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If r is an integer and 9q = 243^r, which of the following expresses q

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If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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If r is an integer and 9q = 243^r, which of the following expresses q in terms of r?

A. q=27^r
B. q=81^(r−9)
C. q=3^(r−3)
D. q=3^(5(r−2))
E. q=3^(5r−2)
[Reveal] Spoiler: OA

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Re: If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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New post 23 Nov 2016, 06:26
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Bunuel wrote:
If r is an integer and 9q = 243^r, which of the following expresses q in terms of r?

A. q=27^r
B. q=81^(r−9)
C. q=3^(r−3)
D. q=3^(5(r−2))
E. q=3^(5r−2)


IMO E
9q= 243^r can be simplified as q= (3^5r)/3^2
q=3^(5r-2)

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Re: If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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New post 23 Nov 2016, 06:46
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I say E as well. I plugged in numbers (q=27, r=1) and then looked at which answer choice yields q.

(E) q=3^(5r−2)

27=3^3

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Re: If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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New post 30 Oct 2017, 06:38
div10 wrote:
If r is an integer and 9q = 243^r, which of the following expresses q in terms of r?

A. q=27^r
B. q=81^(r−9)
C. q=3^(r−3)
D. q=3^(5(r−2))
E. q=3^(5r−2)



hi..

\(9q = 243^r.... 3^2*q=(3^5)^r...........q=\frac{3^{5r}}{3^2}=3^{5r-2}\)
E
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Re: If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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New post 30 Oct 2017, 07:05
div10 wrote:
If r is an integer and 9q = 243^r, which of the following expresses q in terms of r?

A. q=27^r
B. q=81^(r−9)
C. q=3^(r−3)
D. q=3^(5(r−2))
E. q=3^(5r−2)

9q = 243^r

Or, \(3^2q = 3^{5r}\)

So, \(q = 3^{5r-2}\)

Thus, answer will be (E) \(q=3^(5r−2)\)
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Re: If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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New post 30 Oct 2017, 07:36
\(9q=243^r\)
\(3^2q\)=\(3^{5r}\)
\(q=\frac{3^{5r}}{3^2}\)
\(q=3^{5r-2}\)
Answer E.
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Re: If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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New post 30 Oct 2017, 07:46
9q = 243^r
=> q = 243^r/9 = 3^5r/3^2 = 3^(5r-2)

Ans: E.

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Re: If r is an integer and 9q = 243^r, which of the following expresses q [#permalink]

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New post 31 Oct 2017, 08:36
gracie90 wrote:
I say E as well. I plugged in numbers (q=27, r=1) and then looked at which answer choice yields q.

(E) q=3^(5r−2)

27=3^3



I went with this first. But picking those numbers also allows for A to be correct which it is in fact not.

If testing numbers, be careful to test all the choices guys! If you get a duplicate, switch the numbers up.

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Re: If r is an integer and 9q = 243^r, which of the following expresses q   [#permalink] 31 Oct 2017, 08:36
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