Question

Positive integers $a$ and $b$ are each less than $6.$ What is the smallest possible value of the following expression? $2 \cdot a - a \cdot b$

$-20$

$-15$

$-10$

$0$

$2$

Answer: B

Concepts:factoring optimization

Difficulty rating: 870

Small Hint:

Factor the expression as $a(2-b)$

Big Hint:

Make $2-b$ as negative as possible while making $a$ large

Solution:

The expression is $2a-ab=a(2-b)$ .

To make it as small as possible, choose $b$ as large as possible so that $2-b$ is most negative, and choose $a$ as large as possible. Since $a,b<6$ , take $a=b=5$ .

The minimum value is $5(2-5)=-15$ .

Thus, the correct answer is B .

2013 AMC 10B Problem 5

Answer: B

Difficulty rating: 870

Small Hint:

Big Hint:

Solution:

Problem 5 in Other Years