It is currently 19 Oct 2017, 04:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the integer x is greater than 1, does x = 2?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Apr 2010
Posts: 5

Kudos [?]: 7 [1], given: 0

If the integer x is greater than 1, does x = 2? [#permalink]

### Show Tags

27 Jun 2010, 09:37
1
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

48% (01:12) correct 52% (01:03) wrong based on 245 sessions

### HideShow timer Statistics

If the integer x is greater than 1, does x = 2?

(1) x is evenly divisible by exactly two positive integers.
(2) The sum of any two distinct positive factors of x is odd.

[Reveal] Spoiler:
1 Insufficient
2- Sufficient: 1 is always a factor, so x can not be odd, for all other even they have themselves and 2 which will give even sum (Fac(4)= 4,2,1) so only two has two factors ( 2,1).

is it correct because i found an answer says C ?
[Reveal] Spoiler: OA

Kudos [?]: 7 [1], given: 0

Intern
Joined: 04 Jun 2010
Posts: 3

Kudos [?]: [0], given: 0

Re: DS: X>1 , is x=2? [#permalink]

### Show Tags

27 Jun 2010, 10:28
both conditions are required ....sum of two factors can be odd for lot os number but the first condition will determine that 2 is the only number which has exactly two factors ( 1&2) whose addition is odd ....

Kudos [?]: [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128826 [1], given: 12183

Re: DS: X>1 , is x=2? [#permalink]

### Show Tags

27 Jun 2010, 11:21
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
ilaila wrote:
If the integer x is greater than 1, does x = 2?
1) x is evenly divisible by exactly two positive integers.
2) The sum of any two distinct positive factors of x is odd.

1 Insufficient
2- Sufficient: 1 is always a factor, so x can not be odd, for all other even they have themselves and 2 which will give even sum (Fac(4)= 4,2,1) so only two has two factors ( 2,1).

is it correct because i found an answer says C ?

You are right B should be the answer for this question and your reasoning for B is correct.

If the integer x is greater than 1, does x = 2?

Given: $$x=integer>1$$. Question: does $$x=2$$?

(1) x is evenly divisible by exactly two positive integers --> $$x$$ can be any prime (2, 3, 5, 7, ...). Not sufficient.

(2) The sum of ANY TWO distinct positive factors of x is odd If $$x$$ is odd, then 1 (obviously one of the factors of $$x$$) plus $$x$$ itself ($$x$$ is also a factor of itself) will be even not odd, so $$x$$ cannot be odd. Now if $$x$$ is even and more than 2, then 2 (one of the factors of $$x$$) plus $$x$$ itself will be even not odd, so $$x$$ cannot be more than 2 --> $$x=2$$ (2 has exactly two positive factors (1 and 2) and their sum is odd). Sufficient.

Check similar problem: is-n-equal-to-94720.html#p733591

Hope it helps.
_________________

Kudos [?]: 128826 [1], given: 12183

Manager
Joined: 18 Oct 2008
Posts: 187

Kudos [?]: 29 [0], given: 11

Re: DS: X>1 , is x=2? [#permalink]

### Show Tags

28 Jun 2010, 02:38
ilaila wrote:
If the integer x is greater than 1, does x = 2?
1) x is evenly divisible by exactly two positive integers.
2) The sum of any two distinct positive factors of x is odd.

1 Insufficient
2- Sufficient: 1 is always a factor, so x can not be odd, for all other even they have themselves and 2 which will give even sum (Fac(4)= 4,2,1) so only two has two factors ( 2,1).

is it correct because i found an answer says C ?

i still have confusion with B.

it says sum of any two distinct factors of X is odd.
take 10 for ex: factors - 1,2,5,10.
we have 2+5=7 which is odd, thus we have numbers greater than 2 with the condition satisfied.

while considering both A&B, its sure that x=2.

am i missing something?

