euclaise/mathqa_programs huggingface dataset:
Problem: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 12 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the class borrowed a total of 40 * 2 = 80 books . the 26 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 12 * 2 = 36 . to maximize the number of books borrowed by 1 student , let ' s assume that 13 students borrowed 3 books and 1 student borrowed the rest . 80 - 36 - 3 * 13 = 5 the maximum number of books borrowed by any student is 5 . the answer is c ."
Answer: c
Python program:
a = 40 * 2
b = 12 * 1
c = b + 12 
d = c + 2 
e = 40 - d
f = e - 1
g = f * 3
h = 12 * 1
i = 12 * 2
j = h + i 
k = g + j 
l = a - k
Problem: shop offered 40 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 933 , e ) 750
Rationale: "sp * ( 60 / 100 ) = 560 sp = 9.33 * 100 = > cp = 933 answer : d"
Answer: d
Python program:
a = 40 / 100
b = 1 - a
c = 560 / b
Problem: the average score of a cricketer for 12 matches is 48 runs . if the average for first 8 matches is 40 , then average for last 4 matches is
Options: a ) 33.25 , b ) 89 , c ) 64 , d ) 68 , e ) 90
Rationale: explanation : = ( 48 × 12 ) − ( 40 × 8 ) / 4 = ( 576 − 320 ) / 4 = 64 answer : option c
Answer: c
Python program:
a = 48 + 12 
b = 40 / 8
c = a + b 
d = 4 - 3
e = c - d
Problem: the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ?
Options: a ) 34 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a
Answer: a
Python program:
a = 40 * 30
b = 30 * 40
c = a + b 
d = 40 + 30 
e = c / d
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2340 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 7800 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2340 100 % - - - - - - - - - ? = > 7800 answer : d"
Answer: d
Python program:
a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 2340 / d
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 25,000 earned at the end of 2 years from the startingof the business ?
Options: a ) rs . 5,000 , b ) rs . 5,500 , c ) rs . 5,700 , d ) rs . 6,500 , e ) rs . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 25000 x 3 / 10 = rs . 7,500 . e"
Answer: e
Python program:
a = 4 + 1 
b = a * 4
c = 3 * 4
d = 2 * c
e = b * d
Problem: in a box of 12 pens , a total of 4 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 33 , c ) 14 / 33 , d ) 9 / 16 , e ) 3 / 44
Rationale: "method - 1 there are 9 fine pieces of pen and 4 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 8 / 12 ) i . e . probability of second pen not being defective = ( 7 / 11 ) [ 11 pen remaining with 8 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 8 / 12 ) * ( 7 / 11 ) = 14 / 33 answer : option c"
Answer: c
Python program:
a = 12 - 4
b = a / 12
c = 12 - 4
d = c - 1
e = 12 - 1
f = d / e
g = b * f
Problem: a bowl was filled with 10 ounces of water , and 0.007 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 3.5 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 007 * 50 = . 007 * 100 / 2 = . 7 / 2 = . 35 percent of the original amount of water evaporated during this period = ( . 35 / 10 ) * 100 % = 3.5 % answer e"
Answer: e
Python program:
a = 50 * 0
b = a / 10
c = b * 100
Problem: the price of a certain painting increased by 30 % during the first year and decreased by 20 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 104 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.20 = 130 * 0.80 = 104 hence required answer = ( 104 / 100 ) * 100 % = 104 % answer is e ."
Answer: e
Python program:
a = 30 - 20
b = 20 * 30
c = b / 100
d = a - c
e = d + 100
Problem: the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ra ɵ o less than 16 : 21 , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : let x is subtracted . then , ( 6 − x ) ( 7 − x ) < 162121 ( 6 � x ) < 16 ( 7 � x ) = > 5 x > 14 = x > 2.8 least such number is 3 answer : a
Answer: a
Python program:
a = 21 * 6
b = 7 * 16
c = a - b
d = 21 - 16
e = c / d
f = math.floor(e)
g = f + 1
Problem: in what time will a train 134 m long cross an electric pole , it its speed be 169 km / hr ?
