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

 It is currently 09 Dec 2019, 18:43

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59622
If x and y are integers and x^y = 256, what is the number of the diffe  [#permalink]

### Show Tags

15 Nov 2019, 01:25
00:00

Difficulty:

85% (hard)

Question Stats:

30% (01:51) correct 70% (02:05) wrong based on 57 sessions

### HideShow 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

_________________
VP
Joined: 20 Jul 2017
Posts: 1143
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If x and y are integers and x^y = 256, what is the number of the diffe  [#permalink]

### Show Tags

15 Nov 2019, 01:43
1
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
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5466
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If x and y are integers and x^y = 256, what is the number of the diffe  [#permalink]

### Show Tags

15 Nov 2019, 03:56
2
2
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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: If x and y are integers and x^y = 256, what is the number of the diffe  [#permalink]

### Show Tags

15 Nov 2019, 04:22
1

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.
_________________
Director
Joined: 09 Aug 2017
Posts: 623
Re: If x and y are integers and x^y = 256, what is the number of the diffe  [#permalink]

### Show Tags

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
VP
Joined: 20 Jul 2017
Posts: 1143
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If x and y are integers and x^y = 256, what is the number of the diffe  [#permalink]

### Show Tags

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 ?
Re: If x and y are integers and x^y = 256, what is the number of the diffe   [#permalink] 22 Nov 2019, 00:42
Display posts from previous: Sort by