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# If n is positive, is n an integer?

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Intern
Joined: 21 Oct 2016
Posts: 5
If n is positive, is n an integer?  [#permalink]

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Updated on: 12 Dec 2016, 12:43
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00:00

Difficulty:

15% (low)

Question Stats:

80% (01:04) correct 20% (01:02) wrong based on 124 sessions

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If n is positive, is n an integer?

(1) $$\sqrt[3]{n}= integer$$
(2) $$\sqrt[3]{-n} = integer$$

Please explain how to solve Stmt 2.

Thank you,
Abi

Originally posted by abiraami on 12 Dec 2016, 12:35.
Last edited by Bunuel on 12 Dec 2016, 12:43, edited 1 time in total.
EDITED THE QUESTION.
Math Expert
Joined: 02 Sep 2009
Posts: 51280
Re: If n is positive, is n an integer?  [#permalink]

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12 Dec 2016, 12:47
1
1
If n is positive, is n an integer?

(1) $$\sqrt[3]{n}= integer$$ --> take to the third power: $$n = integer^3=integer$$. Sufficient.

(2) $$\sqrt[3]{-n} = integer$$ --> take to the third power: $$-n = integer^3$$ --> $$n=-integer^3=integer$$. Sufficient.

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Re: If n is positive, is n an integer?  [#permalink]

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25 Jan 2017, 16:25
If n is positive, is n an integer?

(1) $$\sqrt[3]{n}= integer$$

Let n=8........then $$\sqrt[3]{8}=2 ....Answer is Yes Let n=27.....then [m]\sqrt[3]{27}=3...Answer is Yes Always n is Integer Sufficient (2) [m]\sqrt[3]{-n} = integer$$

Let n=8........then [m]\sqrt[3]{-8}=-2 ....Answer is Yes

Let n=27.....then [m]\sqrt[3]{-27}=-3...Answer is Yes

Always n is Integer

Sufficient

Director
Joined: 27 May 2012
Posts: 637
If n is positive, is n an integer?  [#permalink]

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25 Jun 2018, 23:11
Bunuel wrote:
If n is positive, is n an integer?

(1) $$\sqrt[3]{n}= integer$$ --> take to the third power: $$n = integer^3=integer$$. Sufficient.

(2) $$\sqrt[3]{-n} = integer$$ --> take to the third power: $$-n = integer^3$$ --> $$n=-integer^3=integer$$. Sufficient.

Sorry Bunuel , but isn't statement 2 contradicting the question stem , lets say -n = $$2^3$$ then n = $$-2^3$$ -> n= -8
but question stem says n = positive , am I missing anything ?
_________________

- Stne

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Joined: 02 Sep 2009
Posts: 51280
Re: If n is positive, is n an integer?  [#permalink]

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25 Jun 2018, 23:46
1
stne wrote:
Bunuel wrote:
If n is positive, is n an integer?

(1) $$\sqrt[3]{n}= integer$$ --> take to the third power: $$n = integer^3=integer$$. Sufficient.

(2) $$\sqrt[3]{-n} = integer$$ --> take to the third power: $$-n = integer^3$$ --> $$n=-integer^3=integer$$. Sufficient.

Sorry Bunuel , but isn't statement 2 contradicting the question stem , lets say -n = $$2^3$$ then n = $$-2^3$$ -> n= -8
but question stem says n = positive , am I missing anything ?

$$\sqrt[3]{-n} = integer$$ does not necessarily mean that n is a negative number. For example, consider n = 2^3, then $$\sqrt[3]{-n} = \sqrt[3]{-2^3}=-2$$
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Joined: 27 May 2012
Posts: 637
Re: If n is positive, is n an integer?  [#permalink]

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26 Jun 2018, 01:54
Bunuel wrote:
stne wrote:
Bunuel wrote:
If n is positive, is n an integer?

(1) $$\sqrt[3]{n}= integer$$ --> take to the third power: $$n = integer^3=integer$$. Sufficient.

(2) $$\sqrt[3]{-n} = integer$$ --> take to the third power: $$-n = integer^3$$ --> $$n=-integer^3=integer$$. Sufficient.

Sorry Bunuel , but isn't statement 2 contradicting the question stem , lets say -n = $$2^3$$ then n = $$-2^3$$ -> n= -8
but question stem says n = positive , am I missing anything ?

$$\sqrt[3]{-n} = integer$$ does not necessarily mean that n is a negative number. For example, consider n = 2^3, then $$\sqrt[3]{-n} = \sqrt[3]{-2^3}=-2$$

Great , didn't think from this angle , thanks a ton !
_________________

- Stne

Re: If n is positive, is n an integer? &nbs [#permalink] 26 Jun 2018, 01:54
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# If n is positive, is n an integer?

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