If x and y are numbers on the number line above, which of the following statements must be true?

BTGmoderatorDC wrote: ↑

Sun Aug 08, 2021 6:19 pm

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If x and y are numbers on the number line above, which of the following statements must be true?

I. |x+y| < y
II. x + y < 0
III. xy < 0

A. I only
B. III only
C. I and II
D. I and III
E. II and III


OA B

Source: Magoosh

I. |x+y| < y
Statement I is not necessarily true.
For example, if x = -5 and y = 1, the inequality |x+y| < y becomes: |(-5) + 1| < 1, which simplifies to be: 4 < 1, which is not true.
This means we can eliminate answer choices A, D and D since they state that statement I is true.

II. x + y < 0
Statement II is not necessarily true.
For example, if x = -1 and y = 2, the inequality x + y < 0 becomes: (-1) + 2 < 0, which simplifies to be: 1 < 0, which is not true.
This means we can eliminate answer choice E since it states that statement II is true.

By the process of elimination, the correct answer is B