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

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Math Expert
Joined: 02 Sep 2009
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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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18 Jul 2018, 23:32
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Difficulty:

65% (hard)

Question Stats:

54% (01:59) correct 46% (02:23) wrong based on 60 sessions

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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

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Joined: 02 Aug 2009
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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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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

A
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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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19 Jul 2018, 00:29
1
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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