Kudos [?]: 29 [0], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128826 [0], given: 12183

Re: DS: X>1 , is x=2? [#permalink]

### Show Tags

28 Jun 2010, 05:44
Expert's post
1
This post was
BOOKMARKED
ramana wrote:
ilaila wrote:
If the integer x is greater than 1, does x = 2?
1) x is evenly divisible by exactly two positive integers.
2) The sum of any two distinct positive factors of x is odd.

1 Insufficient
2- Sufficient: 1 is always a factor, so x can not be odd, for all other even they have themselves and 2 which will give even sum (Fac(4)= 4,2,1) so only two has two factors ( 2,1).

is it correct because i found an answer says C ?

i still have confusion with B.

it says sum of any two distinct factors of X is odd.
take 10 for ex: factors - 1,2,5,10.
we have 2+5=7 which is odd, thus we have numbers greater than 2 with the condition satisfied.

while considering both A&B, its sure that x=2.

am i missing something?

Stem says the sum of ANY two distinct positive factors of x is odd. It doesn't mean that the sum of some factors is odd but rather that the sum of every possible pair of distinct positive factors is odd.

In your example: 2+5=7=odd but 2+10=12=even.

Consider this: "the sum of any two distinct positive factors of x is odd" means that number must have only one odd factor and only one even factor. If odd factors, or even factors >1, then the sum of the pair of two odd factors (or even factors) will be even not odd. Only number to have only one odd and only one even factor is 2.

Hope it's clear.
_________________

Kudos [?]: 128826 [0], given: 12183

Manager
Joined: 18 Oct 2008
Posts: 187

Kudos [?]: 29 [0], given: 11

Re: DS: X>1 , is x=2? [#permalink]

### Show Tags

28 Jun 2010, 06:30
Perfect, thats where i got it wrong.
Thanks Bunuel.

Kudos [?]: 29 [0], given: 11

Intern
Joined: 07 Aug 2012
Posts: 3

Kudos [?]: [0], given: 0

Re: If the integer x is greater than 1, does x = 2? 1) x is [#permalink]

### Show Tags

16 May 2013, 02:29
Hi All,

Answer for this question has to be C.

Pt. 2 Says - 2) The sum of any two distinct positive factors of x is odd.

If X=2 then ..... 1+2 = 3 (ODD) -------> X is 2
If X=4 then ..... 1+4 = 5 (ODD) -------> X is not 2

So B is not sufficient.

However if I combine Pt. 1 to it which says 1) x is evenly divisible by exactly two positive integers. ---- X is Prime

Then only we can come at a conclusion that X=2

Hope I am Clear.

Kudos [?]: [0], given: 0

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1355 [1], given: 136

Re: If the integer x is greater than 1, does x = 2? 1) x is [#permalink]

### Show Tags

16 May 2013, 03:23
1
KUDOS
nicechetan87 wrote:
If X=2 then ..... 1+2 = 3 (ODD) -------> X is 2
If X=4 then ..... 1+4 = 5 (ODD) -------> X is not 2

This part is incomplete. The problem states that sum of ANY 2 distinct positive factors of x is ODD--> This implies that any two positive factors when added will ALWAYS give an odd sum.

For x = 4, all the positive factors are = 1,2,4. If you take 1 & 4, we indeed get an odd sum, however, if we take 2 & 4, we get an even sum.Thus $$x\neq{4}$$

The point to note is that :

odd+even = odd. Any other arrangement will always give you an even sum for integers.X will have at-least one odd factor(that being 1). Now to make the sum of any of the two factors as odd, X will have to have at-least 1 even factor. If X has more than 2 factors(1 already being odd and 1 already being even) that again would be odd/even. Let us assume the no of factors for x is 3 and they are odd,even,odd.Thus, as per the problem, taking sum of any two factors must always yield an odd sum, which gets defied for (odd,odd). Similarly for 3 factors of x which are odd,even,even. This implies that x can only have 2 factors, one of them odd and one of them even. The only positive integer to have 1 odd & 1 even factor is 2. Sufficient.
_________________

Kudos [?]: 1355 [1], given: 136

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128826 [0], given: 12183

Re: If the integer x is greater than 1, does x = 2? 1) x is [#permalink]

### Show Tags

16 May 2013, 04:40
nicechetan87 wrote:
Hi All,

Answer for this question has to be C.

