GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2018, 14:07

### 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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 11 Feb 2011
Posts: 115
Given that both x and y are positive integers, and that y =  [#permalink]

### Show Tags

17 Jun 2011, 07:12
1
8
00:00

Difficulty:

95% (hard)

Question Stats:

51% (02:25) correct 49% (02:19) wrong based on 218 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

_________________

target:-810 out of 800!

Intern
Joined: 13 Feb 2014
Posts: 3
Re: Given that both x and y are positive integers and that  [#permalink]

### Show Tags

14 Feb 2014, 19:36
5
1
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
##### General Discussion
Current Student
Joined: 26 May 2005
Posts: 514

### Show Tags

18 Jun 2011, 03:38
2
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: 29 Mar 2011
Posts: 21

### Show Tags

30 Jun 2011, 10:28
[/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: 30 Mar 2017
Posts: 38
Location: United States (FL)
Re: Given that both x and y are positive integers, and that y =  [#permalink]

### Show Tags

15 Jun 2017, 03:27
For everyone picking numbers that let any expression get large, don't forget that 0 is a multiple of all 3 and 4 as well.

Instead of having to compute 3^5 - 6 to prove statement 1 to be insufficient, you can just compute 3^0 - 0 which gives you 1 which is not divisible by 6.
Senior Manager
Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
Re: Given that both x and y are positive integers, and that y =  [#permalink]

### Show Tags

17 Nov 2017, 12:05
$$y = 3^{x – 1} – x$$

$$3^{x – 1}$$ is odd, for $$y$$ to be divisible by 6, $$x$$ must be odd multiple of 3

question is reduced to x is odd multiple of 3?

Statement 1: $$x$$ is multiple of 3
Not suff, x may be odd or even multiple of 3

Statement 2: $$x$$ is multiple of 4
=> $$x$$ is even
=> $$y = 3^{x – 1} – x$$ => $$y = (odd - even) = odd$$
=> $$y$$ is odd definitely not divisible by 6
=> Sufficient

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
Re: Given that both x and y are positive integers, and that y =  [#permalink]

### Show Tags

17 Nov 2017, 23:27
laxpro2001 wrote:
For everyone picking numbers that let any expression get large, don't forget that 0 is a multiple of all 3 and 4 as well.

Instead of having to compute 3^5 - 6 to prove statement 1 to be insufficient, you can just compute 3^0 - 0 which gives you 1 which is not divisible by 6.

Hi

The method of substituting 0 is cool, and I can see that how it can help in many questions, by making them easy.
However, here in this question, we Cannot substitute x=0 as its given both x and y are positive integers.
Re: Given that both x and y are positive integers, and that y = &nbs [#permalink] 17 Nov 2017, 23:27
Display posts from previous: Sort by