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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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23 Nov 2016, 06:53
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45% (medium)

Question Stats:

64% (01:36) correct 36% (01:54) wrong based on 197 sessions

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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)

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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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23 Nov 2016, 07:26
1
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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23 Nov 2016, 07:46
1
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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30 Oct 2017, 07:38
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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30 Oct 2017, 08:05
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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30 Oct 2017, 08:36
$$9q=243^r$$
$$3^2q$$=$$3^{5r}$$
$$q=\frac{3^{5r}}{3^2}$$
$$q=3^{5r-2}$$
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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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30 Oct 2017, 08:46
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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31 Oct 2017, 09:36
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.
Re: If r is an integer and 9q = 243^r, which of the following expresses q &nbs [#permalink] 31 Oct 2017, 09:36
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