It is currently 10 Sep 2026, 11:35
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Sep 2026
Posts: 113,408
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,408
If x and y are integers and x^y = 256, what is the number of the diffe
Post URL
15 Nov 2019, 00:25
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
Official Answer and Stats are available only to registered users. Register/Login.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

33% (02:10) correct 67% (02:16) wrong based on 321 sessions

History

Date
Time
Result
Not Attempted Yet
If x and y are integers and \(x^y = 256\), what is the number of the different values of \(y^x\)?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT Club?
Signature Read More
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
CareerGeek
User avatar
Joined: 20 Jul 2017
Last visit: 06 Sep 2026
Posts: 1,285
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,285
If x and y are integers and x^y = 256, what is the number of the diffe
Post URL
15 Nov 2019, 00:43
Bunuel
If x and y are integers and \(x^y = 256\), what is the number of the different values of \(y^x\)?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Are You Up For the Challenge: 700 Level Questions
Show more

\(x^y = 256 = 2^8, (-2)^8, 4^4, (-4)^4, 16^2, (-16)^2, 256^1\)
--> Possible values of (x, y) = {(2, 8), (-2,8), (4, 4), (-4, 4), (16, 2), (-16, 2), (256, 1)}
--> Number of different values of \(y^x = {8^2, 8^{-2}, 4^4, 4^{-4}, 2^{16}, 2^{-16}, 1^{256}}\) = 7 values

IMO Option D
1
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
General Discussion
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 10 Sep 2026
Posts: 8,815
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,815
If x and y are integers and x^y = 256, what is the number of the diffe
Post URL
15 Nov 2019, 02:56
Bunuel
If x and y are integers and \(x^y = 256\), what is the number of the different values of \(y^x\)?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Are You Up For the Challenge: 700 Level Questions
Show more
\(x^y = 256\)
x=2 and y = 8
so \(y^x\) = 8^2 ; 64
64 = 2^6 ; total factors = 7
IMO D
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,651
Expert
Expert reply
Posts: 3,651
If x and y are integers and x^y = 256, what is the number of the diffe
Post URL
15 Nov 2019, 03:22

Solution



Given
    • x^y=256

To find
    • Number of the different values of y^x

Approach and Working out

    • We know that 2^8 = 256
      o Hence, x= 2 and y =8
         y ^ x = 8^2 = 64

    • We know that -2^8 = 256
      o Hence, x= -2 and y =8
         y ^ x = 8^-2 = 1/64

    • 4^4 = 256
      o Hence, x= 4 and y =4
         y ^ x = 4^4 = 256

    • -4^4 = 256
      o Hence, x= -4 and y =4
         y ^ x = 4^-4 = 1/256

    • 16^2 = 256
      o Hence, x= 16 and y =2
         y ^ x = 2^16


    • -16^2 = 256
      o Hence, x= -16 and y =2
         y ^ x = 1/2^16

    • 256^1 = 256
      o Hence, x= 256 and y =1
         y ^ x = 1^256 = 1

So, total 7 values are possible.

Thus, option D is the correct answer.
Correct Answer: Option D

_________________
Free Trial: Get 25 AI powered videos | 400 practice questions | 8 free webinars

Case studies: How a personalized study plan can save you 60+ hours

MBA admits: M7 admits | INSEAD admits | ISB admits [40+ case studies]


Learn why e-GMAT has 10X more 700+ verified scores than other GMATClub partners – Read our 2000+ reviews
Signature Read More
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
gvij2017
User avatar
Joined: 08 Aug 2017
Last visit: 18 Jun 2024
Posts: 662
Posts: 662
If x and y are integers and x^y = 256, what is the number of the diffe
Post URL
15 Nov 2019, 04:15
I doubt that explanation is correct though your answer choice is fortunately correct.

For example.
2 is one of the factor of 64, but 2 is not the value of y^x in any case.

Archit3110
Bunuel
If x and y are integers and \(x^y = 256\), what is the number of the different values of \(y^x\)?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Are You Up For the Challenge: 700 Level Questions
\(x^y = 256\)
x=2 and y = 8
so \(y^x\) = 8^2 ; 64
64 = 2^6 ; total factors = 7
IMO D
Show more
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
CareerGeek
User avatar
Joined: 20 Jul 2017
Last visit: 06 Sep 2026
Posts: 1,285
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,285
If x and y are integers and x^y = 256, what is the number of the diffe
Post URL
21 Nov 2019, 23:42
Archit3110
Bunuel
If x and y are integers and \(x^y = 256\), what is the number of the different values of \(y^x\)?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Are You Up For the Challenge: 700 Level Questions
\(x^y = 256\)
x=2 and y = 8
so \(y^x\) = 8^2 ; 64
64 = 2^6 ; total factors = 7
IMO D
Show more

Archit3110

How are factors and values of \(y^x\) same ?
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,213
Posts: 39,213
If x and y are integers and x^y = 256, what is the number of the diffe
Post URL
17 Nov 2025, 03:44
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

_________________

If this question felt shaky, try an adaptive mini quiz of similar problems in GMAT Club Forum Quiz →. Free plan gives 5 questions per day.

Signature Read More
Kudos
Add Kudos
Bookmarks
Bookmark this Post
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
113408 posts