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What is the remainder when 7^9 - 4 is divided by 7?

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amathews
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What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  14 Apr 2017, 04:32
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What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5
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BrentGMATPrepNow
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What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  Updated on: 12 Jul 2021, 09:37
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amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5


KEY STRATEGY: If we take 7^9 - 4 and add zero to it, the value doesn't change.

We're going to add zero by subtracting 3 and adding 3 at the same time.
So, 7^9 - 4 = 7^9 - 4 - 3 + 3
= 7^9 - 7 + 3
= 7(7^8 - 1) + 3
= 7(some integer) + 3

As we can see, our initial number can be rewritten as 3 more than some multiple of 7.
So, if we divide that number by 7, the remainder will be 3

Answer: C

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Originally posted by BrentGMATPrepNow on 14 Apr 2017, 06:27.
Last edited by BrentGMATPrepNow on 12 Jul 2021, 09:37, edited 1 time in total.
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Bunuel
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  14 Apr 2017, 04:36
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amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5


7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  14 Apr 2017, 07:00
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amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5


\(\frac{7^9 - 4}{7}\)

\(= Rem ( 0 - 4 )\)

So, We have remainder -4

Thus, the value of the remainder will be \(7 - 4 = 3\)

Answer, must be (C) 3
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  22 Aug 2020, 09:56
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Can anyone please explain it again in simple terms. I am still not able to understand it. May be i am missing something here.
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  14 Apr 2017, 08:29
Bunuel wrote:
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5


7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.
Hello Bunnel.
When it is 7^8 -4 then what would be remainder. Thanks in advance.
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Bunuel
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  14 Apr 2017, 08:35
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Chemerical71 wrote:
Bunuel wrote:
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?

A)1
B)2
C)3
D)4
E)5


7^9 - 4 = {a multiple of 7} - 4, so it's 4 less than a multiple of 7 (3, 10, 17, ...), so the remainder is 3.

Answer: C.
Hello Bunnel.
When it is 7^8 -4 then what would be remainder. Thanks in advance.


It seems that you did not understand the explanation. The remainder of 7^n - 4 divided by 7 where n is a positive integer is always 3.
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  15 Aug 2020, 09:45
Asked: What is the remainder when 7^9 - 4 is divided by 7?

(7^9-4)mod7 = -4mod7 = 3mod7

IMO C
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Re: What is the remainder when 7^9 - 4 is divided by 7? [#permalink] New post  20 Oct 2022, 10:10
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We need to find What is the remainder when \(7^9\) - 4 is divided by 7

\(7^9\) - 4 = \(7^9\) - 4 - 3 + 3 = \(7^9\) - 7 + 3 = 7*(\(7^8\) - 1) + 3 = (Multiple of 7) + 3

Theory: Remainder of a + b by a number say 7 is same as remainder of a by 7 + remainder of b by 7

=> Remainder of 7*(\(7^8\) - 1) + 3 by 7 is same as remainder of 7*(\(7^8\) - 1) by 7 + remainder of 3 by 7

=> 0 + 3 = 3

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Remainders


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