euclaise/mathqa_programs huggingface dataset:
Problem: if ( t - 8 ) is a factor of t ^ 2 - kt - 40 , then k =
Options: a ) 16 , b ) 1 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 1 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) b"
Answer: b
Python program:
a = 10 + 2
Problem: p alone can complete a job in 4 days . the work done by q alone in one day is equal to one - third of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 1.5 , b ) 2.0 , c ) 2.5 , d ) 3.0 , e ) 3.5
Rationale: p ' s rate is 1 / 4 q ' s rate is 1 / 12 the combined rate is 1 / 4 + 1 / 12 = 1 / 3 if they work together , the job will take 3 days . the answer is d .
Answer: d
Python program:
a = 1 / 4
b = 1 / 4
c = b / 3
d = a + c 
e = 1 / d
Problem: a man ' s speed with the current is 12 km / hr and the speed of the current is 2 km / hr . the man ' s speed against the current is
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "man ' s rate in still water = ( 12 - 2 ) km / hr = 10 km / hr . man ' s rate against the current = ( 10 - 2 ) km / hr = 8 km / hr . answer : a"
Answer: a
Python program:
a = 12 - 2
b = a - 2
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 242 runs ?
Options: a ) 6.25 , b ) 5.25 , c ) 6.29 , d ) 6.39 , e ) 6.13
Rationale: "required run rate = [ 242 - ( 3.2 * 10 ) ] / 40 = 210 / 40 = 5.25 answer : b"
Answer: b
Python program:
a = 10 * 3
b = 242 - a
c = b / 40
Problem: the population of a bacteria colony doubles every day . if it was started 8 days ago with 4 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 131072 , e ) 409600
Rationale: "4 ^ 8 ( 2 ) = 131072 the answer is d ."
Answer: d
Python program:
a = 8 + 1 
b = 4 ** a
c = b - 1
Problem: a coin is tossed six times . what is the probability that there is at the least one tail ?
Options: a ) 63 / 64 , b ) 31 / 37 , c ) 31 / 18 , d ) 31 / 10 , e ) 31 / 19
Rationale: let p ( t ) be the probability of getting least one tail when the coin is tossed six times . = there is not even a single tail . i . e . all the outcomes are heads . = 1 / 64 ; p ( t ) = 1 - 1 / 64 = 63 / 64 answer : a
Answer: a
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 2
d = b * c
e = 1 / 2
f = d * e
g = 1 / 2
h = f * g
i = a * h
j = i * 1
Problem: how many positive integers less than 5,000 are there in which the sum of the digits equals 5 ?
Options: a ) 64 , b ) 62 , c ) 63 , d ) 61 , e ) 56
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . e"
Answer: e
Python program:
a = 4 + 5 
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: what is the rate percent when the simple interest on rs . 5000 amount to rs . 2500 in 5 years ?
Options: a ) 9 % , b ) 8 % , c ) 10 % , d ) 10.5 % , e ) 7.5 %
Rationale: "interest for 1 year = 2500 / 5 = 500 interest on rs 5000 p / a = 500 interest rate = 500 / 5000 * 100 = 10 % answer : c"
Answer: c
Python program:
a = 100 * 2500
b = 5000 * 5
c = a / b
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction q of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is q = 2 / 14 = 1 / 7 . answer : e
Answer: e
Python program:
a = math.lcm(2, 3)
b = a / 2
c = b - 2
Problem: given the two equations 3 x + 2 y = 16 and 5 x + 3 y = 26 , by how much does r exceed s ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 1 , e ) 2
Rationale: solve by simultaneous equations . my answer is e . x = 4 y = 2
Answer: e
Python program:
a = 16 * 2
b = a / 16
Problem: the length of a rectangular floor is more than its breadth by 300 % . if rs . 423 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
Options: a ) 24 , b ) 25 , c ) 26.6 m , d ) 26 , e ) 27
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 400 % of b = l + 4 b = 5 b area of the floor = 423 / 3 = 141 sq m l b = 141 i . e . , l * l / 5 = 141 l 2 = 705 = > l = 26.6 m . answer : c"
Answer: c
Python program:
a = 423 / 3
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: a can finish a work in 18 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day
Options: a ) 1 \ 5 , b ) 1 \ 6 , c ) 1 \ 7 , d ) 1 \ 8 , e ) 1 \ 9
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 18 b ' s 1 day work = 1 / 9 [ because b take half time than a ] ( a + b ) ' s one day work = ( 1 / 18 + 1 / 9 ) = ( 1 + 2 / 18 ) = 1 / 6 so in one day 1 / 6 work will be done . option b"
Answer: b
Python program:
a = 1 / 18
b = 1 / 18
c = b * 2
d = a + c
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 22.51 , b ) 22.0 , c ) 22.15 , d ) 22.17 , e ) 22.63
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 10 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 14 ) = 1 / 2 ( 22 / 7 ) ( 14 ) = 308 / 14 = 22 cm to two decimal places answer : b"
Answer: b
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 198,000 . what was the percent increase in the cost of the home ?
