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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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19 Feb 2017, 07:43
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Difficulty:

75% (hard)

Question Stats:

44% (01:37) correct 56% (00:49) wrong based on 126 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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19 Feb 2017, 09:49
ziyuenlau wrote:
Is $$x^y > 1$$?

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

Easy to get both YES and NO answers to the questions by testing values.

If x = 4 and y = -1, then x^y = 1/4 < 1.
If x = 4 and y = 1/2, then x^y = 2 > 1.

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

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19 Feb 2017, 09:52
Top Contributor
1
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

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

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19 Feb 2017, 10:37
3
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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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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14 Apr 2018, 07:12
Hello from the GMAT Club BumpBot!

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