Given that both x and y are positive integers, and that y = : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 21:46

### 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

# Given that both x and y are positive integers, and that y =

Author Message
TAGS:

### Hide Tags

Manager
Joined: 11 Feb 2011
Posts: 134
Followers: 3

Kudos [?]: 181 [1] , given: 21

Given that both x and y are positive integers, and that y = [#permalink]

### Show Tags

17 Jun 2011, 06:12
1
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:39) correct 58% (01:28) wrong based on 147 sessions

### HideShow timer Statistics

Given that both x and y are positive integers, and that y = 3^(x – 1) – x, is y divisible by 6?

(1) x is a multiple of 3

(2) x is a multiple of 4
[Reveal] Spoiler: OA

_________________

target:-810 out of 800!

Current Student
Joined: 26 May 2005
Posts: 565
Followers: 18

Kudos [?]: 203 [2] , given: 13

### Show Tags

18 Jun 2011, 02:38
2
KUDOS
AnkitK wrote:
Given that both x and y are positive integers and that y=3^(x-1)-x ,is y divisible by 6?
a.x is a multiple of 3
b.x is a multiple of 4

st 1: X can be 3 3^(3-1) - 3 = 9-3 = 6 yes divisible by 6
X can be 6 3^5 - 6 = 243-6 237 not divisble by 6

Hence not sufficient

St 2. X = 4 3^3 - 4= 23/6 = Not divisible by 6
X=8 3^7 - 8 = 2179/6 = not divisble by 6

hence sufficient
Its B
Intern
Joined: 28 Mar 2011
Posts: 25
Followers: 0

Kudos [?]: 11 [0], given: 7

### Show Tags

30 Jun 2011, 09:28
[/quote]

st 1: X can be 3 3^(3-1) - 3 = 9-3 = 6 yes divisible by 6
X can be 6 3^5 - 6 = 243-6 237 not divisble by 6

Hence not sufficient

St 2. X = 4 3^3 - 4= 23/6 = Not divisible by 6
X=8 3^7 - 8 = 2179/6 = not divisble by 6

hence sufficient
Its B[/quote]

Finding the factorial of 3^7, with all the additional simplification ..... will it be possible within 2 mins ?

Regards,
Mustu
Intern
Joined: 13 Feb 2014
Posts: 3
Followers: 0

Kudos [?]: 6 [2] , given: 0

Re: Given that both x and y are positive integers and that [#permalink]

### Show Tags

14 Feb 2014, 18:36
2
KUDOS
1
This post was
BOOKMARKED
A much easier approach:

In order for the expression to be divisible by 6 it must satisfy that it is divisible by 2 and 3.

Another way to view divisibility by 2 is Even/Odd, so the expression must be even to be divisible by 6.

S1. Since 3 to any power will always be odd, the other part of the expression (+X) must be odd for the expression to be even, and possibly divisible by 6. Since X is a multiple of 3 is the constraint, this is satisfied by both even and odd numbers, making the expression even or odd, depending on the value. It will be divisible by 6 when X is odd, given that (3^?) would be a multiple of 3 and so would be (+X) and it will be even.

Not sufficient.

S2. From the conclusion above, and since now we are told that (+X) is a multiple of 4, we now know that (+X) will ALWAYS be even, making the expression never divisible by 2 and by extension, never divisible by 6.

Sufficient
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13441
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: Given that both x and y are positive integers, and that y = [#permalink]

### Show Tags

07 Oct 2015, 07:56
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13441
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: Given that both x and y are positive integers, and that y = [#permalink]

### Show Tags

19 Oct 2016, 10:21
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.
_________________
Re: Given that both x and y are positive integers, and that y =   [#permalink] 19 Oct 2016, 10:21
Similar topics Replies Last post
Similar
Topics:
If x and y are both positive integers, x is a multiple of 3 and y is a 2 15 Sep 2015, 17:36
2 Are x and y both positive? 2 19 May 2015, 00:51
16 Given x and y are positive integers such that y is odd, is x divisible 11 10 Apr 2015, 03:48
11 Are both x and y positive? 16 09 Oct 2013, 22:36
8 If both x and y are positive integers that are divisible by 16 26 Aug 2011, 01:16
Display posts from previous: Sort by