CEMC Fermat, 2020

Algebra Difficulty 1.4 Junior Find the answer Canada

In the list $2,x,y,5$ , the sum of any two adjacent numbers is constant. The value of $x-y$ is

$1$
$-3$
$3$
$-1$
$0$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since the sum of any two adjacent numbers is constant, then $2+x=x+y$ .
This means that $y=2$ and makes the list $2,x,2,5$ .
This means that the sum of any two adjacent numbers is $2+5=7$ , and so $x=5$ .
Therefore, $x-y=5-2=3$ .

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.