NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 13:21 It is currently 25 Apr 2024, 13:21
Decision Tracker
My Rewards
New posts
New comers' posts

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

If x and y are integers and x^y = 256, what is the number of the diffe

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619009 [8]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If x and y are integers and x^y = 256, what is the number of the diffe [#permalink] New post   15 Nov 2019, 01:25
8
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

29% (02:01) correct 71% (02:15) wrong based on 211 sessions
Hide Show timer Statistics
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
D
User avatar
L
CareerGeek
VP
VP
Joined: 20 Jul 2017
Posts: 1300
Own Kudos [?]: 3450 [4]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Send PM
Re: If x and y are integers and x^y = 256, what is the number of the diffe [#permalink] New post   15 Nov 2019, 01:43
1
Kudos
3
Bookmarks
Bunuel wrote:
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


\(x^y = 256 = 2^8, (-2)^8, 4^4, (-4)^4, 16^2, (-16)^2, 256^1\)
--> 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
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8019
Own Kudos [?]: 4097 [4]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: If x and y are integers and x^y = 256, what is the number of the diffe [#permalink] New post   15 Nov 2019, 03:56
2
Kudos
2
Bookmarks
Bunuel wrote:
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
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16841 [1]
Given Kudos: 165
Send PM
Re: If x and y are integers and x^y = 256, what is the number of the diffe [#permalink] New post   15 Nov 2019, 04:22
1
Kudos
Expert Reply

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
User avatar
D
gvij2017
Director
Director
Joined: 09 Aug 2017
Posts: 689
Own Kudos [?]: 415 [0]
Given Kudos: 778
Send PM
Re: If x and y are integers and x^y = 256, what is the number of the diffe [#permalink] New post   15 Nov 2019, 05:15
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 wrote:
Bunuel wrote:
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
User avatar
L
CareerGeek
VP
VP
Joined: 20 Jul 2017
Posts: 1300
Own Kudos [?]: 3450 [0]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Send PM
Re: If x and y are integers and x^y = 256, what is the number of the diffe [#permalink] New post   22 Nov 2019, 00:42
Archit3110 wrote:
Bunuel wrote:
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


Archit3110

How are factors and values of \(y^x\) same ?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32678
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If x and y are integers and x^y = 256, what is the number of the diffe [#permalink] New post   06 Nov 2021, 08:14
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 Bot
gmatclubot
Re: If x and y are integers and x^y = 256, what is the number of the diffe [#permalink]
06 Nov 2021, 08:14
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions