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

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

Source: Ready4Gmat
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C
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nick1816
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Re: If m is a positive integer and q+4=7^m , which of the following could [#permalink] New post   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

Source: Ready4Gmat
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Re: If m is a positive integer and q+4=7^m , which of the following could [#permalink] New post   29 Nov 2019, 12:01
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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

Source: Ready4Gmat


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] New post   16 Dec 2019, 14:12
What worked for me was simply:

q + 4 = \(7^{m}\)

So for:
\(7^{1}\) = 7
\(7^{2}\) = 49
\(7^{3}\) = ..3
\(7^{4}\) = ..1
\(7^{5}\) = ..7
\(7^{6}\) = ..9

and so on.

Substracting 4 leaves me with either (..3, ..5, ..9, ..7). So C is the answer.
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Re: If m is a positive integer and q+4=7^m , which of the following could [#permalink] New post   16 Dec 2019, 23:35
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

Source: Ready4Gmat


7^m is odd
q = 7^m - 4
odd - even has to be odd

q must be odd not even

C is correct
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Re: If m is a positive integer and q+4=7^m , which of the following could [#permalink]
16 Dec 2019, 23:35
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