AMC 8 1996 Problem 5

AMC8 1996 年第 5 题

表达式与运算★★☆☆☆

The letters

P

Q

R

S

, and

T

represent numbers located on the number line as shown.

Which of the following expressions represents a negative number?

字母

P

、

Q

、

R

、

S

和

T

表示数轴上的数，如图所示。

以下哪个表达式表示一个负数？

A.P-Q
B. $P\cdot Q$
C. $\dfrac{S}{Q}\cdot P$
D. $\dfrac{R}{P\cdot Q}$
E. $\dfrac{S+T}{R}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

First, note that P < Q < 0 < R < S < T. Thus,

P

and

Q

are negative, while

R

S

, and

T

are positive.

Option

A

is the difference of two numbers. If the first number is lower than the second number, the answer will be negative. In this case, P < Q, so P - Q < 0, and P-Q is thus indeed a negative number. So option

A

is correct.

Option

B

is the product of two negatives, which is always positive.

Option

C

starts with the quotient of a positive and a negative. This is negative. But this negative quotient is then multiplied by a negative number, which gives a positive number.

Option

D

has the product of two negatives in the denominator. Thus, the denominator is positive. Additionally, the numerator is (barely) positive. A positive over a positive will be positive.

Option

E

has the sum of two positives in the numerator. That will be positive. The denominator is also positive. Again, the quotient of two positives is positive.

继续练习

免费刷 1996 整卷 →