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If a and b are positive integers, what is the remainder when 74a+b is

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If a and b are positive integers, what is the remainder when 74a+b is  [#permalink]

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New post 24 Mar 2017, 05:40
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If a and b are positive integers, what is the remainder when \(7^{4a}+b\) is divided by 4?

1) a=2
2) b=3

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Re: If a and b are positive integers, what is the remainder when 74a+b is  [#permalink]

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New post 24 Mar 2017, 08:36
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ziyuen wrote:
If a and b are positive integers, what is the remainder when \(7^{4a}+b\) is divided by 4?

1) a=2
2) b=3


Hi

\(7^{4a} + b\)

\(7^2\) leaves remainder \(1\) when divided by \(4\) ------> \((7^2)^{2a} + b = 1^{2a} + b = 1 + b\)

To solve the question we need to know only the remainder that \(b\) leaves while divided by \(4\).

Answer B.
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Re: If a and b are positive integers, what is the remainder when 74a+b is  [#permalink]

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New post 24 Mar 2017, 10:07
To solve this question, have to remember the last digit of a power...for 7 the cyclicity is 7,9,3,1 -> since a is a positive integer, the 7^4a will always end with 1 and we know that a number is divisible by 4 when the last two digits are divisible by 4.

A) Irrelevant -> not sufficient
B) since we know b, we know the last digit of our number, therefore can find the remainder. Sufficient.
Re: If a and b are positive integers, what is the remainder when 74a+b is &nbs [#permalink] 24 Mar 2017, 10:07
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