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# If x and y are positive integers and r is the remainder when (7^(4x+3)

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Math Expert
Joined: 02 Sep 2009
Posts: 49993
If x and y are positive integers and r is the remainder when (7^(4x+3)  [#permalink]

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01 Oct 2018, 04:47
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Difficulty:

55% (hard)

Question Stats:

55% (00:57) correct 45% (01:45) wrong based on 22 sessions

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If x and y are positive integers and r is the remainder when $$(7^{4x+3} + y)$$ is divided by 10, what is the value of r ?

(1) x = 10
(2) y = 2

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Re: If x and y are positive integers and r is the remainder when (7^(4x+3)  [#permalink]

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01 Oct 2018, 04:53
Bunuel wrote:
If x and y are positive integers and r is the remainder when $$(7^{4x+3} + y)$$ is divided by 10, what is the value of r ?

(1) x = 10
(2) y = 2

Question: What is the remainder when $$(7^{4x+3} + y)$$ is divided by 10

CONCEPT: When a number is divided by 10 then the remainder will always be the unit digit of the number e.g. 37 divided by 10 leaves remainder 7 and 125 divided by 10 leaves remainder 5

i.e. we need to calculate the unit digit of $$(7^{4x+3} + y)$$

but Unit digit of $$(7^{4x+3})$$ is always same as unit digit of $$7^3$$ because cyclicity of unit digit of 7 is 4 i.e. Unit digit of powers of 7 repeat after every 4 powers

Hence we only need to know the Unit digit of y to answer the question

Statement 1: x = 10

NOT SUFFICIENT

Statement 2: y = 2

SUFFICIENT

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Re: If x and y are positive integers and r is the remainder when (7^(4x+3) &nbs [#permalink] 01 Oct 2018, 04:53
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# If x and y are positive integers and r is the remainder when (7^(4x+3)

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