It is currently 20 Nov 2017, 07:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 526

Kudos [?]: 546 [0], given: 75

Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
If x is an integer greater than 1, is x equal to 2^k for [#permalink]

### Show Tags

09 Jan 2011, 01:33
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

47% (00:46) correct 53% (00:47) wrong based on 32 sessions

### HideShow timer Statistics

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

_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Kudos [?]: 546 [0], given: 75

Math Expert
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132772 [0], given: 12372

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

### Show Tags

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.
_________________

Kudos [?]: 132772 [0], given: 12372

Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 526

Kudos [?]: 546 [0], given: 75

Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Re: If x is an integer greater than 1, is x equal to 2^k for [#permalink]

### Show Tags

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!
_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Kudos [?]: 546 [0], given: 75

Intern
Joined: 23 Nov 2014
Posts: 33

Kudos [?]: 28 [0], given: 4

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

### Show Tags

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

Kudos [?]: 28 [0], given: 4

Re: If x is an integer greater than 1, is x equal to 2^k for   [#permalink] 19 Jun 2015, 12:16
Display posts from previous: Sort by