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

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Senior Manager
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Joined: 31 Oct 2010
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Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
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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, 00:33
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Difficulty:

65% (hard)

Question Stats:

51% (01:35) correct 49% (01:37) wrong based on 76 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.

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

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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, 03:07
1
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, 04:06
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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If x is an integer greater than 1  [#permalink]

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09 Jan 2018, 17:58
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.

Source: Jeff Sackman
Math Expert
Joined: 02 Aug 2009
Posts: 7209
Re: If x is an integer greater than 1  [#permalink]

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09 Jan 2018, 19:20
Soniab 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.

Source: Jeff Sackman

x>1, is x=2^k

1) x has only one prime factor..
So x could be 2,2^k, 3,3^k,5^k...
Insuff

2) every factor of x is even...
Only possible when x=2*2*2.....
So yes x=2^k
Sufficient

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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 2018, 19:56
Soniab 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.

Source: Jeff Sackman

Merging topics. Please check solution here: https://gmatclub.com/forum/if-x-is-an-i ... ml#p849080
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Re: If x is an integer greater than 1, is x equal to 2^k for &nbs [#permalink] 09 Jan 2018, 19:56
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