AMC10 2013 B

AMC10 2013 B · Q5

AMC10 2013 B · Q5. It mainly tests Linear equations.

Positive integers a and b are each less than 6. What is the smallest possible value for 2 · a −a · b ?

正整数a和b各小于6。$2 \cdot a - a \cdot b$ 的最小可能值是多少？

(A) −20 −20

(B) −15 −15

(D) 0 0

(E) 2 2

Answer

Correct choice: (B)

正确答案：（B）

Solution

Note that 2·a−a·b = (2−b)a. This expression is negative when b > 2. Hence the product is minimized when a and b are as large as possible. The minimum value is (2 −5) · 5 = −15.

注意 $2\cdot a - a\cdot b = (2 - b)a$。当 $b > 2$ 时，这个表达式为负。因此，当a和b尽可能大时，积最小。最小值为 $(2 - 5) \cdot 5 = -15$。

Topics

AL.001 Linear equations