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Manager  Joined: 10 Nov 2010
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If x>1, what is the value of integer x?  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 49% (01:45) correct 51% (01:31) wrong based on 308 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 60466
Re: sum of x and any prime number larger than x is odd  [#permalink]

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2
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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.

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Bunuel wrote:
vinnik 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.

Please explain with the help of examples.

Thanks & Regards
Vinni

Thanks Bunuel.

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
Math Expert V
Joined: 02 Sep 2009
Posts: 60466

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vinnik wrote:
Bunuel wrote:
vinnik 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.

Please explain with the help of examples.

Thanks & Regards
Vinni

Thanks Bunuel.

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.
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Joined: 11 Jul 2012
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GMAT 1: 650 Q49 V29
Re: sum of x and any prime number larger than x is odd  [#permalink]

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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.

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....
Math Expert V
Joined: 02 Sep 2009
Posts: 60466
Re: sum of x and any prime number larger than x is odd  [#permalink]

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2
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.

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.

Hope it's clear.
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Re: sum of x and any prime number larger than x is odd  [#permalink]

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Thanks Bunuel... I think I might have got confused by the language of the earlier post......Thank you for the clarification
Senior Manager  Joined: 13 Aug 2012
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Re: If x>1, what is the value of integer x?  [#permalink]

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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

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

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Hi,
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
Math Expert V
Joined: 02 Sep 2009
Posts: 60466
Re: If x>1, what is the value of integer x?  [#permalink]

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2
coolanujdel wrote:
Hi,
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.

Hope it's clear.
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Re: If x>1, what is the value of integer x?  [#permalink]

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

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anu1706 wrote:
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?
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Re: If x>1, what is the value of integer x?  [#permalink]

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The unique factors part tricked me.. Intern  Joined: 29 May 2013
Posts: 21
Concentration: Marketing, Entrepreneurship
Schools: Molson '17 (M\$)
GMAT Date: 08-20-2014
GPA: 3.34

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2
kanusha wrote:
If x > 1, what is the value ofinteger x?

(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??

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.

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

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Bunuel wrote:
anu1706 wrote:
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?

Thank's Bunuel Re: If x>1, what is the value of integer x?   [#permalink] 14 Dec 2019, 01:11
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