Library / CEMC Gauss (Grade 7) /234 of 462

CEMC Gauss (Grade 7), 2013

Algebra Difficulty 1.3 Junior Find the answer Canada

An expression that produces the values in the second row of the table shown, given the values of $n$ in the first row, is

$n$	1	2	3	4	5
value	1	3	5	7	9

Pick one

Solution

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).)

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.