It is currently 11 Dec 2017, 19:59

### 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

# Can a sequence of different positive integers X_{1}, X_{2},

Author Message
Manager
Joined: 14 May 2009
Posts: 191

Kudos [?]: 51 [0], given: 1

Can a sequence of different positive integers X_{1}, X_{2}, [#permalink]

### Show Tags

17 Jun 2009, 22:07
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Can a sequence of different positive integers $$X_{1}, X_{2}, X_{3}, . . . , X_{n}$$ be ordered in such a way that the difference between any two consecutive integers is less than 2?

(1) Each term of the sequence has exactly 4 factors.

(2) $$X_{1}*X_{2}*X_{3}*...*X_{n-1}*X_{n}$$ is divisible by $$2^{n}$$
_________________

Kudos [?]: 51 [0], given: 1

SVP
Joined: 29 Aug 2007
Posts: 2470

Kudos [?]: 867 [0], given: 19

### Show Tags

17 Jun 2009, 23:04
Can a sequence of different positive integers $$X_{1}, X_{2}, X_{3}, . . . , X_{n}$$ be ordered in such a way that the difference between any two consecutive integers is less than 2?

(1) Each term of the sequence has exactly 4 factors.
(2) $$X_{1}*X_{2}*X_{3}*...*X_{n-1}*X_{n}$$ is divisible by $$2^{n}$$

In the highlighted part above, did you mean by any two successive integers ?
If you say any consqcutive integers, then it is obviously yes but neither statement is required and D. If you meant "any two successive integers", then it is A.

(1) is suff. If each term of the sequence has exactly 4 factors, then obviously the difference between any two succesive integers is not <2.
(2) is not suff. To have the difference of < 2 (i.e. 1) between two succesive integers, the integers have to be consecutive.
* If n is even, then the difference could be 2 or >2. If n = 2, and x1 = 2 and x2 = 6, x1+x2 = 8, which is divisible nby 2^n.
* If n is odd, then the difference could be <2. If n = 3, x1 = 7, x2 =8 and x3 = 9, then x1+x2+x3 = 24, which is divisible by 2^n. NSF.

It is A.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Kudos [?]: 867 [0], given: 19

VP
Joined: 05 Jul 2008
Posts: 1402

Kudos [?]: 449 [0], given: 1

### Show Tags

18 Jun 2009, 08:53
The consecutive word in the Q refers to numbers in the sequence, not in general

X_{1}*X_{2}*X_{3}*...*X_{n-1}*X_{n} is divisible by 2^{n}

If you take 6,7,8 it is divisible by 2^3

The way this Q is worded is confusing to me.

It asks can there be such a sequence whose successive terms have a difference less than 2. So Doesnt that mean if we can find one such sequence, we have sufficiency? Or Am I missing some thing basic here? If we have suff in 2 doesnt that contradict with A which yields no

Kudos [?]: 449 [0], given: 1

VP
Joined: 05 Jul 2008
Posts: 1402

Kudos [?]: 449 [0], given: 1

### Show Tags

18 Jun 2009, 19:52
Yes/No DS

Yeah! I guess I analyzed it too much

Kudos [?]: 449 [0], given: 1

Re: Tough DS 13   [#permalink] 18 Jun 2009, 19:52
Display posts from previous: Sort by