GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 Mar 2020, 08:29

### 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

# Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62291
Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +  [#permalink]

### Show Tags

27 Nov 2019, 01:18
00:00

Difficulty:

45% (medium)

Question Stats:

75% (01:54) correct 25% (01:53) wrong based on 72 sessions

### HideShow timer Statistics

Let n, k, and y be positive integers such that $$y > n$$. If $$k*2^n = 2^y + 2^n$$, then k could equal all of the following except:

A. 33
B. 65
C. 123
D. 257
E. 513

Are You Up For the Challenge: 700 Level Questions

_________________
VP
Joined: 20 Jul 2017
Posts: 1460
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +  [#permalink]

### Show Tags

27 Nov 2019, 03:02
Bunuel wrote:
Let n, k, and y be positive integers such that $$y > n$$. If $$k*2^n = 2^y + 2^n$$, then k could equal all of the following except:

A. 33
B. 65
C. 123
D. 257
E. 513

$$k*2^n = 2^y + 2^n$$
--> $$k*2^n = 2^n(1 + 2^{y - n})$$
--> $$k = 1 + 2^{y - n}$$
So, possible value of k is 1 more than any positive power of 2 (Since $$y > n$$)

A. 33 --> $$1 + 2^5$$ --> Possible
B. 65 --> $$1 + 2^6$$ --> Possible
C. 123 --> $$-5 + 2^7$$ --> Not Possible
D. 257 --> $$1 + 2^8$$ --> Possible
E. 513 --> $$1 + 2^9$$ --> Possible

IMO Option C
Director
Joined: 30 Sep 2017
Posts: 800
GMAT 1: 720 Q49 V40
GPA: 3.8
Re: Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +  [#permalink]

### Show Tags

27 Nov 2019, 07:00
Dividing both sides of $$k*2^n = 2^y + 2^n$$ with $$2^n$$, one obtains

$$k = 1 + 2^{y-n}$$, where $$k, n, y, (y-n)$$ are positive integers

A. 33 $$= 2^5+1$$
B. 65 $$= 2^6+1$$
C. 123 $$\neq{2^7+1}$$ (k cannot be 123. This is the answer)
D. 257 $$= 2^8+1$$
E. 513 $$= 2^9+1$$

Final answer is (C)

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 8298
Re: Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +  [#permalink]

### Show Tags

27 Nov 2019, 07:41
Bunuel wrote:
Let n, k, and y be positive integers such that $$y > n$$. If $$k*2^n = 2^y + 2^n$$, then k could equal all of the following except:

A. 33
B. 65
C. 123
D. 257
E. 513

Are You Up For the Challenge: 700 Level Questions

$$k*2^n = 2^y + 2^n.....k*2^n-2^n=2^y.....2^n(k-1)=2^y$$
This will be possible only when k-1 is in the form $$2^x$$, so k should be 1 LESS than some power of 2..
A. 33...$$2^5-1$$
B. 65..$$.2^6-1$$
C. 123...$$2^7-5$$..This is NOT in the form $$2^x-1$$
D. 257....$$2^8-1$$
E. 513...$$2^9-1$$

C
_________________
Re: Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +   [#permalink] 27 Nov 2019, 07:41
Display posts from previous: Sort by

# Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne