cut in amount is 252 the less amount to be spend is 840 - 252 = 588 answer : d"
Answer: d
Python program:
a = 100 - 30
b = a / 100
c = b * 840
Problem: the area of a square is 4900 sq cm . find the ratio of the breadth and the length of a rectangle whose length is same the side of the square and breadth is 20 cm less than the side of the square ?
Options: a ) 5 : 8 , b ) 5 : 10 , c ) 5 : 13 , d ) 5 : 7 , e ) 5 : 16
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4900 a = ( 4900 ) ^ 1 / 2 = 70 l = a and b = a - 20 b : l = a - 20 : a = 50 : 70 = 5 : 7 answer : d"
Answer: d
Python program:
a = math.sqrt(4900)
b = a - 20
c = math.sqrt(4900)
d = c * 2
e = b / d
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 18 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 3000 , c ) 1667 , d ) 1254 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 18 * 60 = 3000 m answer is b"
Answer: b
Python program:
a = 10 * 1000
b = a / const_60
c = b * 18
Problem: the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle .
Options: a ) 84
b ) 86
c ) 82
d ) 80
e ) none of them
Rationale: let inner radius be r metres . then , 2 ( 22 / 7 ) r = 440 = r = ( 440 x ( 7 / 44 ) ) = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer is a
Answer: a
Python program:
a = 440 / math.pi
b = a / 2
c = 14 + b
Problem: r is the set of positive even integers less than 20 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none
b ) two
c ) three
d ) five
e ) seven
Rationale: squares < 20 { 1,4 , 9,16 } s = { 1,4 , 9,16 } r = { 2 , . . . . . 18 } hence c .
Answer: c
Python program:
a = 4 - 1
Problem: elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 7 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28
Rationale: "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 7 we get : 21 b + 28 f = 7 x therefore , we got 21 ounces of butter and 7 x amount of quantity when we use 28 ounces of floor . ans : e"
Answer: e
Python program:
a = 4 * 7
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 45 , find the other ?
Options: a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 45 = 160 answer is b"
Answer: b
Python program:
a = 12 * 45
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
Options: a ) 40 , b ) 36 , c ) 32 , d ) 28 , e ) 24
Rationale: "let c be the capacity of the can . ( 4 / 7 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 12 c - 96 + 168 = 14 c 2 c = 72 c = 36 the answer is b ."
Answer: b
Python program:
a = 1 * 8
b = 3 * 2
c = 1 * 4
d = b - c
e = a / d
f = e * 4
g = f + 8 
h = 1 * 8
i = 3 * 2
j = 1 * 4
k = i - j
l = h / k
m = l * 3
n = g + m
Problem: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice ?
Options: a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its b . total juice rquired = 272 * 6 = 1632 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1632 / 48 = 34 . answer b"
Answer: b
Python program:
a = 272 * 6
b = a / 12
c = b / 4
Problem: to produce an annual income of rs . 1200 from a 12 % stock at 90 , the amount of stock needed is :
Options: a ) rs . 10,000 , b ) rs . 10,800 , c ) rs . 14,400 , d ) rs . 16,000 , e ) none of these
Rationale: solution for an income of rs . 12 , stock needed = rs . 100 . for an income of rs . 1200 , stock needed = rs . 100 / 12 x 1200 = 10000 answer a
Answer: a
Python program:
a = 100 - 90
Problem: if the least common addition of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
Options: a ) 7 , b ) 9 , c ) 14 , d ) 17 , e ) 21
Rationale: "( x + y ) = 10 and both x an y are prime . the only values of x and y can be 7 and 3 ( x = 7 and y = 3 ) 2 x + y = 2 * 7 + 3 = 17 correct option : d"
Answer: d
Python program:
a = 10 * 2
b = 10 / 2
c = a + b 
d = 3 + 3 
e = c + d
Problem: what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 40 seconds ?
Options: a ) 308 , b ) 320 , c ) 332 , d ) 344 , e ) 356
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 156 = 344 meters the answer is d ."
Answer: d
Python program:
a = 45 * const_0_2778
b = a * 40
c = b - 156
Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 11 , b ) 4 / 15 , c ) 6 / 17 , d ) 8 / 21 , e ) 10 / 25
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d ."
Answer: d
Python program:
a = math.comb(6, 3)
b = math.comb(10, 6)
c = a / b
Problem: if 10 men can reap 120 acres of land in 15 days , how many acres of land can 20 men reap in 30 days ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 1200 , e ) 480
Rationale: "10 men 120 acres 15 days 20 men ? 30 days 120 * 20 / 10 * 30 / 15 120 * 2 * 2 120 * 4 = 480 answer : e"
Answer: e
Python program:
a = 20 / 10
b = 30 / 15
c = a * b
d = 120 * c
Problem: the profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 975 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 852 – x = 448 + x or , x = 404 ⁄ 2 = 202 \ cost price of the article = 852 – x = 448 + x = 650 \ sp of the article = 650 × 150 ⁄ 100 = 975 answer b"
Answer: b
Python program:
a = 852 + 448 
b = a / 2
c = 50 / 100
d = 1 + c 
e = b * d
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 1 , e ) 1 : 3
Rationale: "( 10 / 100 ) a + ( 2 / 100 ) b = ( 6 / 100 ) ( a + b ) 4 a = 4 b = > a / b = 1 / 1 answer is d ."