Options: a ) 65 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: "increase = 198000 - 120000 = 78000 % increase = 78000 * 100 / 120000 = 65 % answer : option a"
Answer: a
Python program:
a = 4 * 4
b = 12 * a
c = b * 1000
d = 12 * 1000
e = d * 10
f = c - e
g = 12 * 1000
h = g * 10
i = f / h
j = i * 100
Problem: a is a working partner and b is a sleeping partner in a business . a puts in 80,000 and b 70,000 . a gets 25 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the profit if b get 14000 .
Options: a ) 42000 , b ) 46000 , c ) 54000 , d ) 40000 , e ) none of these
Rationale: "let amount distributed between a and b is x ratio of capital between a and b is 8 : 7 if b get 14000 then x * 7 / 15 = 14000 x * 7 = 210000 x = 30000 let total profit = y y * 75 / 100 = 30000 y = 40000 answer d"
Answer: d
Python program:
a = 25 * 14000
b = a / 100
c = 14000 - b
d = 2 + 3 
e = c * d
f = 2 + 3 
g = 2 + 4 
h = f + g 
i = e / h
j = 25 * 14000
k = j / 100
l = i + k
Problem: how many integers are divisible by 5 between 10 ! and 10 ! + 20 inclusive ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: a - 7 10 ! is divisible by 5 there are 4 numbers between 10 ! and 10 ! + 20 that are divisible by 5 . hence 5
Answer: a
Python program:
a = 20 / 5
b = a + 1
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 150 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: "the distance between the nest and the ditch is 150 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 150 = 4500 . d = st 4500 / 1.5 = t , i think we can take 4500 meters as 4.5 km , then only we get t = 4.5 . ( 1000 meters = 1 km ) d )"
Answer: d
Python program:
a = 15 * 2
b = 150 * a
c = b / 1000
d = 15 / 10
e = c / d
Problem: if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 9 m of the same rod ?
Options: a ) 22.8 kg , b ) 34.2 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 9 : : 42.75 : x = > 11.25 x x = 9 x 42.75 = > x = ( 9 x 42.75 ) / 11.25 = > x = 34.2 answer : b"
Answer: b
Python program:
a = 9 * 42
b = a / 11
Problem: if paint costs $ 3.20 per quart , and a quart covers 120 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60 , b ) $ 16.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 196.00
Rationale: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 120 = 5 cost will be 5 * 3.2 = $ 16 ans : b"
Answer: b
Python program:
a = 3 / 20
b = a * surface_cube
Problem: if 3 / p = 6 & 3 / q = 18 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 1 / 3
Rationale: "p = 3 / 6 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 1 / 2 ) - ( 1 / 6 ) = 1 / 3 answer : e"
Answer: e
Python program:
a = 3 / 6
b = 3 / 18
c = a - b
Problem: two trains 150 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 ) 10.16 sec , b ) 18.8 sec , c ) 14.8 sec , d ) 10.8 sec , e ) 11.16 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 150 + 160 = 310 m . required time = 310 * 9 / 250 = 279 / 25 = 11.16 sec . answer : e"
Answer: e
Python program:
a = 150 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of colors in a pair does not matter )
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Rationale: let # of colors needed be nn , then it must be true that n + c 2 n ≥ 12 n + cn 2 - # of ways to choose the pair of different colors from nn colors when order does n ' t matter ) - - > n + n ( n − 1 ) / 2 ≥ 12 - - > 2 n + n ( n − 1 ) ≥ 24 - - > n is an integer ( it represents # of colors ) n ≥ 5 - - > nmin = 5 answer : b .
Answer: b
Python program:
a = 12 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 12 / 2
i = h - 1
j = g - i
Problem: the average of 5 numbers is 27 . if one number is excluded the average become 25 . the excluded number is :
Options: a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 37
Rationale: solution excluded number = ( 27 × 5 ) - ( 25 × 4 ) = 135 - 100 = 35 . answer d
Answer: d
Python program:
a = 5 * 27
b = 5 - 1
c = b * 25
d = a - c
Problem: a train 200 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 11 , b ) 10 , c ) 5 , d ) 9 , e ) 8
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 200 * 3 / 55 ] sec = 11 sec answer : a"
Answer: a
Python program:
a = 200 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 9 % p . a . in 5 years . what is the sum ?
