, 2013

When $n=4$, we are looking for an expression that produces a value of 7. The results of substituting $n=4$ into each expression and evaluating are shown below. Expression Value (A) $3n-2$ $3(4)-2=12-2=10$ (B) $2(n-1)$ $2(4-1)=2(3)=6$ (C) $n+4$ $4+4=8$ (D) $2n$ $2(4)=8$ (E) $2n-1$ $2(4)-1=8-1=7$ Since $2n-1$ is the only expression which gives a value of 7 when $n=4$, it is the only possible answer. We check that the expression $2n-1$ does give the remaining values, $1,3,5,9$, when $n=1,2,3,5$, respectively. (Alternately, we may have began by substituting $n=1$ and noticing that this eliminates answers (B), (C) and (D). Substituting $n=2$ eliminates (A). Substituting $n=3$, $n=4$ and $n=5$ confirms the answer (E).)