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# If m is a positive integer and q+4=7^m , which of the following could

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If m is a positive integer and q+4=7^m , which of the following could  [#permalink]

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29 Nov 2019, 05:28
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If m is a positive integer and $$q+4=7^m$$ , which of the following could NOT be a value of q ?

A) 3

B) 45

C) 54

D) 339

E) 2397

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Joined: 19 Oct 2018
Posts: 1174
Location: India
Re: If m is a positive integer and q+4=7^m , which of the following could  [#permalink]

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29 Nov 2019, 07:16
7^m= 0 mod 7

q=(7-4) mod 7= 3 mod 7

q must leave 3 remainder when divided by 7

54= 5 mod 7

C

MahmoudFawzy wrote:
If m is a positive integer and $$q+4=7^m$$ , which of the following could NOT be a value of q ?

A) 3

B) 45

C) 54

D) 339

E) 2397

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Joined: 17 Sep 2014
Posts: 290
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Re: If m is a positive integer and q+4=7^m , which of the following could  [#permalink]

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29 Nov 2019, 12:01
MahmoudFawzy wrote:
If m is a positive integer and $$q+4=7^m$$ , which of the following could NOT be a value of q ?

A) 3

B) 45

C) 54

D) 339

E) 2397

q + 4 must be a power of 7. Powers grow very fast so the four correct choices of q will also grow very fast. The numbers that should strike out are B and C since they are too close. One of them will make q + 4 a power of 7 and the other choice won't. Plugging in B gives q + 4 = 49, so the incorrect choice must be C.

Ans: C
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Re: If m is a positive integer and q+4=7^m , which of the following could   [#permalink] 29 Nov 2019, 12:01
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