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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Let n, k, and y be positive integers such that y > n. If k*2^n = 2^y +

Author Message
TAGS:

### Hide Tags

Math Expert V
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 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  V
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

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  V
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

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 $$= 2^9+1$$

Posted from my mobile device
Math Expert V
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

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 +  