euclaise/mathqa_programs huggingface dataset:
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 145 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 2688 , d ) 500 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 145 x = 500 answer : d"
Answer: d
Python program:
a = 6 * 2500
b = a / 100
c = 145 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f
Problem: find the mean proportional between 49 & 64 ?
Options: a ) a ) 59 , b ) b ) 61 , c ) c ) 56 , d ) d ) 65 , e ) e ) 67
Rationale: "formula = √ a × b a = 49 and b = 64 √ 49 × 64 = 7 × 8 = 56 c"
Answer: c
Python program:
a = 49 + 64 
b = a / 2
Problem: one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 4 robots altogether , if the robots build only one robot at a time ?
Options: a ) 70 min , b ) 94 min , c ) 110 min , d ) 112 min , e ) 120 min
Rationale: first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) now the 3 robots work together at the rate of 1 + 1 / 2 + 1 / 2 = 4 / 2 = 2 / 1 so they complete one robot in 1 / 2 an hour , i . e 30 minutes - ( 2 ) and now we have 4 robots so total = ( 1 ) + ( 2 ) = 70 minutes answer - a
Answer: a
Python program:
a = 1/(1)
b = 1/(2)
c = a + b 
d = 1/(2)
e = c + d 
f = 1/(e)
g = 1/(1)
h = 1/(2)
i = g + h 
j = 1/(i)
k = f + j
Problem: 50 % of a number is 10 less than 3 / 5 th of that number . what is the number ?
Options: a ) 100 , b ) 50 , c ) 150 , d ) 200 , e ) 75
Rationale: "let the number be x then , 3 x / 5 - ( 50 % of x ) = 10 3 x / 5 - 50 x / 100 = 10 x = 100 answer is a"
Answer: a
Python program:
a = 10 * 5
b = 100 / 5
c = a * b
d = 100 / 5
e = d * 3
f = e - 50
g = c / f
Problem: 17 + 18 = 35 . how many such 2 consecutive numbers are there less than 200 when added gives a sum which is divisible by 5 ?
Options: a ) 80 , b ) 40 , c ) 50 , d ) 60 , e ) 20
Rationale: since 2 + 3 = 5 & 7 + 8 = 15 any combination with these no be will give u desirable result . . . so total no in 100 will be 20 & that ' s why in 200 , it will be 40 answer : b
Answer: b
Python program:
a = 200 / 5
Problem: the profit earned by selling an article for 872 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 ) 990 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 872 – x = 448 + x or , x = 424 ⁄ 2 = 212 \ cost price of the article = 872 – x = 448 + x = 660 \ sp of the article = 660 × 150 ⁄ 100 = 990 answer b"
Answer: b
Python program:
a = 872 + 448 
b = a / 2
c = 50 / 100
d = 1 + c 
e = b * d
Problem: a candidate got 40 % of the votes polled and he lost to his rival by 2000 votes . how many votes were cast ?
Options: a ) 10000 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 6851
Rationale: "40 % - - - - - - - - - - - l 60 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - 2000 100 % - - - - - - - - - ? = > 10000 answer : a"
Answer: a
Python program:
a = 40 / 100
b = 1 - a
c = 40 / 100
d = b - c
e = 2000 / d
Problem: one night 17 percent of the female officers on a police force were on duty . if 170 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 400 , b ) 420 , c ) 450 , d ) 480 , e ) 500
Rationale: let x be the number of female police officers on the police force . the number of female police officers on duty was 85 . 0.17 x = 85 x = 500 the answer is e .
Answer: e
Python program:
a = 170 / 2
b = 17 / 100
c = a / b
Problem: the circumferences of two circles are 396 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29960 sq m , b ) 26950 sq m , c ) 43120 sq m , d ) 27680 sq m , e ) 27786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 396 and 2 ∏ l = 704 s = 396 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 198 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 198 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 198 - 352 ) ( 198 + 352 ) / ∏ = ( 154 ) ( 550 ) / ( 22 / 7 ) = 26950 sq m answer : b"
Answer: b
Python program:
a = 2 * math.pi
b = 704 / a
c = circle_area - (
Problem: a train 495 m long is running at a speed of 63 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec total distance covered = 495 + 240 = 735 m required time = 700 * 2 / 35 = 42 sec answer : d"
Answer: d
Python program:
a = 63 - 240
b = a * const_0_2778
c = 495 / b
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 27 , find the value of ab .
Options: a ) 12 , b ) 15 , c ) 10 , d ) 18 , e ) 9
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 27 - 9 = 18 ab = 9 . answer is e ."
Answer: e
Python program:
a = math.sqrt(27)
b = a - 3
c = b / 2
d = 3 + c 
e = math.sqrt(27)
f = e - 3
g = f / 2
h = d * g
i = h * 2
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is ?
Options: a ) 75 , b ) 78 , c ) 80 , d ) 82 , e ) 86
Rationale: "divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 e )"
Answer: e
Python program:
a = 6 * 3
b = a + 2 
c = 6 * 3
d = c + 2 
e = d / 5
f = b * e
g = f + 6
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 6 years ?
Options: a ) 3277 , b ) 2977 , c ) 7119 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 6 answer : c"
Answer: c
Python program:
a = 100 * 100
b = 4 * a
c = 3 / 4
d = c ** 6
e = b * d
Problem: there are 50 employees in the office of abc company . of these , 22 have taken an accounting course , 14 have taken a course in finance and 15 have taken a marketing course . 10 of the employees have taken exactly two of the courses and 1 employee has taken all 3 of the courses . how many of the 50 employees have taken none of the courses ?
Options: a ) 11 , b ) 5 , c ) 9 , d ) 8 , e ) 10
Rationale: 50 employees . counting every different attendand to the courses we have : accounting : 22 finance : 14 marketing : 15 which would add up to 51 different attendands , which is not possible . now 10 have taken exactly 2 courses , which means that there are 10 less different attendands . say that 10 of the finance attentands also attended accounting . 51 - 10 = 41 1 person has taken all three courses . as above , we subtract him from the number of different attendands . since this time the person took all three courses , we have to substract him two times . 41 - 2 = 39 . answer : a
Answer: a
Python program:
a = 22 + 14 
b = a + 15 
c = b - 10
d = 1 * 2
e = c - d
f = 50 - e
Problem: if an object travels 80 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 21.21 , b ) 24.24 , c ) 27.27 , d ) 30.35 , e ) 33.33
Rationale: "80 feet / 2 seconds = 40 feet / second ( 40 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 27.27 miles / hour ( approximately ) the answer is c ."
Answer: c
Python program:
a = 80 / 5280
b = 1 / 3600
c = 2 * b
d = a / c
Problem: what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 2 , and 4 if each digit can be used only once in each number ?
Options: a ) 1210 , b ) 1221 , c ) 1332 , d ) 1443 , e ) 1554
Rationale: there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 222 ) + 2 ( 444 ) = 1554 the answer is e .
Answer: e
Python program:
a = 4 + 2 
b = a + 1 
c = b * 100
d = 4 + 2 
e = d + 1 
f = e * 10
g = c + f 
h = 4 + 2 
i = h + 1 
j = g + i 
k = j * 2
Problem: if x is real , find the maximum value of the expression - 2 x ^ 2 + 11 x + 13 .
Options: a ) 16.125 , b ) 20.125 , c ) 24.125 , d ) 28.125 , e ) 32.125
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 11 x + 13 = ( - 2 x + 13 ) ( x + 1 ) the roots are 13 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 2.75 the maximum value is - 2 ( 2.75 ) ^ 2 + 11 ( 2.75 ) + 13 = 28.125 the answer is d ."
