The values $2,3,4$, and 5 are each assigned to exactly one of the letters $V, W, X$, and $Y$ to give $Y^{X}-W^{V}$ the greatest possible value. The value of $X+V$ is equal to
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
To give $Y^{X}-W^{V}$ the greatest possible value, we make $Y^{X}$ as large as possible while making $W^{V}$ as small as possible.

To make $Y^{X}$ as large as possible, we make $Y$ and $X$ as large as possible.

Thus, we must assign $Y$ and $X$ the two largest values, and assign $W$ and $V$ the two smallest values.

Let $Y$ and $X$ equal 4 and 5 in some order.

Since $4^{5}=1024$ and $5^{4}=625$, we let $Y=4$ and $X=5$ so that $Y^{X}$ is as large as possible.

Similarly, we assign $W$ and $V$ the smallest possible numbers, 2 and 3 .

Since $2^{3}=8$ and $3^{2}=9$, we let $W=2$ and $V=3$ so that $W^{V}$ is as small as possible.

Thus, the greatest possible value of $Y^{X}-W^{V}$ is equal to $4^{5}-2^{3}=1024-8=1016$, which gives $X+V=5+3=8$.

ANSWER: (D)