Question

which is the set of integers that are multiples of 8 and greater than -20?
{-24, -32, -40, -48, ...}
{-16, -8, 0, 8, ...}
{-16, -8, 8}
{-16, -8, 0, 8}

Explanation:

Step1: Identify multiples of 8 > -20

First, list negative multiples of 8 greater than -20:
$-16$ (since $8\times(-2)=-16$, and $-16 > -20$), $-8$ ($8\times(-1)=-8$).
Positive multiples and 0 are also valid: $0, 8, 16,...$

Step2: Eliminate invalid sets

• $\{-24, -32, -40, -48,...\}$: $-24 < -20$, invalid.
• $\{-16, -8, 8\}$: Missing 0 and infinite positive multiples.
• $\{-16, -8, 0, 8\}$: Missing infinite positive multiples (the set should be infinite).

Step3: Confirm correct set

$\{-16, -8, 0, 8,...\}$ includes all valid multiples.

Answer:

$\boldsymbol{\{-16, -8, 0, 8,...\}}$