Answer: d
Python program:
a = 2 * 2
b = a / 11
c = 11 * b
d = c + 13 
e = 2 * 2
f = e / 11
g = f ** 2
h = 2 * g
i = d - h
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number x is
Options: a ) 74 , b ) x = 75 , c ) x = 175 , d ) x = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Python program:
a = 34 * 2
b = 34 * 2
c = 8 * 5
d = b - c
e = 5 - 1
f = d / e
g = a + f
Problem: if 1 = x . 2 = 2 x 3 = 4 x . . . . what is 2 x * 6 x + 5 x / 4 x - 56 x
Options: a ) 1 , b ) 22 , c ) 23 , d ) 10 , e ) 25
Rationale: let 1 = x 2 = 2 x 3 = 4 x 4 = 8 x 5 = 16 x 6 = 32 x 7 = 64 x now given 2 x * 6 x + 5 x / 4 x - 56 x i can write it as = 2 x * ( 2 x + 4 x ) + ( x + 4 x ) / 4 x - ( 64 x - 8 x ) now by putting the values i get = 2 * ( 2 + 3 ) + ( 8 + 1 ) / 3 - ( 7 - 4 ) = 2 * 5 + 9 / 3 - 3 = 10 + 9 / 3 - 3 = 10 + 3 - 3 = 10 answer : d
Answer: d
Python program:
a = 2 * 6
b = a * 2
c = b / 2
d = c - 2
Problem: the closest approximation of a ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: "a ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c"
Answer: c
Python program:
a = 0 / 4
b = a * 69
Problem: a number exceeds 20 % of itself by 40 . the number is ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 320 , e ) none
Rationale: answer ∵ a - 20 % of a = 40 ⇒ a - a / 5 = 40 ⇒ 4 a / 5 = 40 ∴ a = ( 5 x 40 ) / 4 = 50 . correct option : a
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 40 / b
Problem: 9.009 / 5.005 =
Options: a ) 1.08 , b ) 1.4 , c ) 1.8018 , d ) 1.4014 , e ) 1.8
Rationale: "9.009 / 5.005 = 9009 / 5005 = 9 ( 1001 ) / 5 ( 1001 ) = 9 / 5 = 1.8 the answer is e ."
Answer: e
Python program:
a = 9 / 9
b = a * 100
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 294 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 294 2 l ^ 2 / 3 = 294 l ^ 2 = 441 l = 21 cm the answer is c ."
Answer: c
Python program:
a = 294 / 10
Problem: if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } is used exactly once , in how many ways can the digits be arranged ?
Options: a ) 36,100 , b ) 38,210 , c ) 40,320 , d ) 42,430 , e ) 44,540
Rationale: "8 ! = 40,320 the answer is c ."
Answer: c
Python program:
a = math.factorial(6)
Problem: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 8 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "if n = 9 mark sold 1 box and ann sold 7 boxes total 8 < 9 answer : e"
Answer: e
Python program:
a = 8 + 1
Problem: a store reduced the price of all items in the store by 9 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 80.9 , c ) 81.0 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 9 % price becomes = 0.91 * 100 = $ 91 after the final reduction of 10 % price becomes = 0.9 * 91 = $ 81.9 price of all items on second day is 81.9 % of price on first day correct answer option e"
Answer: e
Python program:
a = 100 - 9
b = a / 100
c = 100 - 10
d = c / 100
e = b * d
f = e * 100
Problem: the maximum number of students among them 890 pens and 630 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 10 , b ) 910 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 890 and 630 = 10 . answer : a"
Answer: a
Python program:
a = math.gcd(890, 630)
Problem: a certain bacteria colony doubles in size every day for 22 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 21 , d ) 15 , e ) 19
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 20 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 21 times . answer : c . similar questions to practice : hope it helps ."