Options: a ) 2.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 169 * 5 / 18 = 46.9 m / sec time taken = 134 / 46.9 = 2.9 sec . answer : c"
Answer: c
Python program:
a = 169 * const_0_2778
b = 134 / a
Problem: a train 75 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 28 , b ) 50 , c ) 88 , d ) 22 , e ) 32
Rationale: "speed of the train relative to man = ( 75 / 10 ) m / sec = ( 15 / 2 ) m / sec . [ ( 15 / 2 ) * ( 18 / 5 ) ] km / hr = 27 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 27 = = > x = 32 km / hr . answer : e"
Answer: e
Python program:
a = 10 * const_0_2778
b = a * 10
c = 75 - b
d = c / 5
e = d / const_0_2778
Problem: a train 200 m long crosses a platform 150 m long in 20 sec ; find the speed of the train ?
Options: a ) 73 , b ) 63 , c ) 65 , d ) 70 , e ) 83
Rationale: "d = 200 + 150 = 350 t = 20 s = 350 / 20 * 18 / 5 = 63 kmph . answer : b"
Answer: b
Python program:
a = 150 * const_0_2778
b = 20 * a
c = b - 200
Problem: if ( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: ( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) = > 5 ^ 13 * 3 ^ 14 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 13 * 3 ^ 14 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 13 answer d
Answer: d
Python program:
a = 5 ** 13
b = 9 ** 7
c = a * b
d = c / 3
e = math.log(d)
f = math.log(15)
g = e / f
Problem: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , d are sitting together ?
Options: a ) 1 / 5 , b ) 3 / 28 , c ) 1 / 7 , d ) 1 / 14 , e ) 5 / 28
Rationale: "total number of arrangement is = 8 ! = 40320 favorable event i . e a , b and d can be arranged in 3 ! and the remaining can be arranged in 6 ! since abd can be in any of the six positions . so 3 ! * 6 ! / 8 ! = 3 / 28 answer : b"
Answer: b
Python program:
a = 4 + 4 
b = a - 3
c = b + 1 
d = math.factorial(c)
e = math.factorial(3)
f = d * e
g = 4 + 4 
h = math.factorial(g)
i = f / h
Problem: the divisor is 21 , the quotient is 14 and the remainder is 7 . what is the dividend ?
Options: a ) 201 , b ) 394 , c ) 302 , d ) 301 , e ) 294
Rationale: d = d * q + r d = 21 * 14 + 7 d = 294 + 7 d = 301
Answer: d
Python program:
a = 21 * 14
b = a + 7
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 6 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
Rationale: "( 1 mph + 6 mph ) / 2 = 3.5 mph correct option is : c"
Answer: c
Python program:
a = 1 + 6 
b = a / 2
Problem: what annual payment will discharge a debt of rs . 1050 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 551.25 , c ) 534.33 , d ) 543.33 , e ) 564.69
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1050 820 x + 1050 * 441 x = 564.69 so , value of each installment = rs . 564.69 answer : option e"
Answer: e
Python program:
a = 5 / 100
b = a + 1 
c = b ** 2
d = c * 1050
e = d / 2
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 880 grams per kg , what is his percent ?
