1996 AMC 8 第 5 题

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5.

字母 PPQQRRSSTT 表示数轴上所示位置的数。

下列哪个表达式表示负数?

The letters P,P, Q,Q, R,R, S,S, and TT represent numbers located on the number line as shown.

Which of the following expressions represents a negative number?

PQP - Q

PQP \cdot Q

SQP\dfrac{S}{Q} \cdot P

RPQ\dfrac{R}{P \cdot Q}

S+TR\dfrac{S + T}{R}

答案:A
知识点:不等式分类讨论
难度评级:820
小提示:

从数轴上看,PPQQ 是负数,RRSSTT 是正数。

From the number line, PP and QQ are negative while R,R, S,S, and TT are positive

大提示:

乘积或商只有在负因子个数为奇数时才为负;逐项检查。

A product or quotient is negative only with an odd number of negative factors; check each choice

解答:

从数轴上看,PPQQ 是负数,而 RRSSTT 是正数。

PQP \cdot Q 为正;SQP\dfrac{S}{Q} \cdot P 有两个负因子,所以为正;RPQ\dfrac{R}{P \cdot Q} 为正;S+TR\dfrac{S + T}{R} 也为正。因为 PPQQ 左边,所以 PQP - Q 为负。

所以正确答案是 A

From the number line, PP and QQ are negative and R,R, S,S, and TT are positive.

Then PQP \cdot Q is positive; SQP\dfrac{S}{Q} \cdot P has two negative factors, so it is positive; RPQ\dfrac{R}{P \cdot Q} is positive; and S+TR\dfrac{S + T}{R} is positive. Since PP is to the left of Q,Q, PQP - Q is negative.

Thus, the correct answer is A .

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