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If K is a positive integer, is (2^k)-1 a prime number?
1)K is a prime number
2)K has exactly 2 positive divisors
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Prime Number
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vineeshp
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D Either statement is sufficient.
I dont see a mathematical way of solving this, Maybe experts have. But 2 ^ 1 -1, 2 ^ 3 -1 , 2 ^ 5 -1, 2 ^ 7 -1, 2 ^ 11 -1 all lead us to prime numbers. I think we can safely conclude that they lead us to prime numbers.
1) k is prime, so 2 ^ k -1 leads us to prime.
2) Has stated the same thing in another way. 2 divisors = Prime.
I dont see a mathematical way of solving this, Maybe experts have. But 2 ^ 1 -1, 2 ^ 3 -1 , 2 ^ 5 -1, 2 ^ 7 -1, 2 ^ 11 -1 all lead us to prime numbers. I think we can safely conclude that they lead us to prime numbers.
1) k is prime, so 2 ^ k -1 leads us to prime.
2) Has stated the same thing in another way. 2 divisors = Prime.
Vineesh,
Just telling you what I know and think. I am not the expert.
Just telling you what I know and think. I am not the expert.
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fskilnik@GMATH
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Hi there!rohu27 wrote:Source:gmatprepnow.com
If K is a positive integer, is (2^k)-1 a prime number?
1)K is a prime number
2)K has exactly 2 positive divisors
First of all, statements (1) and (2) are equivalent (in fact the same), therefore the answer to the question is certainly (D) or (E).
The correct answer is (E), as shown below:
> Take k=2 , then 2^k-1 = 3 answering in the affirmative;
> Take k=11, then 2^k-1 = 2047 = 23*29 answering in the negative.
For the interested readers in this very famous subject ("Mersenne primes") I suggest:
https://primes.utm.edu/mersenne/index.html
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Ian Stewart
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This is based on a famous problem in Number Theory, as fskilnik points out, but it most certainly is not a realistic GMAT question. To see why Statement 1 is not sufficient, you need to plug in a value for k at least as large as 11, and there is no quick way to prime factorize 2^11 - 1. The GMAT will never ask you to do that.rohu27 wrote:Source:gmatprepnow.com
If K is a positive integer, is (2^k)-1 a prime number?
1)K is a prime number
2)K has exactly 2 positive divisors
There is no formula for generating prime numbers, and I suppose if you know that, you can answer E here instantly, but that's not something the GMAT will ever test.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
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Brent@GMATPrepNow
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As the one who created that question, I should point out that it was never intended to be an actual practice question. As Ian pointed out, the question is beyond the scope of what the GMAT tests.
The question is actually from a Data Sufficiency lesson on Guessing Strategically (https://youtu.be/2GOt0yZbrVg). In this video we examine how we might eliminate answer choices if we cannot answer a certain DS question. So, even though the question is well beyond the scope of the GMAT, we can easily eliminate answer choices A, B and C, since statements 1 and 2 provide the same information, and when the two statements provide the same information, the correct answer must be either D or E
Cheers,
Brent
The question is actually from a Data Sufficiency lesson on Guessing Strategically (https://youtu.be/2GOt0yZbrVg). In this video we examine how we might eliminate answer choices if we cannot answer a certain DS question. So, even though the question is well beyond the scope of the GMAT, we can easily eliminate answer choices A, B and C, since statements 1 and 2 provide the same information, and when the two statements provide the same information, the correct answer must be either D or E
Cheers,
Brent
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rohu27
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Thanks Brent. I did pick it up from tht video and was scared when i saw the solution (calculate 2^11).But anyways i get to learn a new quant concept though may not be useful for gmat.Brent Hanneson wrote:As the one who created that question, I should point out that it was never intended to be an actual practice question. As Ian pointed out, the question is beyond the scope of what the GMAT tests.
The question is actually from a Data Sufficiency lesson on Guessing Strategically (https://youtu.be/2GOt0yZbrVg). In this video we examine how we might eliminate answer choices if we cannot answer a certain DS question. So, even though the question is well beyond the scope of the GMAT, we can easily eliminate answer choices A, B and C, since statements 1 and 2 provide the same information, and when the two statements provide the same information, the correct answer must be either D or E
Cheers,
Brent
the video was really good btw. things you already knw but tend to ignore at pressure times.
