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

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Joined: 23 Jun 2009
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If r is an integer, what is the value of 3^(2r)/27^(r-1)  [#permalink]

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26 Sep 2016, 18:13
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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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26 Sep 2016, 21:03
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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.)

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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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27 Sep 2016, 05:46
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Only Statement 1 gives one definite value for 'r'

HEnce 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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08 Aug 2018, 18:57
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Re: If r is an integer, what is the value of 3^(2r)/27^(r-1) &nbs [#permalink] 08 Aug 2018, 18:57
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