Pt. 2 Says - 2) The sum of any two distinct positive factors of x is odd.

If X=2 then ..... 1+2 = 3 (ODD) -------> X is 2
If X=4 then ..... 1+4 = 5 (ODD) -------> X is not 2

So B is not sufficient.

However if I combine Pt. 1 to it which says 1) x is evenly divisible by exactly two positive integers. ---- X is Prime

Then only we can come at a conclusion that X=2

Hope I am Clear.

The correct answer is B, not C.

Check here: if-the-integer-x-is-greater-than-1-does-x-2-1-x-is-96422.html#p742632

Hope it helps.
_________________

Kudos [?]: 128826 [0], given: 12183

Manager
Joined: 04 Mar 2013
Posts: 87

Kudos [?]: 10 [0], given: 6

Location: India
Concentration: General Management, Marketing
GPA: 3.49
WE: Web Development (Computer Software)
Re: If the integer x is greater than 1, does x = 2? 1) x is [#permalink]

### Show Tags

16 Jun 2013, 02:56
nicechetan87 wrote:
Hi All,

Answer for this question has to be C.

Pt. 2 Says - 2) The sum of any two distinct positive factors of x is odd.

If X=2 then ..... 1+2 = 3 (ODD) -------> X is 2
If X=4 then ..... 1+4 = 5 (ODD) -------> X is not 2

So B is not sufficient.

However if I combine Pt. 1 to it which says 1) x is evenly divisible by exactly two positive integers. ---- X is Prime

Then only we can come at a conclusion that X=2

Hope I am Clear.

hey nope any two factors doesn't mean as u have considered, it means for 4 factors 1,2,4 of these any two , so 2 and 4 can be considered which is not correct. and hence 4 is not the valid number to check
only 2 is the number avialable in NS so b is quite good

Kudos [?]: 10 [0], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128826 [0], given: 12183

Re: If the integer x is greater than 1, does x = 2? [#permalink]

### Show Tags

16 Jun 2013, 03:35

Kudos [?]: 128826 [0], given: 12183

Manager
Joined: 24 Apr 2013
Posts: 67

Kudos [?]: 14 [0], given: 23

Location: United States
Re: DS: X>1 , is x=2? [#permalink]

### Show Tags

10 Oct 2013, 07:15
Bunuel wrote:
ilaila wrote:
If the integer x is greater than 1, does x = 2?
1) x is evenly divisible by exactly two positive integers.
2) The sum of any two distinct positive factors of x is odd.

1 Insufficient
2- Sufficient: 1 is always a factor, so x can not be odd, for all other even they have themselves and 2 which will give even sum (Fac(4)= 4,2,1) so only two has two factors ( 2,1).

is it correct because i found an answer says C ?

You are right B should be the answer for this question and your reasoning for B is correct.

If the integer x is greater than 1, does x = 2?

Given: $$x=integer>1$$. Question: does $$x=2$$?

(1) x is evenly divisible by exactly two positive integers --> $$x$$ can be any prime (2, 3, 5, 7, ...). Not sufficient.

(2) The sum of ANY TWO distinct positive factors of x is odd If $$x$$ is odd, then 1 (obviously one of the factors of $$x$$) plus $$x$$ itself ($$x$$ is also a factor of itself) will be even not odd, so $$x$$ cannot be odd. Now if $$x$$ is even and more than 2, then 2 (one of the factors of $$x$$) plus $$x$$ itself will be even not odd, so $$x$$ cannot be more than 2 --> $$x=2$$ (2 has exactly two positive factors (1 and 2) and their sum is odd). Sufficient.

