M is a list of 12 consecutive integers and N...

[BTGmoderatorLU]

M is a list of 12 consecutive integers and N is a list of 31 consecutive integers. The median of N is equal to the greatest integer of M. If the two lists are combined into one list of 43 integers, how many integers are repeated?

A. 0
B. 6
C. 12
D. 15
E. 31

The OA is C.

I need help with this PS question. Can any expert explain it please? Thanks.

[ceilidh.erickson]

The question implies that it doesn't actually matter what these integers are - we'd get the same answer whether set M started with -5 or 456,724. When that's the case, the easiest thing to do is pick numbers.

Since N is the larger set, I chose to start it with 1, so the set is from 1-31. The median of this set would be 16, so that's also the largest term in set M. That means that M must go from 5-16.

On these problems, it often helps to visualize on a number line:


Here, we can clearly see that all of the terms in set M are also in set N. Thus, there are 12 terms in common.