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

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

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15 Nov 2019, 01:25
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85% (hard)

Question Stats:

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

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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

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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]

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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
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Re: If x and y are integers and x^y = 256, what is the number of the diffe  [#permalink]

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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
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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]

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

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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]

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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
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