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Number Property

by gmatusa2010 » Fri Dec 31, 2010 9:15 pm
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.

I still don't understand this. How is it B? All statement 2 says is X is 2 to the something. Whether X =2^k depends on what K is. It could and it couldnt.
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by ragz » Fri Dec 31, 2010 9:25 pm
gmatusa2010 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.

I still don't understand this. How is it B? All statement 2 says is X is 2 to the something. Whether X =2^k depends on what K is. It could and it couldnt.
When every factor of x is even, it basically means that x should have factors which are powers of 2.

Example, if x has a factor of 6, then it means it has a factor of 3 as well. Hence, if every factor of x is even, then x should be a power of 2 or in other words, x = 2^k.
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by goyalsau » Fri Dec 31, 2010 9:27 pm
gmatusa2010 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.

I still don't understand this. How is it B? All statement 2 says is X is 2 to the something. Whether X =2^k depends on what K is. It could and it couldnt.

(2) Every factor of x is even. { Is this statement Wrong}

Every positive Integer will have 1 as a factor.
Eg. 2^4 = 16

Factors are 1 , 2 , 4 , 8 , 16
So according to me every positive integer will always have a odd factor . i.e. 1
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by gmatusa2010 » Fri Dec 31, 2010 9:31 pm
let's say X = 4 and k is 6 then 4 is not equal to 64. u can run many examples. unless it says can x= 2^k then i think you might be able to put B

ragz wrote:
gmatusa2010 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.

I still don't understand this. How is it B? All statement 2 says is X is 2 to the something. Whether X =2^k depends on what K is. It could and it couldnt.
When every factor of x is even, it basically means that x should have factors which are powers of 2.

Example, if x has a factor of 6, then it means it has a factor of 3 as well. Hence, if every factor of x is even, then x should be a power of 2 or in other words, x = 2^k.
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by gmatusa2010 » Fri Dec 31, 2010 9:34 pm
the statement is correct and u are right. but i think its implying that X is even. Also, the explanation said so. let's just say they explicitly state that every factor greater than 1 is even. would the problem still make sense to you?
goyalsau wrote:
gmatusa2010 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.

I still don't understand this. How is it B? All statement 2 says is X is 2 to the something. Whether X =2^k depends on what K is. It could and it couldnt.

(2) Every factor of x is even. { Is this statement Wrong}

Every positive Integer will have 1 as a factor.
Eg. 2^4 = 16

Factors are 1 , 2 , 4 , 8 , 16
So according to me every positive integer will always have a odd factor . i.e. 1
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by Anurag@Gurome » Sat Jan 01, 2011 4:15 am
gmatusa2010 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.
Statement 1: x has only one prime factor.
x can be any prime integer.

Not Sufficient.

Statement 2: Every factor of x is even.
It is possible when x has only 2 as its prime factor.
Thus x will be always of the form 2^k, for some positive integer k.

Sufficient.

The correct answer is B
gmatusa2010 wrote:let's say X = 4 and k is 6 then 4 is not equal to 64. u can run many examples. unless it says can x= 2^k then i think you might be able to put B
The question asks "is x equal to 2^k for some positive integer k?"
It doesn't ask whether x is of the form 2^k for all positive integer k. Thus for x = 4, x is of the form 2^k for k = 2.
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by lunarpower » Sun Jan 02, 2011 12:39 am
um ... what's the source of the problem?

because this statement
Every factor of x is even
is impossible.

the number 1, which is odd, is a factor of EVERY positive integer; therefore, it's impossible for "every factor of x" to be even.

sketchy sketchy...
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by goyalsau » Sun Jan 02, 2011 11:28 pm
lunarpower wrote:um ... what's the source of the problem?

because this statement
Every factor of x is even
is impossible.

the number 1, which is odd, is a factor of EVERY positive integer; therefore, it's impossible for "every factor of x" to be even.

sketchy sketchy...
thanks Ron..
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