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# If m is a positive integer, what is the value of 5^(3m)27^(m-5)?

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If m is a positive integer, what is the value of 5^(3m)27^(m-5)?  [#permalink]

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03 Aug 2019, 20:36
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55% (hard)

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61% (01:07) correct 39% (01:28) wrong based on 33 sessions

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If m is a positive integer, what is the value of $$(5^{3m})(27^{m-5})$$?

(1) $$2^m=32$$

(2) $$m^2-4m=5$$

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Re: If m is a positive integer, what is the value of 5^(3m)27^(m-5)?  [#permalink]

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03 Aug 2019, 21:34
Solution as attached.
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Re: If m is a positive integer, what is the value of 5^(3m)27^(m-5)?  [#permalink]

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03 Aug 2019, 21:55
(1) 2^m=32
m=5 ---> 5^(3m) * 27^(m−5) can be calculated.
SUFFICIENT

(2) m^2−4m=5
m=-1 or m=5. Since m is positive integer, eliminate m=-1.
m=5 ---> 5^(3m) * 27^(m−5) can be calculated.
SUFFICIENT

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Re: If m is a positive integer, what is the value of 5^(3m)27^(m-5)?  [#permalink]

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03 Aug 2019, 22:15
gmatbusters wrote:
If m is a positive integer, what is the value of $$(5^{3m})(27^{m-5})$$?

(1) $$2^m=32$$

(2) $$m^2-4m=5$$

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Given: m is a positive integer,
Asked: What is the value of $$(5^{3m})(27^{m-5})$$?

Quote:
(1) $$2^m=32$$

m=5
SUFFICIENT

Quote:
(2) $$m^2-4m=5$$

m=5 or m=-1
Since m is a positive integer
m=-1 is not allowed
m=5
SUFFICIENT

IMO D
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Re: If m is a positive integer, what is the value of 5^(3m)27^(m-5)?   [#permalink] 03 Aug 2019, 22:15
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