Is 0 between x and y? (1) x - y 0 (2) x^2 - y^2 0

Question

Is 0 between  x  and  y ?

(1)  x-y>0 
(2)  x^2-y^2>0

gmatophobia · Answer

Question  :

On a number line, does 0 lie between x and y?

---- x ---- 0 ---- y ----

OR

---- y ---- 0 ---- x ----

Statement 1  :

(1)  x-y>0

x > y

Hence, on a number line, x lies on the right of y.

However, with this information alone, we cannot conclude whether zero lies between x and y. For example, x and y can have the following positions on the number line.

Case 1 : ------- y -------- 0 ---------- x --------- ⇒ In this case, 0 lies between x and y

Case 2 : ------- 0 -------- y ---------- x --------- ⇒ In this case, 0 does not lie between x and y

As we have two answers to the question, we can eliminate A and D.

Statement 2  :

(2)  x^2-y^2>0

x^2 > y^2

Hence, on a number line,  x^2  lies on the right of  y^2 .

However, with this information alone, we cannot conclude whether zero lies between x and y. For example, x and y can have the following positions on the number line.

Case 1 : ------- y -------- 0 ----  y^2  ----- x ------  x^2 ---- ⇒ In this case, 0 lies between x and y

Case 2 : ------- 0 -------- y ----- y^2  ----- x ---------  x^2 ---- ⇒ In this case, 0 does not lie between x and y

As we have two answers to the question, we can eliminate B.

Combined

The statements combined do not help, as both the cases from Statement 1 and Statement 2 hold true with the information in both statements combined.

Option E

Is 0 between x and y? (1) x - y > 0 (2) x^2 - y^2 > 0

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