Options: a ) 3888 , b ) 2988 , c ) 2777 , d ) 8925 , e ) 288
Rationale: principal = ( 100 * 4016.25 ) / ( 9 * 5 ) = rs . 8925 . answer : d
Answer: d
Python program:
a = 4016 * 25
b = a / 9
c = b / 5
Problem: the captain of a cricket team of 11 members is 24 years old and the wicket keeper is 7 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "let the average age of the whole team be x years . 11 x - ( 24 + 31 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is c ."
Answer: c
Python program:
a = 24 + 7 
b = 24 + a 
c = 3 * 0
d = b - c
e = d / 2
Problem: in a box of 16 pens , a total of 3 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 / 9 , c ) 6 / 20 , d ) 13 / 20 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 3 defective in a lot of 16 pens i . e . probability of first pen not being defective = ( 13 / 16 ) i . e . probability of second pen not being defective = ( 12 / 15 ) [ 15 pen remaining with 12 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 12 / 15 ) * ( 13 / 16 ) = 13 / 20 answer : option d"
Answer: d
Python program:
a = 16 - 3
b = a / 16
c = 16 - 3
d = c - 1
e = 16 - 1
f = d / e
g = b * f
Problem: during a pizza buffet where a eats more times 2.6 than b , and b eats 4 times less than c . find the least number of times all the 3 has to eat
Options: a ) 250 , b ) 260 , c ) 270 , d ) 280 , e ) 285
Rationale: a eats more than b if b eats 1 times than the ratio of a and b is a : b is 2.6 : 1 or 13 : 5 and as b eat 4 times less the c the the ratio of b : c is 5 : 20 the the least number of times all three has eat is the lcm of a , b , c that is 260 . . answer : b
Answer: b
Python program:
a = 2 * 6
b = a / 2
c = 4 * 10
d = c / 2
e = math.lcm(b, d)
Problem: if the mean of numbers 28 , x , 42 , 78 and 104 is 62 , what is the mean of 48 , 62 , 98 , 124 and x ?
Options: a ) 78 , b ) 58 , c ) 390 , d ) 310 , e ) 66
Rationale: "x is common to both the series . so , x is not going to make a difference to the average . only the remaining 4 numbers will contribute to the difference in average between the two series . sum of the 4 numbers , excluding x , of the first series is 28 + 42 + 78 + 104 = 252 sum of the 4 numbers , excluding x , of the second series is 48 + 62 + 98 + 124 = 332 the difference between the sum of the two sets of numbers = 332 - 252 = 80 the sum of the second series is 80 more than the sum of the first series . if the sum of the second series is 80 more , the average of the second series will be 80 / 5 = 16 more than the first series . therefore , the average of the second series = 62 + 16 = 78 . answer a"
Answer: a
Python program:
a = 4 + 1 
b = 62 * a
c = 28 + 42 
d = c + 78 
e = d + 104 
f = b - e
g = f + 48 
h = g + 62 
i = h + 98 
j = i + 124 
k = 4 + 1 
l = j / k
Problem: company p had 15 percent more employees in december than it had in january . if company p had 450 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 392 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 450 j = 450 / 1.15 j = 45,000 / 115 = 392 thus b is the correct answer ."
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 450 / b
Problem: salley ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning salley makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?
Options: a ) 15 , b ) 24 , c ) 25 , d ) 26 , e ) 13
Rationale: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now salley can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional paymentsi . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c
Answer: c
Python program:
a = 7 + 5 
b = a / 0
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 700 more than that by the previous schema , his sales were worth ?
Options: a ) s . 8,000 , b ) s . 9,000 , c ) s . 20,000 , d ) s . 10,000 , e ) s . 50,000
Rationale: [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 700 x = 8000 answer a
Answer: a
Python program:
a = 5 * 4
b = a - 12
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 150 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 10 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 150 rs . 5 m + 5 m + 5 m - - - - - 150 rs . 15 m - - - - - - 150 rs . = > 1 m = 10 rs . answer : e"
Answer: e
Python program:
a = 3 * 5
b = 150 / a
Problem: if a : b : : 3 : 4 , then what is ( 5 a + 6 b ) : ( a - 2 b ) ?
