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# If x is an integer greater than 1, is x equal to 2^k for

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If x is an integer greater than 1, is x equal to 2^k for [#permalink]

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09 Jan 2011, 01:33
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48% (01:46) correct 52% (00:46) wrong based on 31 sessions

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If x is an integer greater than 1, is x equal to 2^k for some positive integer k?

(1) x has only one prime factor.
(2) Every factor of x is even.

[Reveal] Spoiler:
Can anyone please explain the statements to me?

Statement 1 says x has only one prime factor. Am I to assume that x is a prime number? or am i to assume that x is a number such as 9, whose only prime factor is 3. Or the number can be 2,3... its confusing to me,

Statement 2 says every factor of x is even. Does such a number exist?

Source: Jeff Sackmann's questions
[Reveal] Spoiler: OA

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Re: If x is an integer greater than 1, is x equal to 2^k for [#permalink]

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09 Jan 2011, 04:07
gmatpapa wrote:
If x is an integer greater than 1, is x equal to $$2^k$$ for some positive integer k?
(1) x has only one prime factor.
(2) Every factor of x is even.

Can anyone please explain the statements to me?

Statement 1 says x has only one prime factor. Am I to assume that x is a prime number? or am i to assume that x is a number such as 9, whose only prime factor is 3. Or the number can be 2,3... its confusing to me,

Statement 2 says every factor of x is even. Does such a number exist?

Source: Jeff Sackmann's questions

If x is an integer greater than 1, is x equal to 2^k for some positive integer k?

Basically question ask whether x is some power of 2: 2 (for k=1), 4 (for k=2), 8 (for k=3), ...

(1) x has only one prime factor --> x can be ANY prime in ANY positive integer power: 2, 2^3, 3, 3^7, 5, 5^2, ... Note that all this numbers have only one prime factor. Not sufficient.

(2) Every factor of x is even --> this statement makes no sense, every positive integer has at least one positive odd factor: 1. I think it should be: x has no odd factor more than 1 (or: every factor of x, except 1, is even). In this case as x don't have any odd factors >1 then x has no odd primes in its prime factorization --> x is of the form of 2^k for some positive integer k. Sufficient.

Not a good question.
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Re: If x is an integer greater than 1, is x equal to 2^k for [#permalink]

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09 Jan 2011, 05:06
Bunuel wrote:
gmatpapa wrote:
If x is an integer greater than 1, is x equal to $$2^k$$ for some positive integer k?
(1) x has only one prime factor.
(2) Every factor of x is even.

Can anyone please explain the statements to me?

Statement 1 says x has only one prime factor. Am I to assume that x is a prime number? or am i to assume that x is a number such as 9, whose only prime factor is 3. Or the number can be 2,3... its confusing to me,

Statement 2 says every factor of x is even. Does such a number exist?

Source: Jeff Sackmann's questions

If x is an integer greater than 1, is x equal to 2^k for some positive integer k?

Basically question ask whether x is some power of 2: 2 (for k=1), 4 (for k=2), 8 (for k=3), ...

(1) x has only one prime factor --> x can be ANY prime in ANY positive integer power: 2, 2^3, 3, 3^7, 5, 5^2, ... Note that all this numbers have only one prime factor. Not sufficient.

(2) Every factor of x is even --> this statement makes no sense, every positive integer has at least one positive odd factor: 1. I think it should be: x has no odd factor more than 1 (or: every factor of x, except 1, is even). In this case as x don't have any odd factors >1 then x has no odd primes in its prime factorization --> x is of the form of 2^k for some positive integer k. Sufficient.

Not a good question.

Yes. if statement 2 is rephrased as you said, it will be a sufficient statement. I think this what even the question maker had in mind but it slipped off his mind somehow. I will mail him to correct this.

Thanks Bunuel!
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Re: If x is an integer greater than 1, is x equal to 2^k for [#permalink]

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19 Jun 2015, 12:16
Bunuel can you please check the interpretation of the following?

Every Factor of X is even: Means (2,6,8,12) breaking down of primes in 2 and 3 is possible.

Every prime factor of X is even; Means (2 raised to some power)

Thanks
Re: If x is an integer greater than 1, is x equal to 2^k for   [#permalink] 19 Jun 2015, 12:16
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