adi wrote:Is x<y ?

(1) 2x <3y> 0

I really thought this one would be C (both would answer the question), but the key says it's E.

Any thoughts as to why?

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Thanks for pointing out the error.

I have edited my initial post. 8)

adi wrote:Is x<y ?

(1) 2x < 3y
(2) xy > 0

I really thought this one would be C (both would answer the question), but the key says it's E.

Any thoughts as to why?

Whenever inequalities are involved, we want to focus on the signs of the variables.

(1) 2x < 3y

or

x < (3/2)y

Does this tell us if x is less than y?

Nope, we could pick x=1 and y=50 to get a "yes" answer or we could pick x = 1.1 and y = 1 to get "no" answer: insufficient.

(2) xy > 0

This tells us that x and y are both positive or both negative, but nothing about the values: insufficient.

When we combine the statements, we can still get both a "yes" and a "no", since both sets of numbers from statement (1) could still be used.

Choose (E).