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# Is p^2 an odd integer?

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Math Expert
Joined: 02 Sep 2009
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Is p^2 an odd integer?  [#permalink]

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06 Feb 2014, 01:22
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2
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Difficulty:

5% (low)

Question Stats:

93% (00:44) correct 7% (00:33) wrong based on 601 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is p^2 an odd integer?

(1) p is an odd integer.
(2) $$\sqrt{p}$$ is an odd integer.

Data Sufficiency
Question: 73
Category: Arithmetic Properties of numbers
Page: 158
Difficulty: 600

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Re: Is p^2 an odd integer?  [#permalink]

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06 Feb 2014, 01:22
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SOLUTION

Is p^2 an odd integer?

(1) p is an odd integer --> $$p^2=odd^2=odd$$. Sufficient.

(2) $$\sqrt{p}$$ is an odd integer --> $$\sqrt{p}=odd$$ --> $$p=odd^2=odd$$ --> $$p^2=odd^2=odd$$. Sufficient.

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Re: Is p^2 an odd integer?  [#permalink]

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06 Feb 2014, 02:55
2
D.

(1) p is odd. $$p^2$$ is odd*odd = odd Sufficient.
(2)$$\sqrt{p}$$ is odd, hence $$p^2 = ( \sqrt{p})^4$$ is also odd. Sufficient.
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Re: Is p^2 an odd integer?  [#permalink]

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07 Feb 2014, 00:44
3
p^2 can be odd, only if p is an odd integer; So, we can rephrase the question: Is p odd?

(1) Sufficient;
(2) \sqrt{p}=odd, only if p is odd; Sufficient;

Ans is (D).
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Posts: 49430
Re: Is p^2 an odd integer?  [#permalink]

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08 Feb 2014, 06:08
2
SOLUTION

Is p^2 an odd integer?

(1) p is an odd integer --> $$p^2=odd^2=odd$$. Sufficient.

(2) $$\sqrt{p}$$ is an odd integer --> $$\sqrt{p}=odd$$ --> $$p=odd^2=odd$$ --> $$p^2=odd^2=odd$$. Sufficient.

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Re: Is p^2 an odd integer?  [#permalink]

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11 Sep 2015, 00:55
ohh i missed it

1) p is odd. p2 is odd*odd = odd Sufficient.
(2)p√ is odd, squaring it p2=(p√)4 is also odd. Sufficient
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Is p^2 an odd integer?  [#permalink]

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05 Dec 2015, 14:09
the question just test the principle that the orientation of an integer i.e. if an int is odd or even doesnt change if we raise it to any exponent as long as the exponent is a positive integer
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Re: Is p^2 an odd integer?  [#permalink]

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02 Jul 2018, 18:19
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# Is p^2 an odd integer?

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