We need to know 2 things to answer this question.

First, each student's lucky number will ALWAYS be an ODD INTEGER.
We know this because...
lucky number = 7^(student's favorite day of the week - 1,2,3.. or 7) x 3 + (doubled ages of students in years)
In other words, lucky number = (ODD INTEGER x ODD INTEGER) + EVEN INTEGER
= ODD INTEGER + EVEN INTEGER
= ODD INTEGER

Second, when we have an even number of values (28 values), the MEDIAN equals the average (arithmetic mean) of the two middle-most integers (when all of the integers are arranged in ascending order).

Since all 28 values are guaranteed to be ODD (see point #1 above), then we know that the two middle-most integers will be ODD.
So, the median of the 28 values = (some ODD integer + some ODD integer)/2
= (an even integer)/2
= an integer.
In other words, the median of the 28 values is GUARANTEED to be an integer.

So, P(the median of the lucky numbers will be a non-integer) = 0%

Answer: A

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Brent Hanneson – Founder of gmatprepnow.com

Student's age is integral value. In question, we are multiplying student's age by 2 and adding some 3* 7^x something over there.


It means Even (2* age of students) + Odd (3) * 7 ^x (where x is day of week).

We know that 7^x is always odd. (e.g. 7, 49, 243, 1701, and repeat).
=> 3* odd is again odd.


2 * age of students is always even.

So final equation is even +odd = odd.

Avg of any number of odd digits or any number of even digits can never be non integral value. So 0% is the answer.
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