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Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

# Pros and Cons

##### Age 14 to 16 Short Challenge Level:

Answer: $p-q$

Trying out numbers
Imagine $p = 5$ and $q = -2$

$p - q = 5 - -2 = 7$
$q - p = -2 - 5 = -7$
$p + q = 5 + -2 = 3$
$-p - q = -5 - -2 = -3$

Using positives and negatives
$p$ is positive so use $+p$ (not $-p$)
$q$ is negative so subtract $q$
$p-q$ will be the greatest.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.