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Re: sum of x and any prime number larger than x is odd [#permalink]

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10 Mar 2011, 07:07

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GMATD11 wrote:

If x>1, what is the value of integer x?

1) There are x unique factors of x. 2) The sum of x and any prime number larger than x is odd

1) x can be 1 or 2 but as x>1 so x=2 --S

2) according to me statement is saying x is even prime number so x=2-- S

But OA is different

If x>1, what is the value of integer x?

(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.

In statement (1), I understand that "x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive", but what confuses me is the next line that mentions "x-1." I have understood other numbers that are not divisible. But what is the logic behind "x-1." Well i do understand that in x>1 i can take 1 to the other side which makes x-1. But i am not able to understand this method clearly.

Can you please elaborate more on it. Statement (2) is fine. I was able to get it.

In statement (1), I understand that "x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive", but what confuses me is the next line that mentions "x-1." I have understood other numbers that are not divisible. But what is the logic behind "x-1." Well i do understand that in x>1 i can take 1 to the other side which makes x-1. But i am not able to understand this method clearly.

Can you please elaborate more on it. Statement (2) is fine. I was able to get it.

Regards Vinni

Not sure I understand your question here, but we use the fact that x cannot be divisible by x-1 unless x=2 to proof that x can only be 2. _________________

Re: sum of x and any prime number larger than x is odd [#permalink]

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18 Sep 2012, 03:09

Bunuel wrote:

GMATD11 wrote:

If x>1, what is the value of integer x?

1) There are x unique factors of x. 2) The sum of x and any prime number larger than x is odd

1) x can be 1 or 2 but as x>1 so x=2 --S

2) according to me statement is saying x is even prime number so x=2-- S

But OA is different

If x>1, what is the value of integer x?

(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.

Answer: A.

Need an explanation for statement 2.... the number to be added to x has to be a odd prime...for the result to be odd...but then why cannot x be 2 here.... I agree with the OA...it will be A...but I don't understand why can't x = 2 be one of the possible values....

Re: sum of x and any prime number larger than x is odd [#permalink]

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18 Sep 2012, 03:15

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This post received KUDOS

Expert's post

avaneeshvyas wrote:

Bunuel wrote:

GMATD11 wrote:

If x>1, what is the value of integer x?

1) There are x unique factors of x. 2) The sum of x and any prime number larger than x is odd

1) x can be 1 or 2 but as x>1 so x=2 --S

2) according to me statement is saying x is even prime number so x=2-- S

But OA is different

If x>1, what is the value of integer x?

(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.

Answer: A.

Need an explanation for statement 2.... the number to be added to x has to be a odd prime...for the result to be odd...but then why cannot x be 2 here.... I agree with the OA...it will be A...but I don't understand why can't x = 2 be one of the possible values....

From (2) x can be 2, but it can also be any other even number, for example 4: 4+5=9=odd.

Re: If x>1, what is the value of integer x? [#permalink]

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20 Sep 2012, 01:36

X > 1, what is x?

(1) if x=2, unique factor is 2 If x=3, unique factor is 2 Moving up the unqie factor count minimum is 2 and only 2 qualifies for the condition X=2, SUFFICIENT

(2) x + odd = odd We don't know x yet excep it is x>1. so if prime is even, x should be odd If prime is odd, x should be even. INSUFFICIENT

Re: If x>1, what is the value of integer x? [#permalink]

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07 Jun 2013, 03:37

Hi, Pls answer below points: 1) x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x- Not clear about this statement. As per my understanding factors are those which completely divide the number.So how can factors will be divisible and that too why from all the number b/w 1 to x. 2) What do you understand by 'unique factors'.

Please explain me the strategy to adopt while attempting to comprehend the concepts.

Re: If x>1, what is the value of integer x? [#permalink]

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07 Jun 2013, 07:45

Expert's post

coolanujdel wrote:

Hi, Pls answer below points: 1) x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x- Not clear about this statement. As per my understanding factors are those which completely divide the number.So how can factors will be divisible and that too why from all the number b/w 1 to x. 2) What do you understand by 'unique factors'.

Please explain me the strategy to adopt while attempting to comprehend the concepts.

Regards Anuj

Factor of x is a positive integer which divides x evenly (without a remainder). Notice that each factor of x must be less than or equal to x: the smallest factor of a positive integer is 1 and the greatest factor is that integer itself. For example, the smallest factor of 12 is 1 and the greatest factor of 12 is 12 itself.

Now, x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x: 1, 2, 3, ..., x-1, x --> total of x factors.

As for your second question: unique factors are distinct factors. For example 12 has 6 unique (distinct) factors: 1, 2, 3, 4, 6, and 12.

Re: If x>1, what is the value of integer x? [#permalink]

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07 Jun 2013, 23:19

I have got your point completely.Thanks for giving your time! one thing i need to get clarify is Why we are taking X-1 always instead for any series X+1 for consecutive integers is also possible or not?

Re: If x>1, what is the value of integer x? [#permalink]

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08 Jun 2013, 03:23

Expert's post

anu1706 wrote:

I have got your point completely.Thanks for giving your time! one thing i need to get clarify is Why we are taking X-1 always instead for any series X+1 for consecutive integers is also possible or not?

Not sure understand your question: where are we taking x-1 consecutive integers? Can you please elaborate? _________________

(1) There are x unique factors of x (2) The sum of x and any prime number larger than x is odd.

What i Understood was If an Integer x >1 Should have x unique factors Ex if the integer is 12 its Unique factors are 1, 2, 3, 4, 6, 12

Can any One pls Explain What the statment 1 Mean??

Pls reply

Hey,

When they say there are x unique factors of x try substituting values for x. As x> 1 , suppose x= 5 There ARE NOT 5 unique factors of 5. (There are just 2:- 1,5) .Try substituting different numbers, u will realize that the only possible case is when x=1 and x =2 .[1 has 1 unique factor(1), 2 has 2 unique factors (1,2)] Question stem says that x > 1 , thus x= 2. Sufficient.

Statement 2 is insufficient as x could be 2/4/6 etc.

Re: If x>1, what is the value of integer x? [#permalink]

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