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by Brent@GMATPrepNow » Thu Dec 06, 2012 1:38 pm
saadiagha wrote:is x^y>0

1. Y=2

2. X is an integer
Target question: is x^y > 0

Statement 1: Y=2
There are several pairs of values that meet this condition. Here are two:
Case a: x=1 and y=2, in which case x^y is greater than 0
Case b: x=0 and y=2, in which case x^y is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: X is an integer
There are several pairs of values that meet this condition. Here are two:
Case a: x=1 and y=2, in which case x^y is greater than 0
Case b: x=0 and y=2, in which case x^y is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are several pairs of values that meet both conditions. Here are two:
Case a: x=1 and y=2, in which case x^y is greater than 0
Case b: x=0 and y=2, in which case x^y is not greater than 0
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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by saadiagha » Thu Dec 06, 2012 1:55 pm
Hey Brent, thanks for the solution
will the answer remain the same if the question is reversed, that is;



Is x^y < 0?

y = 2.
x is an integer.



I had chosen answer C- Both statements together. Thanks for your reply.

However, Veritas had marked the answer as A. Thats why I was confused.

This is their answer;

Statement (1) alone allows us to answer this question with a definitive "no." If x is positive or negative and we square it, we'll get a positive number.. If x is 0 and we square it, we'll get 0. So, we will either get 0 or a positive number, and in either case, the answer to the question "is
xy
< 0?" will unequivocally be no. Statement (2) alone is not sufficient, because, for instance, if y is 1, then
xy
will retain whatever sign x itself carries.

P.S- I hope I am posting the question correctly, the sign ^ refers to "raised to the power" right?
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by Brent@GMATPrepNow » Thu Dec 06, 2012 2:10 pm
saadiagha wrote:Hey Brent, thanks for the solution
will the answer remain the same if the question is reversed, that is;

Is x^y < 0?

1) y = 2.
2) x is an integer.
Let's try it.

Target question: is x^y < 0

Statement 1: Y=2
We know that x^2 > 0 for all values of x.
Given this, we can conclude that x^y is definitely not less than 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: X is an integer
There are several pairs of values that meet this condition. Here are two:
Case a: x= -1 and y=1, in which case x^y is less than 0
Case b: x= 1 and y=1, in which case x^y is not less than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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by Brent@GMATPrepNow » Thu Dec 06, 2012 2:11 pm
saadiagha wrote: P.S- I hope I am posting the question correctly, the sign ^ refers to "raised to the power" right?
Right!

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by saadiagha » Thu Dec 06, 2012 3:36 pm
Let's try it.

Target question: is x^y < 0

Statement 1: Y=2
We know that x^2 > 0 for all values of x.
Given this, we can conclude that x^y is definitely not less than 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT


Ok great! I have one little querry though, I thought we should try values of x between 0 and 1.

In case x=0.5, and y=2, wont the square be 0.25?

How come in our analysis we tried x=1 or -1 but not a non integer?

Its only in the second statement that we realize that x is an integer, and hence can use the info from the first statement- that was my reasoning for choosing C.

Could you tell me where I am messing up here?

Thanks a lot!
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by Brent@GMATPrepNow » Thu Dec 06, 2012 4:02 pm
saadiagha wrote:Let's try it.

Target question: is x^y < 0

Statement 1: Y=2
We know that x^2 > 0 for all values of x.
Given this, we can conclude that x^y is definitely not less than 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT


Ok great! I have one little querry though, I thought we should try values of x between 0 and 1.

In case x=0.5, and y=2, wont the square be 0.25?

How come in our analysis we tried x=1 or -1 but not a non integer?

Its only in the second statement that we realize that x is an integer, and hence can use the info from the first statement- that was my reasoning for choosing C.

Could you tell me where I am messing up here?

Thanks a lot!
I think there might be a mix up between the two different questions we're examining here. The original question asked "Is x^y > 0?" and your follow-up question asked "Is x^y < 0?"

In your question here, you are referring to different parts of different questions. The red part is from my solution to the follow-up question. The green part is referring to my solution to the original question.


If you're asking me why, in the original question, I didn't use non-integer values for x when showing two different cases for statement 1, my answer is that, even though, I was not confined to integer values I still chose to use them. Had I used non-integer values for x, the results would have been the same:

Target question: Is x^y > 0?

Statement 1: Y=2
There are several pairs of values that meet this condition. Here are two:
Case a: x=0.5 and y=2, in which case x^y is greater than 0
Case b: x=0 and y=2, in which case x^y is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Cheers,
Brent
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