Andy, Jen, Sally, Mike, and Tom are sitting in a row of five seats. Andy is not beside Jen. Sally is beside Mike. Who cannot be sitting in the middle seat?
(A) Andy
(B) Jen
(C) Sally
(D) Mike
(E) Tom

## Part C: Each correct answer is worth 8.
Solution 1

To determine who cannot be sitting in the middle seat, we may eliminate the 4 people who can be sitting in the middle seat.

First, assume that Sally and Mike, who must be beside one another, are in seats 1 and 2, or in seats 2 and 1 .

Since Andy and Jen are not beside each other, either Andy is in seat 3 (the middle seat) and Jen is in seat 5 , or vice versa.

Thus, Andy and Jen can each be sitting in the middle seat and are eliminated as possible choices.

Next, assume that Sally and Mike are in seats 2 and 3, or in seats 3 and 2.

That is, either Sally is in the middle (seat 3), or Mike is.

In either case, seats 1, 4 and 5 are empty, allowing either Andy or Jen to choose seat 1 and hence, they are not next to one another.

This demonstrates that Sally and Mike can each be sitting in the middle seat.

Having eliminated Andy, Jen, Sally, and Mike, it must be Tom who cannot be sitting in the middle seat.

## Solution 2

Assume that Tom is sitting in the middle (seat 3).

Since Sally and Mike are seated beside each other, they are either sitting in seats 4 and 5 or seats 1 and 2 .

In either case, seats 1 and 2 remain empty or seats 4 and 5 remain empty.

However, Andy and Jen cannot sit beside each other.

Therefore, this arrangement is not possible.

Thus, Tom cannot be sitting in the middle seat.

Since the question implies that there is a unique answer, then Tom is the answer.

ANSWER: (E)