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

Question

Is 3n an integer?

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

Kurtosis · Answer

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

Answer: C

adkikani · Answer

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Any alternative approach than picking numbers?

niks18 · Answer

hi  adkikani ,

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

KarishmaB · Answer

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).

Answer (C)

YashKothari94 · Answer

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.

GMATGuruNY · Answer

Statement 1:
6n = 1, 2, 3...
Dividing every value by 2, we get:
3n = 1/2, 1, 3/2...
If 3n = 1/2, the answer to the question stem is NO.
If 3n = 1, the answer to the question stem is YES.
INSUFFICIENT.

Statement 2:
9n = 1, 2, 3...
Dividing every value by 3, we get:
3n = 1/3, 2/3, 1...
If 3n = 1/3, the answer to the question stem is NO.
If 3n = 1, the answer to the question stem is YES.
INSUFFICIENT.

Statements combined:
3n = 9n - 6n = INTEGER - INTEGER = INTEGER.
Thus, the answer to the question stem is YES.
SUFFICIENT.

C

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

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

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