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What is the value of x if x is the remainder obtained when 2^(8p + 2)

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What is the value of x if x is the remainder obtained when 2^(8p + 2)  [#permalink]

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New post 18 Jul 2018, 23:32
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Re: What is the value of x if x is the remainder obtained when 2^(8p + 2)  [#permalink]

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New post 19 Jul 2018, 00:16
What is the value of x if x is the remainder obtained when \(2^{8p+2} + Z\) is divided by 5 and p is a positive integer?
Due to cyclicity the units digit of \(2^{8p+2}\) will be SAME as \(2^2\)
So the units digit will be 2^2+z=4+z
since we are looking for divisiblity by 5, which requires 5, or 0 as units digit to divide a number, we can get the remainder by knowing units digit of the term
hence we require only z

(1) Z = 6
z =6, so units digit = 4+6=10
remainder is 0
suff

(2) Z is even
nothing much
insuff

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Re: What is the value of x if x is the remainder obtained when 2^(8p + 2)  [#permalink]

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New post 19 Jul 2018, 00:29
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Bunuel wrote:
What is the value of x if x is the remainder obtained when \(2^{8p+2} + Z\) is divided by 5 and p is a positive integer?

(1) Z = 6
(2) Z is even



2^{8p+2} + Z
Given:
P>0
Substitute p in the equation. For all the values of p we get cyclicity of 2 as 4m+2, which will give us a unit digit of 4

Statement 1:
Z=6
unit digit of 2^{8p+2} is 4+6 gives 10 which is divisible by 5. Hence remainder 0
Sufficient

Statement 2:
Z is even
We get a different remainder for different values of Z. Hence insufficient
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Re: What is the value of x if x is the remainder obtained when 2^(8p + 2)   [#permalink] 19 Jul 2018, 00:29
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