Options: a ) 15 % , b ) 13.6 % , c ) 65 % , d ) 45 % , e ) 35 %
Rationale: "explanation : 880 - - - 120 100 - - - ? = > 13.6 % answer : b"
Answer: b
Python program:
a = 100 / 880
b = 3 + 2 
c = b * 2
d = 100 * c
e = a * d
f = e - 100
Problem: the number of positive integer solutions for the equation x + y + z + t = 21 is
Options: a ) 1140 , b ) 1145 , c ) 1240 , d ) 1340 , e ) 15640
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 21 - 1 c 4 - 1 = 20 c 3 = 1140 answer : a"
Answer: a
Python program:
a = 21 - 1
b = math.factorial(a)
c = 4 - 1
d = math.factorial(c)
e = 21 - 1
f = 4 - 1
g = e - f
h = math.factorial(g)
i = d * h
j = b / i
Problem: a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 5 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 33 % , c ) 20 % , d ) 35 % , e ) 30 %
Rationale: "the total number of mangoes bought by the shopkeeper be 30 . if he buys 6 a rupee , his cp = 5 he selling at 5 a rupee , his sp = 6 profit = sp - cp = 6 - 5 = 1 profit percent = 1 / 5 * 100 = 20 % answer : c"
Answer: c
Python program:
a = 5 * 100
b = a / 6
Problem: machine p and machine q are each used to manufacture 330 sprockets . it takes machine p 10 hours longer to produce 330 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 3 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 330 / x = 330 / 1.1 x + 10 1.1 ( 330 ) = 330 + 11 x 11 x = 33 x = 3 the answer is c ."
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = 330 / b
d = 330 - c
e = d / 10
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 160 male associates , how many female managers are there ?
Options: a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: 250 employees : 90 male , 160 female 40 managers , 210 associates 160 male associates implies 50 female associates which means the remaining 40 females must be managers a . 40
Answer: a
Python program:
a = 40 * 1
Problem: think of a number , divide it by 5 and add 8 to it . the result is 61 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 265 , e ) 29
Rationale: "explanation : 61 - 6 = 53 53 x 5 = 265 answer : d"
Answer: d
Python program:
a = 61 - 8
b = a * 5
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 8 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 8 pounds of clothes doubles the ratio of books to clothes , then 8 pounds represents half the weight of the clothes . 2 k = 8 pounds and then k = 4 pounds . the electronics weigh 3 ( 4 ) = 12 pounds . the answer is d .
Answer: d
Python program:
a = 7 + 4 
b = a + 3 
c = b * 8
d = negate / (
e = 7 + 4 
f = e + 3 
g = f * 2
h = 7 + 4 
i = h + 3 
j = i * 4
k = g - j
l = 3 * d
Problem: the radius of a semi circle is 2.1 cm then its perimeter is ?
Options: a ) 32.5 , b ) 11.12 , c ) 32.1 , d ) 10.8 , e ) 32.3
Rationale: "36 / 7 r = 2.1 = 10.80 answer : d"
Answer: d
Python program:
a = circumface / (
b = a + 2
Problem: the dimensions of a rectangular solid are 4 inches , 5 inches , and 10 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17 , b ) 2 : 5 , c ) 10 : 19 , d ) 25 : 7 , e ) 32 : 25
Rationale: answer : c .
Answer: c
Python program:
a = 10 * 2
b = a + 2 
c = b + 1 
d = 10 / c
Problem: which number should replace both the asterisks in ( * / 21 ) x ( * / 189 ) = 1 ?
Options: a ) 21 , b ) 63 , c ) 3969 , d ) 147 , e ) 167
Rationale: "answer let ( y / 21 ) x ( y / 189 ) = 1 then , y 2 = 21 x 189 = 21 x 21 x 9 ∴ y = ( 21 x 3 ) = 63 . option : b"
Answer: b
Python program:
a = 189 * 21
b = math.sqrt(a)
Problem: a tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume . if 6,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 15 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 6,000 = 4,000 gallons and sodium chloride is 600 gallons ( 6 % of initial solution of 10,000 gallons ) then sodium chloride is 600 / 4,000 * 100 = 15 % of the remaining solution of 4,000 gallons . answer : e ."
