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# Understand the problem

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

##### Source of the problem

2013 AMC 10B Problem 5

Inequality
3 out of 10
##### Suggested Book
Inequalities: A Mathematical Olympiad Approach

Do you really need a hint? Try it first!

Play with the expression. Write $2 \cdot a - a \cdot b$ = $a(2 - b)$. How does this help? Think about it.
As $a$ is positive, we can see that to obtain the least possible value, $2 - b$ should be negative, and should be as small as possible. To do so, $b$ should be maximized.
Because $2 - b$ is negative, we should maximize the positive value of $a$ as well
The maximum values of both $a$ and $b$ are $5$, so the answer is 5(2-5) = -15.

# Connected Program at Cheenta

#### Math Olympiad Program

Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.

# Similar Problems

## INMO 1996 Problem 1

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