Please also guide me to understand the basic!

[soniadiana2011]

If n and t are positive integers, is n a factor of t ?
(1) n = 3n - 2
(2) t = 3n

[Mike@Magoosh]

Hi, there. I'm happy to contribute to this.

If n and t are positive integers, is n a factor of t?

n is a factor of t if and only if there exist some other integer k such that n = k*t.

(1) n = 3n - 2

This allows us to solve for the value of n, and gives us no information about t. Normally, that would be not sufficient. BUT, here


n = 3n - 2
2 = 2n
1 = n

n equals 1, which is a factor of every single positive integer. It's the universal factor. Therefore, regardless of what positive integer t is, n = 1 is a factor of it. This statement is sufficient to give a definitive "yes" answer to the prompt question.

(2) t = 3n

This is the very definition of a factor. If you can multiply n by an integer and get a product of t, by definition, that means n is a factor of t. This statement, by itself, is also sufficient.

Each statement alone by itself is sufficient. Answer = D

Here's a blog you may find helpful:
https://magoosh.com/gmat/2012/gmat-math-factors/

Does all this make sense to you? Please let me know if you have any additional questions.

Mike

[soniadiana2011]

Thank you so much for the reply and explanation. I knew I know the math part it is just I am unable to catch the trick! Need more practise for sure!

Thanks again

[svd.kumar]

Hi,

I think question was mistunderstood here,

Option 1 is not 3n minus 2, it is 3 power n-2
Option 2 is not 3n, it is 3 power n

Both Option1 and option2 alone were not sufficient,

Together,
n=3^n-2=3^n/9=t/9
n=t/9

Answer is C

If you are sure your version of question is correct, then try this version also. Both versions are very interesting.

[Mike@Magoosh]

Hi,
I think question was mistunderstood here,

Option 1 is not 3n minus 2, it is 3 power n-2
Option 2 is not 3n, it is 3 power n

Thank you, svd.kumar, that's an important distinction.

soniadiana2011, was that version your original question? It's answer & solution are very different from the question which you posted and I answered.

Just so you and anyone else reading this are clear ----- "3 to the power of n", when printed on a page, is a 3 with a superscripted n immediately to its right. We can't superscript in this plaintext format of BTG, so we have to write "3 to the power of n" as 3^n, not as 3 with an n simply next to it, 3n, which means 3*n, "3 times n".

If anyone would like to see a full explanation of the version of the question that svd.kumar kindly posted, please let me know.

Mike

[gmattesttaker2]

Hi Mike,

Had a basic question here. When I combine both the options in the version of svd.kumar I get the following:

9 = t/n

The way I am trying to understand this is when say 27 is divided by 3, the answer is 9 i.e. 3 is a factor of 27. Is this reasoning correct? Thanks a lot for your help.

Best Regards,
Sri

[Mike@Magoosh]

Hi Mike,

Had a basic question here. When I combine both the options in the version of svd.kumar I get the following:

9 = t/n

The way I am trying to understand this is when say 27 is divided by 3, the answer is 9 i.e. 3 is a factor of 27. Is this reasoning correct? Thanks a lot for your help.

Best Regards,
Sri

Yes, that reasoning is correct. Kudos to you on using the laws of exponents correctly.

Mike

[jrakhe]

According to me the best way to solve the question posted by svd.kumar is as follows:

1) n=3^(n-2)
NS

2) t = 3^n
NS

togather we can write: t = 3^1 * 3^2 * 3^3 ....... * 3^(n-2)* 3^(n-1)* 3^n

and here we can clearly see that n is the factor of t . So answer is C.

Please correct me if I am wrong.

[gmattesttaker2]

Hi Mike,

Thank you very much for your reply.

Best Regards,
Sri