Answer: e
Python program:
a = 100 * 100
b = 6 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: two pipes a and b can fill a cistern in 12 and 20 minutes respectively , and a third pipe c can empty it in 30 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 15 min , b ) 13 min , c ) 12 min , d ) 10 min , e ) 17 min
Rationale: "1 / 12 + 1 / 20 - 1 / 30 = 1 / 10 10 / 1 = 10 answer : d"
Answer: d
Python program:
a = 1/(12)
b = 1/(20)
c = a + b 
d = c * 30
e = 1 - d
f = 12 * e
g = f + 30
Problem: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 231 marks in the second test and failed by 48 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 625 , e ) 248
Rationale: "let the maximum mark in each test be m . the candidate failed by 48 marks in the second test . pass mark in the second test = 231 + 48 = 279 45 / 100 m = 279 pass mark in the first test = 40 / 100 m = 40 / 45 * 279 = 248 . answer : e"
Answer: e
Python program:
a = 231 + 48
Problem: trains a and b start simultaneously from stations 200 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 20 miles per hour and 20 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
Options: a ) 100 , b ) 133 , c ) 150 , d ) 167 , e ) 188
Rationale: "since we know the distance ( 200 ) and the combined rate ( 40 ) , we plug it into the formula : distance = rate * time 200 = 40 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 200 / 40 from dividing 40 on both sides to isolate time in the equation above . time will be 5 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 20 * 5 distance = 100 according to answer choice a ."
Answer: a
Python program:
a = 20 + 20 
b = 200 / a
c = 20 * b
Problem: x = 13.165 y = 7.686 z = 11.545 the number a is obtained by first rounding the values of x , y , and z to the hundredths place and then adding the resulting values . the number b is obtained by first adding the values of x , y , and z and then rounding the sum to the hundredths place . what is the value of a – b ?
Options: a ) 0.01 , b ) 0.02 , c ) 0.03 , d ) 0.1 , e ) 0.2
Rationale: rounding off the values : x = 13.17 y = 7.69 z = 11.55 a = 13.17 + 7.69 + 11.55 = 32.41 x + y + z = 13.165 + 7.686 + 11.545 = 32.206 b = 32.21 a - b = 0.2 option e
Answer: e
Python program:
a = 13 + 165 
b = a + 11 
c = b * 100
d = math.floor(c)
e = d + 1 
f = 11 * 545
g = math.floor(f)
h = 13 * 165
i = math.floor(h)
j = 7 * 686
k = math.floor(j)
l = i + k 
m = g + l 
n = e - m
o = n / 10
Problem: how is 1 % expressed as a decimal fraction ?
Options: a ) 0.1 , b ) 0.001 , c ) 0.01 , d ) 0.0001 , e ) 1
Rationale: "1 / 100 = 0.01 answer : c"
Answer: c
Python program:
a = 1 / 100
Problem: salesperson a ' s compensation for any week is $ 350 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 14,500 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 350 + 0.06 ( x - 1000 ) = 0.08 x x = 14,500 ans : d"
Answer: d
Python program:
a = 6 / 100
b = a * 1
c = 350 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1
j = 350 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2430 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920
Rationale: "2430 * 1 / 3 = 810 option b"
Answer: b
Python program:
a = 1 / 3
b = 2430 * a
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 8 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 0.5 , b ) 1.5 , c ) 2.5 , d ) 3.5 , e ) 4.5
Rationale: "time = 4 / 4 + 4 / 8 = 12 / 8 = 1.5 hours the answer is b ."
Answer: b
Python program:
a = 8 / 2
b = a / 4
c = 8 / 2
d = c / 8
e = b + d
Problem: dacid obtained 45 , 35 , 52 , 47 and 55 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 47 , d ) 89 , e ) 45
Rationale: average = ( 45 + 35 + 52 + 47 + 55 ) / 5 = 234 / 5 = 47 . answer : c
Answer: c
Python program:
a = 45 + 35 
b = a + 52 
c = b + 47 
d = c + 55 
e = 10 / 2
f = d / e
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a quarter circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 9000 , d ) 3,600 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 90 degrees = 9000 anglets answer - c"
Answer: c
Python program:
a = 2 + 4 
b = 1 / a
c = 3600 / 10
d = c * 100
e = b * d
Problem: the product of a and b is equal to 10 more than twice the sum of a and b . if b = 9 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 10 + 2 ( a + b ) 9 a = 10 + 2 a + 18 7 a = 28 a = 4 b - a = 9 - 4 = 5 b is the answer"
Answer: b
Python program:
a = 9 * 2
b = a + 10 
c = 9 - 2
d = b / c
e = 9 - d
Problem: how many times digit 2 is used while writing numbers from 400 to 700 ?
