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# Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.

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Math Expert
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Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.  [#permalink]

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15 Apr 2016, 01:31
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Difficulty:

55% (hard)

Question Stats:

56% (01:39) correct 44% (01:18) wrong based on 77 sessions

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Is 3n an integer?

(1) 6n is an integer.
(2) 9n is an integer.

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Marshall & McDonough Moderator
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Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.  [#permalink]

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15 Apr 2016, 02:10
St1: 6n is integer --> n can be 1/2, 1/3, 1/6,.......
If n = 1/3 then 3n is an integer
If n = 1/2 then 3n is not an integer
Not Sufficient

St2: 9n is an integer --> n can be 1/3, 1/9, .....
If n = 1/3 then 3n is an integer
If n = 1/9 then 3n is not an integer
Not Sufficient

Combining St1 and St2: n can be 1/3, 2/3, 6/9 or any integer
3n will always be integer.
Sufficient

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Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.  [#permalink]

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26 Aug 2018, 18:17
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pikolo2510 niks18 chetan2u gmatbusters VeritasKarishma Bunuel pushpitkc GMATPrepNow

Any alternative approach than picking numbers?
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Re: Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.  [#permalink]

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26 Aug 2018, 23:39
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pikolo2510 niks18 chetan2u gmatbusters VeritasKarishma Bunuel pushpitkc GMATPrepNow

Any alternative approach than picking numbers?

Statement 1: implies $$6n=p$$, for any integer $$p => 3n=\frac{p}{2}$$

now if $$p$$ is even then $$3n$$ is an integer, if not then $$3n$$ is not an integer. insufficient

Statement 2: implies $$9n=q$$, for any integer $$q => 3n=\frac{q}{3}$$.

now if $$q$$ is a multiple of $$3$$, then $$3n$$ is an integer, if not then $$3n$$ is not an integer. insufficient

Combining 1 & 2: we have $$\frac{p}{2}=\frac{q}{3} => q=\frac{3p}{2}$$. Now $$q$$ is an integer so $$p$$ has to be an even number.

Therefore from Statement 1, we have $$3n=\frac{p}{2}=Integer$$. Sufficient

Option C
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Re: Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.  [#permalink]

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27 Aug 2018, 03:53
2
Bunuel wrote:
Is 3n an integer?

(1) 6n is an integer.
(2) 9n is an integer.

This is how I would approach it:

(1) 6n is an integer.
6n = Integer = 2 * 3n
3n may be 'I' (an integer) or 'I/2' (in its simplest form). (No other form is possible i.e. 3n cannot be I/3 or I/4 or I/20 ins simplest form since 6n will not be integer then)

Not necessary.

(2) 9n is an integer.
So 9n = Integer = 3 * 3n
3n may be 'I' (an integer) or 'I/3' (in its simplest form). (No other form is possible i.e. 3n cannot be I/2 or I/4 or I/20 in simplest form since 9n will not be integer then)

Not necessary.

Using both, 3n must be 'I' (common to both statements).

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Re: Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.  [#permalink]

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19 Sep 2019, 04:27
1
Hi

The question asks whether 3n is an integer and provides tells us that 6n and 9n are integers. Since we know that an INTEGER +- another INTEGER is ALWAYS an Integer, we can conclude than 9n - 6n => 3n is an integer.
Re: Is 3n an integer? (1) 6n is an integer. (2) 9n is an integer.   [#permalink] 19 Sep 2019, 04:27
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