Question

If $a$ and $b$ are integers and $-4\le a\le 3$ and $-4\le b\le 5$, what is the maximum possible value for $ab$?

• A. 12
• B. 15
• C. 16
• D. 20

Answer 1

Answer: (C)

16

In order to maximise $ab$,you need to test the endpoints of the ranges for $a$ and $b$:

If $a=-4$ and $b=-4$, $ab=16$.

If $a=-4$ and $b=5$, the product is negative (smaller than $16$)

If $a=3$ and $b=-4$, the product is negative (smaller than $16$)

If $a=3$ and $b=5,ab=15$.

Thus, the maximum value for $ab$ is $16$. Notice that this maximum occurs when $a$ and $b$ are both negative in this case.