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Hello,

I picked up this question from the manhattan flashcards, topic positives and negatives.

Is the statement sufficient? Is x < 0? 1) xy2 < 0 (Read as X*Y to the power of 2, ==> only y is squared)

The answer provided is that Statement1 is sufficient. since in the flashcards only 1 statement was given.

Explanation in flashcards : "Any number, except for 0, raised to an even power will be positive. If y were 0, the inequality would not be true, so we know that y2, regardless of the sign of y, will be positive. For xy2 to be less than zero, that means that x must be negative. The statement is sufficient.""

But i feel it is not sufficient. My reasons: 1. Lets test values, X = 0. then 0 < 0 ==> So not suffiicient. No condition is provided either in statement or option that it X <> 0 . 2. Lets text values for Y = 0 , then again 0 < 0 ==> so not sufficient. No condition is provided either in statement or option that it Y <> 0 .

So i feel that the statement is not sufficient. I understand the concept of negative value and also when the value will be < 0. Just was curious to know if my analysis is right. No need of explaning me the concept, i already know it.

While you do understand your number properties, you need to understand how Data Sufficiency works in the GMAT.

You MUST accept that the statement xy^2 <0 is a TRUTHFUL statement. Since we must accept that statement as true, then that by definition rules out the possibility that X or Y is zero. Thus, you can rule zero out when you test numbers.

That was a hard part for me too initially; realizing that the statement is true. IF the statement was not known to be true, then yes, it would be insufficient, but because DS statements on the GMAT are always true, then it's sufficient.

While you do understand your number properties, you need to understand how Data Sufficiency works in the GMAT.

You MUST accept that the statement xy^2 <0 is a TRUTHFUL statement. Since we must accept that statement as true, then that by definition rules out the possibility that X or Y is zero. Thus, you can rule zero out when you test numbers.

That was a hard part for me too initially; realizing that the statement is true. IF the statement was not known to be true, then yes, it would be insufficient, but because DS statements on the GMAT are always true, then it's sufficient.

Hope this helps.

Hello Turbine, Subhash, Thanks for the explanation..

I agree to what you are saying. Just have one more clarification. I have learnt that in DS, we should always try to prove the statement "not sufficient" which is a preferrable approach. For ex: if the number fails the condition mentioned then we have proved it as "not sufficient".

So my question is : 1. Do i always have to trust GMAT that the statements given are true ? or 2. Do i follow the strategy i mentioned above and go ahead and try to prove the statements not sufficient..

Actually, you must use both. I think you just have the application of the rules confused. You MUST accept both statements 1) and 2) as ALWAYS true.

However, your goal is to use each statement, one at a time, to prove that they are insufficient to answer the QUESTION. Do not try to disprove the statements, they are always true.

Here is what I mean: Let's say the question is "Does X + Y = 2?"

Statement 1): X>Y (X is greater than Y).

You must accept statement 1) as true. That means even if x and y are negative, fractions, squares, or whatever, X will ALWAYS be bigger than Y. BUT... Now your job is to see if that Statement is sufficient to answer the question "Does X +Y = 2". So now, you want to use your second tactic, by trying to prove that Statement 1) is insufficient.

Let's say X can be 3 and Y can be 2 as per stmt 1). 3 is bigger than 2. This is True. But it does not tell us if X +Y equals 2, because X could also be 1/4 and Y could be 1/8, which does not equal 2.

Actually, you must use both. I think you just have the application of the rules confused. You MUST accept both statements 1) and 2) as ALWAYS true.

However, your goal is to use each statement, one at a time, to prove that they are insufficient to answer the QUESTION. Do not try to disprove the statements, they are always true.

Here is what I mean: Let's say the question is "Does X + Y = 2?"

Statement 1): X>Y (X is greater than Y).

You must accept statement 1) as true. That means even if x and y are negative, fractions, squares, or whatever, X will ALWAYS be bigger than Y. BUT... Now your job is to see if that Statement is sufficient to answer the question "Does X +Y = 2". So now, you want to use your second tactic, by trying to prove that Statement 1) is insufficient.

Let's say X can be 3 and Y can be 2 as per stmt 1). 3 is bigger than 2. This is True. But it does not tell us if X +Y equals 2, because X could also be 1/4 and Y could be 1/8, which does not equal 2.

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