Options: a ) 150 , b ) 190 , c ) 250 , d ) 80 , e ) 130
Rationale: "in 400 to 500 there are 50 two ' s in 500 to 600 there are 50 two ' s in 600 to 700 there are 50 two ' s so total is 150 two ' s correct option : a"
Answer: a
Python program:
a = 700 - 400
b = a / 10
c = 10 + 1 
d = 10 + 1 
e = c * d
f = b + e 
g = 2 * 2
h = f + g
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 28
Rationale: in the first 2 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 2 * 2 = 4 miles . so , the distance between him and walt was 48 - 4 = 44 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 44 / 8 = 5.5 hours . total time that lionel was walking is 2 + 5.5 = 7.5 hours , which means that he covered in that time interval distance = rate * time = 2 * 7.5 = 15 miles . answer : b .
Answer: b
Python program:
a = 2 * 2
b = 48 - a
c = 6 + 2 
d = b / c
e = d + 2 
f = 2 * e
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 15 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 29.1 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 15 = 10 * 4 = 40 time difference = 29.1 ans : c"
Answer: c
Python program:
a = 55 + 10 
b = a - 1
c = 10 / 15
d = 10 / 55
e = c - d
f = b * e
g = max(f)
Problem: the ratio of the volumes of two cubes is 2744 : 3375 . what is the ratio of their total surface areas ?
Options: a ) 71 : 76 , b ) 71 : 131 , c ) 71 : 145 , d ) 71 : 167 , e ) 71 : 113
Rationale: "ratio of the sides = ³ √ 2744 : ³ √ 3375 = 14 : 15 ratio of surface areas = 142 : 152 = 71 : 76 answer : a"
Answer: a
Python program:
a = 2744 / 3375
b = 1 / 3
c = a ** b
Problem: a and b started a business investing rs . 90,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 90000 : 20000 = 90 : 20 = 18 : 4 = 9 : 2 answer : b"
Answer: b
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 2 
f = 3 * 3
g = f + 1 
h = 2 * g
i = e / h
Problem: the compound interest on $ 2000 at 10 % per annum is $ 662 . the period ( in years ) is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: a = p ( 1 + r / 100 ) ^ t 2662 = 2000 ( 1 + 10 / 100 ) ^ t ( 11 / 10 ) ^ t = 2662 / 2000 ( 11 / 10 ) ^ t = ( 11 / 10 ) ^ 3 t = 3 years answer is b
Answer: b
Python program:
a = 2000 / 662
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 150 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,350 , d ) $ 1,100 , e ) $ 1,210
Rationale: "10 / 100 p = 150 > > p = 150 * 100 / 10 = 1500 1500 - 150 = 1350 answer : c"
Answer: c
Python program:
a = 100 / 10
b = 150 * a
c = b - 150
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 15 seconds . the speed of the train is ?
Options: a ) 35 , b ) 50 , c ) 88 , d ) 22 , e ) 12
Rationale: "speed of the train relative to man = ( 125 / 15 ) m / sec = ( 25 / 3 ) m / sec . [ ( 25 / 3 ) * ( 18 / 5 ) ] km / hr = 30 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 30 = = > x = 35 km / hr . answer : a"
Answer: a
Python program:
a = 5 * const_0_2778
b = a * 5
c = 125 - b
d = c / 5
e = d / const_0_2778