Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 162
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

If x>1, what is the value of integer x?
[#permalink]
Show Tags
10 Mar 2011, 06:50
Question Stats:
49% (01:45) correct 51% (01:31) wrong based on 308 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 60466

Re: sum of x and any prime number larger than x is odd
[#permalink]
Show Tags
10 Mar 2011, 07:07
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 x1 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.
_________________




Manager
Joined: 14 Dec 2011
Posts: 72

Re: Number properties
[#permalink]
Show Tags
13 Sep 2012, 11:50
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 Merging similar topics. Please ask if anything remains unclear. Also, please read and follow: rulesforpostingpleasereadthisbeforeposting133935.htmlThanks 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 "x1." I have understood other numbers that are not divisible. But what is the logic behind "x1." Well i do understand that in x>1 i can take 1 to the other side which makes x1. 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
Joined: 02 Sep 2009
Posts: 60466

Re: Number properties
[#permalink]
Show Tags
14 Sep 2012, 04:12
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: rulesforpostingpleasereadthisbeforeposting133935.htmlThanks 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 "x1." I have understood other numbers that are not divisible. But what is the logic behind "x1." Well i do understand that in x>1 i can take 1 to the other side which makes x1. 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 x1 unless x=2 to proof that x can only be 2.
_________________



Intern
Joined: 11 Jul 2012
Posts: 47

Re: sum of x and any prime number larger than x is odd
[#permalink]
Show Tags
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 x1 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....



Math Expert
Joined: 02 Sep 2009
Posts: 60466

Re: sum of x and any prime number larger than x is odd
[#permalink]
Show Tags
18 Sep 2012, 03:15
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 x1 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.
_________________



Intern
Joined: 11 Jul 2012
Posts: 47

Re: sum of x and any prime number larger than x is odd
[#permalink]
Show Tags
18 Sep 2012, 03:30
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
Posts: 394
Concentration: Marketing, Finance
GPA: 3.23

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



Intern
Joined: 27 Aug 2012
Posts: 14
Location: India
Concentration: International Business, Strategy
WE: Project Management (Manufacturing)

Re: If x>1, what is the value of integer x?
[#permalink]
Show Tags
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.
Regards Anuj



Math Expert
Joined: 02 Sep 2009
Posts: 60466

Re: If x>1, what is the value of integer x?
[#permalink]
Show Tags
07 Jun 2013, 07:45
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, ..., x1, 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.
_________________



Intern
Joined: 15 Jul 2012
Posts: 35

Re: If x>1, what is the value of integer x?
[#permalink]
Show Tags
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 X1 always instead for any series X+1 for consecutive integers is also possible or not?



Math Expert
Joined: 02 Sep 2009
Posts: 60466

Re: If x>1, what is the value of integer x?
[#permalink]
Show Tags
08 Jun 2013, 03:23
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 X1 always instead for any series X+1 for consecutive integers is also possible or not? Not sure understand your question: where are we taking x1 consecutive integers? Can you please elaborate?
_________________



Director
Status: My Thread Master Bschool Threads>Krannert(Purdue),WP Carey(Arizona),Foster(Uwashngton)
Joined: 28 Jun 2011
Posts: 807

Re: If x>1, what is the value of integer x?
[#permalink]
Show Tags
08 Jun 2013, 09:19
The unique factors part tricked me..



Intern
Joined: 29 May 2013
Posts: 21
Concentration: Marketing, Entrepreneurship
GMAT Date: 08202014
GPA: 3.34

Re: MGmat Question
[#permalink]
Show Tags
01 May 2014, 21:07
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.



Intern
Joined: 31 Dec 2016
Posts: 7

Re: If x>1, what is the value of integer x?
[#permalink]
Show Tags
14 Dec 2019, 01:11
Bunuel wrote: 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 X1 always instead for any series X+1 for consecutive integers is also possible or not? Not sure understand your question: where are we taking x1 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






