value of n?value of n?

[Ahmed MS]

Q. If 63^n / 3^16, then what is the value of n?

1. n >7
2. n<7

Please help me solve this problem.


Cheers.

[kmittal82]

Your question seems incomplete. Can you please double check it

[Ahmed MS]

Well, the question is " if 63^n is divisible by 3^16 then

1. n > 7
2. n < 7

That is what I have found written.

Cheers.

[beatthegmat.garry]

If a number is divisible by 3^16 then the number should be able a multiple of 3^16.

63^n can be written as = (9*7)^n=(3^2 * 7)^n

if you have noticed above each power of 63 will contribute 2 powers of 3 (i.e. 3^2). And for 63^n to be a multiple of 3^16 it has to contribute in atleast 16 powers of 3 (i.e. 3^16).
If n>7 , let assume n=8 then 63^8=(3^16) *(7 ^16).

Hence n had to be greater than 7 for the given statement to be true.

statement 1: N>7 ==> Exactly what we looking for. It is sufficient

statement 2: N<7 ==> 63^n is not divisible by 3^16. It is sufficient.

Answer is D

[edge]

Isn't this an invalid question because the two statements lead to different solutions? Can the experts weigh in on this?

[GmatKiss]

Is it not E, OA please!

n>7 means n can be 8,9.... any positive number > 7.
n<7 means n can be 6,5,4,3,2,1,0 and negative numbers as well.

[Ahmed MS]

Answer is B.

= 63^n / 3^16
= (9*7)^n / 3^16
=3^2n*7^n/ 3^16
= (3^2n /3^16) * (7^n / 3^16)

So the value would be n=8, which is <7.


Cheers.

[GmatKiss]

Does only 8 satisfy the condition!!?

[Ahmed MS]

As (3^2n / 3^16) will give you the value 8, (3^2n*8= 3^16).

So answer would be B.

Cheers.

[Frankenstein]

Hey,

Q. If 63^n is divisible 3^16, then what is the value of n?

1. n >7
2. n<7

Firstly, this question is badly framed. You cannot even consider statements(1) and (2) together.
Now, for 63^n to be divisible by 3^16, we know that n should be an integer greater than 7.
From(1):
n>7. So, every integer value of n >7 satisfies. How do we find the value of n from this? We cannot find a unique solution
Not sufficient
From(2):
n<7, then 63^n will not be divisible by 3^16. Nothing can be said about n.

If at all I have to give an answer, I would better choose E.

[Ahmed MS]

Thanks for the clarification. At first my answer was also E. However, the source of the question said as n= 8, so answer would be B as it satisfy the condition n>7.

I hope in real GMAT exam, we will not face such an ambiguous problem.


Cheers.

[Brian@VeritasPrep]

Hey guys,

Please rest assured that this is not a valid GMAT question.

1) The statements will NEVER contradict each other, so this one is invalid. Statements 1 and 2 are direct contradictions, and that cannot happen on the GMAT.

2) The statements cannot contradict the given information either. The fact that 63^n is divisible by 3^16 means that, at minimum, n = 8. But Statement 2 contradicts that. It cannot - in a DS problem the given information, Statement 1, and Statement 2 are all facts. They must be true, and are indisputable. If you think you've found information that contradicts a fact, you're wrong and that's a clear indication that you need to re-check your work.

3) Statement 1, if it is indeed a DS statement, is not sufficient. We already know it has to be greater than 7; at minimum it's 8. But it could be a trillion...


My guess is that this originated as a true false question NOT in a DS context. Someone was asking what we knew about n given that 63^n was divisible by 3^16, and from there it became misconstrued as a Data Sufficiency question. It's not. All we know is that the first "choice", n>7 is true and that the second "choice" is not true.

So, in summary:

This is NOT a Data Sufficiency question.

and

In terms of learning about factors and multiples it's a decent exercise. 63^n can be phrased as 3^n * 3^n * 7^n, or 3^2n * 7^n. Breaking apart the exponent bases into prime factors is a very useful skill, so if that was your first step you've gotten 100% value out of this thread!

[sharmishtha_goel]

Answer is B.

= 63^n / 3^16
= (9*7)^n / 3^16
=3^2n*7^n/ 3^16
= (3^2n /3^16) * (7^n / 3^16)

So the value would be n=8, which is <7.


Cheers.

ahhhhhhhh............and how is n i.e 8 < 7??