Answer: d
Python program:
a = 6 - 2
b = 10 - 6
c = a / b
Problem: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 7 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 7 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 7 3 x - 2 ( 7 - x ) = 25 3 x - 14 + 2 x = 25 5 x = 39 x = 7.8 or between 7 and 8 . ( ans b )"
Answer: b
Python program:
a = 7 - 2
b = 2 * a
c = 3 * 2
d = b - c
e = d + 31 
f = 3 + 2 
g = e / f
Problem: find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case .
Options: a ) 366 , b ) 236 , c ) 367 , d ) 365 , e ) 386
Rationale: "explanation : the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 35 , 11 ) + 1 = 386 . answer : e"
Answer: e
Python program:
a = math.lcm(35, 11)
b = 1 + a
Problem: the speed of a car is 90 km in the first hour and 75 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 82.5 kmph , c ) 75 kmph , d ) 65 kmph , e ) 77 kmph
Rationale: "s = ( 90 + 75 ) / 2 = 82.5 kmph b"
Answer: b
Python program:
a = 90 + 75 
b = a / 2
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 8 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 34 hr , e ) 36 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 8 ) = 1 / 34 leak will empty the tank in 34 hrs . answer : d"
Answer: d
Python program:
a = 1 / 2
b = 2 * 8
c = b + 1 
d = c / 8
e = 1/(d)
f = a - e
g = 1/(f)
Problem: two buses each 3125 m long are running in opposite directions on parallel roads . their speeds are 40 km / hr and 35 km / hr respectively . find the time taken by the slower bus to pass the driver of the faster one ?
Options: a ) 50 sec , b ) 66 sec , c ) 48 sec , d ) 55 sec , e ) 45 sec
Rationale: relative speed = 40 + 35 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 3125 + 3125 = 6250 m . required time = 6250 * 6 / 125 = 50 sec . answer : a
Answer: a
Python program:
a = 40 + 35 
b = a * 1000
c = b / 3600
d = 3125 / c
e = d / 3
Problem: if the perimeter of a rectangular garden is 500 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 777 m , c ) 200 m , d ) 167 m , e ) 150 m
Rationale: "2 ( l + 100 ) = 500 = > l = 150 m answer : e"
Answer: e
Python program:
a = 500 / 2
b = a - 100
Problem: a man goes from a to b at a speed of 15 kmph and comes back to a at a speed of 12 kmph . find his average speed for the entire journey ?
Options: a ) 13.7 kmph , b ) 13.3 kmph , c ) 13.8 kmph , d ) 13.9 kmph , e ) 12.3 kmph
Rationale: distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 15 ) + ( d / 12 ] = ( 2 d ) / [ 9 d / 60 ) = > 13.3 kmph . answer : b
Answer: b
Python program:
a = 15 + 12 
b = a / 2
Problem: a cube is divided into 729 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that the cube is coloured with green colour on one set of adjacent faces , red on the other set of adjacent faces , blue on the third set . so , how many cubelets are there which are painted with exactly one colour ?
Options: a ) 293 , b ) 294 , c ) 295 , d ) 296 , e ) 298
Rationale: "total cubes created are 729 so a plane of big cube has 9 * 9 cubes out of that ( n - 2 ) * ( n - 2 ) = 7 * 7 = 49 are painted only one side and a cube has six sides = 6 * 49 = 294 answer : b"
Answer: b
Python program:
a = 4 * 2
b = a * 3
c = 729 - b
d = c / 2
Problem: in a mixed college 160 students are there in one class . out of this 160 students 3 / 4 students are girls . how many boys are there ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 120 , e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 4 = 120 total boys : 160 - 120 = 40 answer is a"
Answer: a
Python program:
a = 160 / 4
b = a * 3
Problem: the product z of two prime numbers is between 10 and 30 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24 , then what is z ?
Options: a ) 21 , b ) 15 , c ) 14 , d ) 10 , e ) 6
Rationale: "the smallest possible product is 21 which is 3 * 7 . all other products are too big . the answer is a ."
