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.
1. n >7
2. n<7
Please help me solve this problem.
Cheers.
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value of n?value of n?
Source: Beat The GMAT — Data Sufficiency |
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.
1. n > 7
2. n < 7
That is what I have found written.
Cheers.
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
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
Isn't this an invalid question because the two statements lead to different solutions? Can the experts weigh in on this?
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.
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.
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.
= 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.
Hey,
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.
Firstly, this question is badly framed. You cannot even consider statements(1) and (2) together.Q. If 63^n is divisible 3^16, then what is the value of n?
1. n >7
2. n<7
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.
Cheers!
Things are not what they appear to be... nor are they otherwise
Things are not what they appear to be... nor are they otherwise
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.
I hope in real GMAT exam, we will not face such an ambiguous problem.
Cheers.
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Brian@VeritasPrep
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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!
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!
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
Ahmed MS wrote: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??
