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# If x and y are positive integers and x^y = x^(2y – 3), what is the

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If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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01 May 2017, 12:02
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If x and y are positive integers and $$x^y = x^{(2y – 3)}$$, what is the value of $$x^y$$?

(1) $$x = 2$$

(2) $$x^3 = 8$$

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Re: If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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01 May 2017, 12:12
1. If x=2, we can say that 2^y = 2^{2y-3}. This is possible only if y=3. Hence sufficient.

2. X^3 = 8 or x=2
Hence sufficient.(Option D)

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If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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01 May 2017, 12:14
Bunuel wrote:
If x and y are positive integers and $$x^y = x^{(2y – 3)}$$, what is the value of $$x^y$$?

(1) $$x = 2$$

(2) $$x^3 = 8$$

$$x^y = x^{(2y – 3)}$$

$$y=2y-3$$

$$y=3$$

We need the value of x to find $$x^y$$

(1) $$x = 2$$

Sufficient.

(2) $$x^3 = 8$$

$$x=2$$

Sufficient.

D IMO.
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Re: If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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01 May 2017, 14:06
x^y = x^(2y – 3)
=>y=2y-3
=>y=3
option:1(x=2)
x^y=2^3=8
sufficient

option:2(x^3=8 or x^3=2^3 or x=2)
x^y=2^3=8
sufficient
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Re: If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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01 May 2017, 19:41
1. x=2. Sufficient, as we can solve for one answer for y, and hence can solve for x^y.
2. x^3=8. Sufficient, as x=+/- 2, though the stem tells us x>0, and as such we can solve for x^y in the same was as Statement 1.
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Re: If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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01 May 2017, 22:38
both the statements give the same info

x = 2...

stem says : x^y = x^(2y – 3)
implies ---- y=2y-3
y = 3

hence ans D
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Re: If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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20 May 2017, 08:45
Bunuel wrote:
If x and y are positive integers and $$x^y = x^{(2y – 3)}$$, what is the value of $$x^y$$?

(1) $$x = 2$$

(2) $$x^3 = 8$$

In order to solve this question we just need to know what X equals so we can set the equations , which are exponents, equal.

Statement 1 does just that- x= 2 so we can set the equations equal. Suff

Statement 2 does not give us X^1 in simplest form, but if we take the cube root of 8 then we can see that x is 2. Suff
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Re: If x and y are positive integers and x^y = x^(2y – 3), what is the  [#permalink]

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01 Dec 2019, 00:48
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Re: If x and y are positive integers and x^y = x^(2y – 3), what is the   [#permalink] 01 Dec 2019, 00:48
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