Problem 120

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).)