Answer: c
Python program:
a = 22 / 22
b = 22 - a
Problem: on a purchase of $ 110 , a store offered a payment plan consisting of a $ 10 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 ) 9.5 % , b ) 10.5 % , c ) 11.5 % , d ) 9.1 % , e ) 12.5 %
Rationale: "12 * 10 + 10 = 130 ( 10 / 110 ) * 100 = 9.1 answer : d"
Answer: d
Python program:
a = 10 * 12
b = a + 10 
c = 10 * 12
d = b - c
e = d / 110
f = e * 100
Problem: laura took out a charge account at the general store and agreed to pay 9 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.15
Rationale: principal that is amount taken by laura at year beginning = 35 $ rate of interest = 9 % interest = ( 9 / 100 ) * 35 = 3.15 $ total amount that laura owes a year later = 35 + 3.15 = 38.15 $ answer e
Answer: e
Python program:
a = 9 / 100
b = a * 35
c = b + 35
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 9 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in ap whose first term is 30 and last term is 46 = 9 / 2 [ 30 + 46 ] = 342 km . answer : a"
Answer: a
Python program:
a = 2 * 9
b = 30 + a 
c = b + 30 
d = c / 2
Problem: the sum of two numbers is 72 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 30 - 42 , e ) 21 - 63
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 72 : word problem = 72 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 72 â ˆ ’ 12 = 60 . x = 60 / 2 = 30 . this is the first number . therefore the other number is x + 12 = 30 + 12 = 42 . the sum of 30 + 42 is 72 . d"
Answer: d
Python program:
a = 72 - 12
b = a / 2
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 20 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 7 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 620 secs . his sis ' time = 576 secs . percent increase needed = ( 620 - 576 / 620 ) * 100 = 44 / 640 * 100 = 7 % . ans ( c ) ."
Answer: c
Python program:
a = 10 * 10
b = 9 * const_60
c = b + 36 
d = 10 * const_60
e = d + 20 
f = c / e
g = 1 - f
h = a * g
Problem: which digits should come in place of * and $ if the number 62684 * $ is divisible by both 8 and 5 ?
Options: a ) 8,5 , b ) 4,0 , c ) 1,4 , d ) 0,8 , e ) 8,0
Rationale: "since the given number is divisible by 5 , so 0 or 5 must come in place of $ . but , a number ending with 5 is never divisible by 8 . so , 0 will replace $ . now , the number formed by the last three digits is 4 * 0 , which becomes divisible by 8 , if * is replaced by 4 . hence , digits in place of * and $ are 4 and 0 respectively . answer b 4,0"
Answer: b
Python program:
a = math.lcm(8, 5)
b = a * 2
c = b / 10
d = c / 2
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 3200 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 4000 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 3200 5 - - - ? = > 4000 answer : b"
Answer: b
Python program:
a = 12 - 7
b = 7 - 3
c = 3200 / b
d = a * c
Problem: a man can row downstream at 24 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 2 , 7 , b ) 7 , 4 , c ) 8 , 7 , d ) 4 , 7 , e ) 17 , 7
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 24 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 7 answer : e"
Answer: e
Python program:
a = 24 + 10 
b = a / 2
c = b / 2
Problem: john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 4 % and the mobile phone at a profit of 15 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 620 , c ) s . 600 , d ) s . 650 , e ) s . 690
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 15 / 100 ) = 8000 + 120 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 1200 = rs . 600 as this is positive , an overall profit of rs . 600 was made . c"
Answer: c
Python program:
a = 8000 / 100
b = 15 * a
c = 15000 / 100
d = 4 * c
e = b - d
Problem: in a kilometer race , a beats b by 50 meters or 20 seconds . what time does a take to complete the race ?