Options: a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 39 : 5 , e ) - 1 : 10
Rationale: "a / b = 3 / 4 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 6 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 4 ) + 6 ] / [ ( 3 / 4 ) - 2 ] = - 39 / 5 answer : d"
Answer: d
Python program:
a = 5 * 3
b = 4 * 6
c = a + b 
d = 2 * 4
e = 3 - d
f = c / e
Problem: a began business with rs . 45000 and was joined afterwards by b with rs . 36000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1.5 , b ) 6 , c ) 7.5 , d ) 8.5 , e ) 2
Rationale: "45 * 12 : 36 * x = 2 : 1 x = 7.5 12 - 7.5 = 4.5 answer : c"
Answer: c
Python program:
a = 4 * 3
b = 4 * 3
c = 45000 * b
d = c / 36000
e = d / 2
f = a - e
Problem: in the xy - coordinate system , what is the slope of the line that goes through point ( 2 , 4 ) and is equidistant from the two points p = ( 9 , 3 ) and q = ( 5 , 9 ) ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "first , get the middle coordinate between ( 9,3 ) and ( 5,9 ) . x = 9 + ( 5 - 9 ) / 2 = 7 y = 3 + ( 9 - 3 ) / 2 = 6 second , get the slope of ( 7,6 ) and ( 2,4 ) . m = 6 - 4 / 7 - 2 = 2 / 5 = 0.4 answer : d"
Answer: d
Python program:
a = 4 + 3 
b = a / 3
c = 4 + 0 
d = c / 2
e = b / d
Problem: two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 28 , b ) 266 , c ) 990 , d ) 20 , e ) 22
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 160 + 280 = 440 m . the time required = d / s = 440 / 20 = 22 sec . answer : e"
Answer: e
Python program:
a = 160 + 280 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 47.14 cm , c ) 26.71 cm , d ) 94.94 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 20 + 14 ) = 68 cm parameter of the square = 68 cm i . e . 4 a = 68 a = 17 diameter of the semicircle = 17 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 17 ) = 1 / 2 ( 22 / 7 ) ( 17 ) = 374 / 14 = 26.71 cm to two decimal places answer : c"
Answer: c
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: if x > 0 , x / 10 + x / 25 is what percent of x ?
Options: a ) 6 % , b ) 14 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 10 + 100 / 25 = 10 + 4 = 14 14 is 14 % of 100 = b"
Answer: b
Python program:
a = 1 / 10
b = 1 / 25
c = a + b 
d = c * 100
Problem: evaluate : 30 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 12 , e ) 22
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 30 - 12 * 3 * 2 = 30 - 8 = 22 correct answer e"
Answer: e
Python program:
a = 12 * 2
b = a * 2
c = 30 - b
Problem: one day , raviraj left home and cycled 20 km southwards , turned right and cycled 10 km and turned right and cycled 20 km and turned left and cycled 20 km . how many kilometres will he have to cycle to reach his home straight ?
Options: a ) 50 , b ) 30 , c ) 40 , d ) 60 , e ) 80
Rationale: raviraj starts from home at a , moves 20 km in south upto b . then he turns right and moves 10 km upto c , then he turns right and moves 20 km upto d , then he turns lefts and moves 20 km upto e . so from image it is clear that , if he moves straight then he will have to move ad + de , ad = bc = 10 km so , he will have to move 10 + 20 = 30 km answer b
Answer: b
Python program:
a = 20 + 10
Problem: a train running at a speed of 36 km / h passes an electric pole in 14 seconds . in how many seconds will the whole train pass a 370 - meter long platform ?
Options: a ) 45 , b ) 47 , c ) 49 , d ) 51 , e ) 53
Rationale: let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 14 * 10 = 140 m . the time taken to pass the platform = ( 140 + 370 ) / 10 = 51 seconds the answer is d .
Answer: d
Python program:
a = 36 * const_0_2778
b = a * 14
c = b + 370 
d = 36 * const_0_2778
e = c / d
Problem: a train is 360 meter long is running at a speed of 50 km / hour . in what time will it pass a bridge of 140 meter length .
Options: a ) 26 seconds , b ) 36 seconds , c ) 46 seconds , d ) 56 seconds , e ) none of these
Rationale: "explanation : speed = 50 km / hr = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 125 / 9 = 36 seconds answer : b"
Answer: b
Python program:
a = 360 + 140 
b = 50 * 1000
c = b / 3600
d = a / c
Problem: if 50 % of x is 30 less than 25 % of 1500 , then x is ?
Options: a ) 690 , b ) 860 , c ) 560 , d ) 875 , e ) 880
Rationale: "50 % of x = x / 2 ; 25 % of 1500 = 25 / 100 * 1500 = 375 given that , x / 2 = 375 - 30 = > x / 2 = 345 = > x = 690 . answer : a"
Answer: a
Python program:
a = 25 / 100
b = 1500 * a
c = b - 30
d = 50 / 100
e = c / d