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

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If x>1, what is the value of integer x? [#permalink] New post 10 Mar 2011, 05:50
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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

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA

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Re: sum of x and any prime number larger than x is odd [#permalink] New post 10 Mar 2011, 06:07
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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.

Answer: A.
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Re: Number properties [#permalink] New post 13 Sep 2012, 10:50
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


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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
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Re: Number properties [#permalink] New post 14 Sep 2012, 03:12
Expert's post
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


Merging similar topics. Please ask if anything remains unclear.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html


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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Re: sum of x and any prime number larger than x is odd [#permalink] New post 18 Sep 2012, 02:09
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....
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Re: sum of x and any prime number larger than x is odd [#permalink] New post 18 Sep 2012, 02:15
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.

Hope it's clear.
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Re: sum of x and any prime number larger than x is odd [#permalink] New post 18 Sep 2012, 02:30
Thanks Bunuel... I think I might have got confused by the language of the earlier post......Thank you for the clarification
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Re: If x>1, what is the value of integer x? [#permalink] New post 20 Sep 2012, 00:36
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

Answer: A
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Re: If x>1, what is the value of integer x? [#permalink] New post 07 Jun 2013, 02:37
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.

Regards
Anuj
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Re: If x>1, what is the value of integer x? [#permalink] New post 07 Jun 2013, 06:45
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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.

Hope it's clear.
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Re: If x>1, what is the value of integer x? [#permalink] New post 07 Jun 2013, 22:19
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?
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Re: If x>1, what is the value of integer x? [#permalink] New post 08 Jun 2013, 02:23
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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?
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Re: If x>1, what is the value of integer x? [#permalink] New post 08 Jun 2013, 08:19
The unique factors part tricked me.. :(
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MGmat Question [#permalink] New post 01 May 2014, 19:53
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??

Pls reply
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Re: MGmat Question [#permalink] New post 01 May 2014, 20:07
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??

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.

Answer :-A
Hope it helps.
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Re: MGmat Question [#permalink] New post 02 May 2014, 00:15
Expert's post
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??

Pls reply


Merging similar topics. Please ask if anything remains unclear.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 2, 3, and 7. Thank you.
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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.


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Re: MGmat Question   [#permalink] 02 May 2014, 00:15
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