2007 AMC 8 Problems/Problem 15

Problem

Let $a, b$ and $c$ be numbers with $0 < a < b < c$ . Which of the following is impossible?

$\mathrm{(A)} \ a + c < b \qquad \mathrm{(B)} \ a * b < c \qquad \mathrm{(C)} \ a + b < c \qquad \mathrm{(D)} \ a * c < b \qquad \mathrm{(E)}\frac{b}{c} = a$

Solution

According to the given rules,

Every number needs to be positive.

Since $c$ is always greater than $b$ ,

adding a positive number ( $a$ ) to $c$ will always make it greater than $b$ .

Therefore, the answer is $\boxed{A}$

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2007 AMC 8 Problems/Problem 15

Problem

Solution