Bunuel wrote:

Note: Figure not drawn to scale

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

Kudos for a correct solution.given Y>0 and X<0 .

I |x+y| < y

at |X|=|Y| the inequality will change to is 0<Y? Answer YES

at |X|=|2Y| the inequality will change to is Y<Y? Answer NO

II X+Y<0 . If |X| > |Y| then YES . if |X| > |Y| then NO . also |X| can be equal to |Y| in which case X+Y =0 .

III

XY <0 yes.

Answer

B

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Lucky

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