Check similar problem: is-n-equal-to-94720.html#p733591

Hope it helps.

Hey Bunuel
Sorry I still don't understand B
if I choose x=14
then factors are {1,2,7,14} for which the sum of any two factors could be odd. Take 7+2=9 or 2+1=3 0r 14+1=15 -----> all these option qualify for (B) but x is not 2! where is the error?
_________________

Struggling: make or break attempt

Kudos [?]: 14 [0], given: 23

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128826 [0], given: 12183

Re: DS: X>1 , is x=2? [#permalink]

### Show Tags

10 Oct 2013, 07:19
SaraLotfy wrote:
Bunuel wrote:
ilaila wrote:
If the integer x is greater than 1, does x = 2?
1) x is evenly divisible by exactly two positive integers.
2) The sum of any two distinct positive factors of x is odd.

1 Insufficient
2- Sufficient: 1 is always a factor, so x can not be odd, for all other even they have themselves and 2 which will give even sum (Fac(4)= 4,2,1) so only two has two factors ( 2,1).

is it correct because i found an answer says C ?

You are right B should be the answer for this question and your reasoning for B is correct.

If the integer x is greater than 1, does x = 2?

Given: $$x=integer>1$$. Question: does $$x=2$$?

(1) x is evenly divisible by exactly two positive integers --> $$x$$ can be any prime (2, 3, 5, 7, ...). Not sufficient.

(2) The sum of ANY TWO distinct positive factors of x is odd If $$x$$ is odd, then 1 (obviously one of the factors of $$x$$) plus $$x$$ itself ($$x$$ is also a factor of itself) will be even not odd, so $$x$$ cannot be odd. Now if $$x$$ is even and more than 2, then 2 (one of the factors of $$x$$) plus $$x$$ itself will be even not odd, so $$x$$ cannot be more than 2 --> $$x=2$$ (2 has exactly two positive factors (1 and 2) and their sum is odd). Sufficient.

Check similar problem: is-n-equal-to-94720.html#p733591

Hope it helps.

Hey Bunuel
Sorry I still don't understand B
if I choose x=14
then factors are {1,2,7,14} for which the sum of any two factors could be odd. Take 7+2=9 or 2+1=3 0r 14+1=15 -----> all these option qualify for (B) but x is not 2! where is the error?

(2) does not say that the sum could be odd it says that is IS odd: the sum of ANY TWO distinct positive factors of x is odd.

If we take x=14, then 2+14=16=even, so it's not true that the sum of ANY TWO distinct positive factors of x is odd.
_________________

Kudos [?]: 128826 [0], given: 12183

Current Student
Joined: 21 Oct 2013
Posts: 193

Kudos [?]: 44 [0], given: 19

Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: If the integer x is greater than 1, does x = 2? [#permalink]

### Show Tags

22 Jul 2014, 03:38
Short question here, from a non-native english-speaking guy:

"Evenly divisible" means x/y = even or x/y = integer?

Thanks!

Kudos [?]: 44 [0], given: 19

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128826 [0], given: 12183

Re: If the integer x is greater than 1, does x = 2? [#permalink]

### Show Tags

22 Jul 2014, 03:41
Expert's post
1
This post was
BOOKMARKED
unceldolan wrote:
Short question here, from a non-native english-speaking guy:

"Evenly divisible" means x/y = even or x/y = integer?

Thanks!

Evenly divisible means divisible without a remainder, so it means x/y = integer.
_________________

Kudos [?]: 128826 [0], given: 12183

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16678

Kudos [?]: 273 [0], given: 0

Re: If the integer x is greater than 1, does x = 2? [#permalink]

### Show Tags

11 Aug 2017, 21:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Re: If the integer x is greater than 1, does x = 2?   [#permalink] 11 Aug 2017, 21:31
Display posts from previous: Sort by