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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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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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New post 09 Jan 2011, 03:07
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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.

Answer: B.

Not a good question.
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GMAT 1: 710 Q48 V40
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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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New post 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.

Answer: B.

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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New post 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
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Math Expert
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Joined: 02 Aug 2009
Posts: 5660
Re: If x is an integer greater than 1 [#permalink]

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

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New post 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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: If x is an integer greater than 1, is x equal to 2^k for   [#permalink] 09 Jan 2018, 19:56
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