Big mess of different concepts

[Anindya Madhudor]

During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If the class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer?

a. 0%
b. 10%
c. 20%
d. 30%
e. 40%

[eaakbari]

IMO A

The term can be summarized as 7^d*3 + 2(a)

where d denotes days and a denotes age.

From the above term we can state that the first term will always be odd and the second even

even + odd = odd

Since all numbers of the set will be odd

The median of 14th and 15th term = (odd + odd)/2

since odd + odd is always even

The answer will always be an integer

Hence A

Whats OA

[Anindya Madhudor]

Thanks for the response. Your approach makes perfect sense. I misinterpreted the part "adding this to the doubled age of the student in years, rounded to the nearest year". I thought we need to round after multiplying by two. Sorry, don't have the OA.