Answer: a
Python program:
a = 10 - 4
b = a * 3
Problem: how many integers from 0 to 44 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 13 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 43 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 43 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 42 or , n - 1 = 12 or , n = 13 a"
Answer: a
Python program:
a = 44 / 10
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c"
Answer: c
Python program:
a = 150 / 2
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 7 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 24 hr , e ) 30 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 7 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : e"
Answer: e
Python program:
a = 1 / 2
b = 2 * 7
c = b + 1 
d = c / 7
e = 1/(d)
f = a - e
g = 1/(f)
Problem: a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 33 , b ) 37 , c ) 41 , d ) 45 , e ) 49
Rationale: "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 3 = 24 . the minimum number of horses and ponies is 45 . the answer is d ."
Answer: d
Python program:
a = 7 / 2
b = a * 3
c = math.lcm(7, b)
d = c + 3 
e = 7 / 2
f = e * 3
g = math.lcm(7, f)
h = d + g
Problem: there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ?
Options: a ) 88 , b ) 90 , c ) 92 , d ) 96 , e ) 98
Rationale: "n ( s ) = sample space = 23 c 3 = 1771 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 13 or 1 girl from 10 = 13 c 2 + 10 c 1 = 88 ans - a"
Answer: a
Python program:
a = math.comb(13, 2)
b = math.comb(10, 1)
c = a * b
Problem: a student gets 70 % in one subject , 80 % in the other . to get an overall of 75 % how much should get in third subject .
Options: a ) 75 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "a student gets 70 % in one subject , 80 % in the other . average of 2 subjects is 75 % , if they have equal weightage . to get an overall of 75 % , he should get 75 % in third subject to maintain same % age . . if they have equal weightage . answer : a"
Answer: a
Python program:
a = 75 * 3
b = 70 + 80 
c = a - b
Problem: carina has 85 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 85 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 75 / 15 . = 5 a"
Answer: a
Python program:
a = 5 * 2
b = 85 - a
c = 10 + 5 
d = b / c
Problem: how much water must be added to 56 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 14 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 56 litres of milk = ( 1 ⁄ 4 × 56 ) litres = 14 litres . answer c"
Answer: c
Python program:
a = 1 / 2
b = 1 + a 
c = 20 / b
Problem: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2000 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2507 , d ) 3200 , e ) 11500
Rationale: "p - 2000 = ( p * 5 * 4 ) / 100 p = 2500 answer : b"
Answer: b
Python program:
a = 4 * 5
b = a / 100
c = 1 - b
d = 2000 / c
Problem: if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 21 c 2 = 21 * 20 / 2 = 210 . therefore , the answer is d"
Answer: d
Python program:
a = 10 + 10 
b = 10 + 2 
c = a + b 
d = 10 + 1 
e = c + d 
f = e + 10 
g = f + 10 
h = g + 2 
i = h + 1
Problem: jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 926 . answer : e ."
Answer: e
Python program:
a = 3 / 100
b = 2 / 100
c = 100 ** 2
d = b * c
e = 100 ** 2
f = d + e 
g = a * f
h = 2 / 100
i = 100 ** 2
j = h * i
k = 100 ** 2
l = j + k 
m = g + l 
n = 4 / 100
o = m * n
p = 3 / 100
q = 2 / 100
r = 100 ** 2
s = q * r
t = 100 ** 2
u = s + t 
v = p * u
w = o + v
Problem: the sum of the numbers is 110 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 30 , b ) 54 , c ) 72 , d ) 84 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 110 11 x / 3 = 110 x = 30 answer : a"
Answer: a
Python program:
a = 110 * 3
b = 10 + 1 
c = a / b
Problem: total dinning bill of 3 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 50.96 , c ) 53.84 , d ) 24.84 , e ) 50.26
Rationale: "dinner bill of 3 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 3 = $ 50.96 answer : b"
Answer: b
Python program:
a = 1 / 10
b = a + 1 
c = 139 * 0
d = c / 3
Problem: the ratio of the radius of two circles is 5 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 25 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 5 : 3 π r 12 : π r 22 r 12 : r 22 = 25 : 9 answer : c"
Answer: c
Python program:
a = circle_area / (
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 512,000 locusts ?
Options: a ) 18 , b ) 15 , c ) 13 , d ) 14 , e ) 12
Rationale: "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 + 12 hours : 256,000 + 14 hours : 512,000 answer : d"
Answer: d
Python program:
a = 4 ** 4
b = a / 2
c = math.log(b)
d = c * 2
e = d - 4
Problem: if the price of gasoline increases by 20 % and a driver intends to spend only 14 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 1 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.14 ( p * x ) y = ( 1.14 / 1.2 ) x = 0.95 x which is a reduction of 5 % . the answer is d .
Answer: d
Python program:
a = 20 + 100 
b = 14 + 100 
c = a - b
d = 20 + 100 
e = c / d
f = e * 100
Problem: a cube is divided into 343 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225
Rationale: "each side of the cube has 7 x 7 = 49 cubelets . only the interior cubelets are painted one colour . on each side , 5 x 5 = 25 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 25 = 150 the answer is b ."
Answer: b
Python program:
a = 4 * 2
b = a * 3
c = 343 - b
d = c / 2