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If r is an integer, what is the value of 3^(2r)/27^(r-1)

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If r is an integer, what is the value of 3^(2r)/27^(r-1)  [#permalink]

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If r is an integer, what is the value of \(\frac{3^{2r}}{27^{r-1}}\)?

(1) \(2^r=32\)

(2) \(r^2-4r=5\)
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Re: If r is an integer, what is the value of 3^(2r)/27^(r-1)  [#permalink]

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New post 26 Sep 2016, 22:03
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felippemed wrote:
If r is an integer, what is the value of \(\frac{3^{2r}}{27^{r-1}}\)?

(1) \(2^r=32\)

(2) \(r^2-4r=5\)


r is an integer.

(1) \(2^r=32\)
\(2^r = 2^5\)
\(r = 5\)
We have a single value for r so we can find a unique value of the given expression. Sufficient.

(2) \(r^2-4r=5\)
\(r^2 - 4r - 5 = 0\)
\((r - 5)(r + 1) = 0\)
r = 5 or -1
We have 2 possible values for r. So we will get two values for the expression. Not sufficient.
(Note here that ensure you take a look at the expression to KNOW that the two values will give different values for the expression.)

Answer (A)
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Re: If r is an integer, what is the value of 3^(2r)/27^(r-1)  [#permalink]

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New post 27 Sep 2016, 06:46
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Only Statement 1 gives one definite value for 'r'

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Re: If r is an integer, what is the value of 3^(2r)/27^(r-1)  [#permalink]

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Re: If r is an integer, what is the value of 3^(2r)/27^(r-1)   [#permalink] 08 Aug 2018, 19:57
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