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What is the remainder when 7^9 - 4 is divided by 7?
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12 Jul 2021, 05:46
12 Jul 2021, 05:46
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Question Stats:
66% (00:40) correct
33% (00:49) wrong based on 18 sessions
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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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Re: What is the remainder when 7^9 - 4 is divided by 7?
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12 Jul 2021, 08:37
12 Jul 2021, 08:37
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Carcass 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
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What is the remainder when 7^9 - 4 is divided by 7?
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20 Oct 2022, 09:07
20 Oct 2022, 09:07
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
\(7^9\) - 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
