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What is the remainder when 7^9 - 4 is divided by 7?
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14 Apr 2017, 04:32
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
A)1
B)2
C)3
D)4
E)5
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What is the remainder when 7^9 - 4 is divided by 7?
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Updated on: 12 Jul 2021, 09:37
Updated on: 12 Jul 2021, 09:37
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Top Contributor
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?
A)1
B)2
C)3
D)4
E)5
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
RELATED VIDEO
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.
Last edited by BrentGMATPrepNow on 12 Jul 2021, 09:37, edited 1 time in total.
Re: What is the remainder when 7^9 - 4 is divided by 7?
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14 Apr 2017, 04:36
14 Apr 2017, 04:36
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Expert Reply
amathews wrote:
What is the remainder when 7^9 - 4 is divided by 7?
A)1
B)2
C)3
D)4
E)5
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.