Options: a ) 380 sec , b ) 190 sec , c ) 726 sec , d ) 127 sec , e ) 128 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 20 ) / 50 = 400 sec . time taken by a = 400 - 20 = 380 sec . answer : a"
Answer: a
Python program:
a = 1 * 1000
b = 50 / 20
c = a / b
d = c - 20
Problem: what is the least value of x . so that 24 x 57 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 4 + x + 5 + 7 = 18 + x least value of x may be 0 therefore 18 + 0 = 18 is divisible by 3 . answer : option b"
Answer: b
Python program:
a = math.lcm(24, 57)
b = a / 57
c = b / 4
d = c / 4
Problem: if i walk at 5 km / h , i miss the bus by 12 minutes . if i walk at 6 km / h , i reach 15 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 11.0 km , b ) 13.8 km , c ) 11.5 km , d ) 12.5 km , e ) 13.5 km
Rationale: "d = product of speed difference of time / difference of speed d = 5 x 6 / 60 [ 12 â ˆ ’ ( â ˆ ’ 15 ) / 6 - 5 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 13.5 km answer e"
Answer: e
Python program:
a = 5 * 6
b = 6 - 5
c = a / b
d = 12 + 15 
e = d / const_60
f = c * e
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 3 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 1220 , b ) $ 1330 , c ) $ 1550 , d ) $ 1770 , e ) $ 1880
Rationale: "the total surface area is 2 ( 3 * 4 + 4 * 5 + 3 * 5 ) = 94 square feet the total cost is 94 * $ 20 = $ 1880 the answer is e ."
Answer: e
Python program:
a = surface_rectangular_prism * (
Problem: a sum of money deposited at c . i . amounts to rs . 3650 in 2 years and to rs . 4015 in 3 years . find the rate percent ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "explanation : 3650 - - - - - - - - 365 100 - - - - - - - - ? ( 10 % ) answer : option a"
Answer: a
Python program:
a = 4015 - 3650
b = a / 3650
c = b * 100
Problem: if 5 - 5 / x = 4 + 4 / x , then x =
Options: a ) 1 , b ) 9 , c ) - 1 , d ) 5 / 4 , e ) - 4 / 5
Rationale: "we ' re given the equation 5 - 5 / x = 4 + 4 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 5 x - 5 x / x = 4 x + 4 x / x we can then eliminate that denominator , which gives us . . . . 5 x - 5 = 4 x + 4 9 = x b"
Answer: b
Python program:
a = 4 + 5 
b = 5 - 4
c = a / b
Problem: the sum of the squares of two numbers is 3341 and the diference of their squares is 891 . the numbers are :
Options: a ) 35 and 46 , b ) 35 and 49 , c ) 35 and 42 , d ) 35 and 41 , e ) 35 and 48
Rationale: explanation : let the numbers be x and y . then , adding ( i ) and ( ii ) , we get : subtracting ( ii ) from ( i ) , we get : so , the numbers are 35 and 46 answer : a
Answer: a
Python program:
a = 3341 - 891
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 3341 - 891
f = e / 2
g = 3341 - f
h = math.sqrt(g)
i = d + h
Problem: two trains are moving in opposite direction @ 60 kmph and 90 kmph . their lengths are 1.10 km and 0.9 km respectively . the time taken by the slower train to cross the faster train in seconds is
Options: a ) 36 , b ) 45 , c ) 48 , d ) 49 , e ) 50
Rationale: r . s = ( 60 + 90 ) kmph = > ( 150 * 5 / 18 ) m / sec = > ( 125 / 3 ) m / sec distance covered = ( 1.10 + 0.9 ) km = ( 2 * 1000 ) = 2000 m . required time = ( 2000 * 3 / 125 ) = 48 sec . answer : c
Answer: c
Python program:
a = 1 + 1 
b = 1000 * a
c = 60 + 90 
d = 1000 / 3600
e = c * d
f = 1/(e)
g = b * f
Problem: a sum amounts to rs . 8820 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 4000 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 8000
Rationale: "ci = 8820 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 8820 = p [ 21 / 20 ] ^ 2 8820 [ 20 / 21 ] ^ 2 8000 answer : e"
Answer: e
Python program:
a = 5 / 100
b = a + 1 
c = b ** 2
d = 8820 / c