# 2006 iTest Problems/Problem 4

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## Problem

Four couples go ballroom dancing one evening. Their first names are Henry, Peter, Louis, Roger, Elizabeth, Jeanne, Mary, and Anne. If Henry's wife is not dancing with her husband (but with Elizabeth's husband), Roger and Anne are not dancing, Peter is playing the trumpet, and Mary is playing the piano, and Anne's husband is not Peter, who is Roger's wife?

$\mathrm{(A)}\, \text{Elizabeth} \quad\mathrm{(B)}\,\text{Jeanne}\quad\mathrm{(C)}\,\text{Mary}\quad\mathrm{(D)}\,\text{Anne}$

## Solution

From the description, Peter, Roger, Mary, and Anne are not dancing. This peaves the possible dancers to Henry, Louis, Elizabeth, and Jeanne.

Because Henry’s wife is dancing with Elizabeth’s husband and Henry’s wife does not dance with Henry, Elizabeth’s husband must be Louis. That means Henry’s wife is Jeanne.

Since Anne’s husband is not Peter, Anne’s husband is Roger, so Roger’s wife is $\boxed{\textbf{(D) } \text{Anne}}$.