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Is x^y>1? (1) x>1 (2) y<1

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Is x^y>1? (1) x>1 (2) y<1  [#permalink]

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New post 19 Feb 2017, 07:43
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E

Difficulty:

  95% (hard)

Question Stats:

41% (01:37) correct 59% (00:47) wrong based on 101 sessions

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Is \(x^y > 1\)?

(1) \(x>1\)
(2) \(y<1\)

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Re: Is x^y>1? (1) x>1 (2) y<1  [#permalink]

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New post 19 Feb 2017, 09:49
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Re: Is x^y>1? (1) x>1 (2) y<1  [#permalink]

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New post 19 Feb 2017, 09:52
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ziyuenlau wrote:
Is \(x^y > 1\)?

(1) \(x>1\)
(2) \(y<1\)


Target question: Is x^y > 1?

Each statement alone is NOT SUFFICIENT, so let's jump straight to . . .

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 9 and y = 1/2, in which case x^y = 9^(1/2) = 3. In this case, x^y > 1
Case b: x = 2 and y = -1, in which case x^y = 2^(-1) = 1/2. In this case, x^y < 1
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Is x^y>1? (1) x>1 (2) y<1  [#permalink]

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New post 19 Feb 2017, 10:37
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How to approach these types of problem :

Question Stem : Is \(x^y>1\)?

Observations : X and Y could be anything.So we will check following values for X and Y .
X = \(-2,-1,\frac{-1}{2},0,\frac{1}{2},1,2\)
Y = \(-2,-1,\frac{-1}{2},0,\frac{1}{2},1,2\)

These are very basic values which we should keep in mind when no restrictions about variables are given as is the case in this case. Say in some other question If this was given that X is an integer so we will use.
X = \(-1,0,1\)

Ok so back to question.

Statement 1 : \(X > 1\)

Observations :
Y could be anything: Y = \(-1,\frac{-1}{2},0,\frac{1}{2},1\)
X will have following values : \(2,3,4\)

let's test these values:
X=2 and Y = 0 ==> \(2^0\) = 1 so 1 > 1 ==> NO
X = 2 and Y = 1 ==> \(2^1\) = 2 So2 > 1 ==> YES

Not Sufficient.

Statement 2 : \(Y < 1\)

Observations :
X xould be anything :X = \(-2,-1,\frac{-1}{2},0,\frac{1}{2},1,2\)
Y will have follwoing values : Y = \(-1,\frac{-1}{2},0,\frac{1}{2}\)
let's test these values:

X=2 and Y = 0 ==> \(2^0\) = 1 so 1 > 1 ==> NO
X=3 and Y=\(\frac{1}{2}\) ==> \(2^{1/2}\) = \(\sqrt{2}\) > 1 ==> YES

Not Sufficient.

St1 + St2
X=2 and Y = 0 ==> NO
X=3 and Y=\(\frac{1}{2}\) ==> YES

Not sufficient .Ans E

So always check for these values \(-2,-1,\frac{-1}{2},0,\frac{1}{2},1,2\) .In most of the cases exceptions fall in this range .

Please +1 kudos if this post helps :)
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Re: Is x^y>1? (1) x>1 (2) y<1  [#permalink]

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New post 19 Feb 2017, 11:13
Ans is E
As Statement 1 don't say anything about y and statement 2 about x and combined not much information about Y like if y is negative then x^y<1.


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Re: Is x^y>1? (1) x>1 (2) y<1  [#permalink]

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New post 14 Apr 2018, 07:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is x^y>1? (1) x>1 (2) y<1 &nbs [#permalink] 14 Apr 2018, 07:12
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