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# If x and y are positive integers, what is the remainder when

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If x and y are positive integers, what is the remainder when [#permalink]  19 Mar 2012, 23:40
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If x and y are positive integers, what is the remainder when $$10^x +y$$ is divided by 3?

(1) x = 5
(2) y = 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jun 2014, 01:14, edited 1 time in total.
Edited the question
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Re: If x and y are positive integers, what is the remainder when [#permalink]  19 Mar 2012, 23:51
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Expert's post
If x and y are positive integers, what is the remainder when 10^x +y is divided by 3?

Since, the sum of the digits of 10^x is always 1 then the remainders when 10^x+y is divided by 3 is only dependant on the value of the number added to 10^x, so on y. If y is a multiple of 3 then 10^x+y will yield the remainder of 1 (since the sum of the digits of 10^x+y will be one more than a multiple of 3), if y is one more than a multiple of 3 then 10^x+y will yield the remainder of 2 and finally if y is two more than a multiple of 3 then 10^x+y will yield the remainder of 0,

(1) x=5. Not sufficient.
(2) y=2. Sufficient.

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Re: If x and y are positive integers, what is the remainder when [#permalink]  09 May 2012, 13:07
So the question should be ((10^x)+y)/3?

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Re: If x and y are positive integers, what is the remainder when [#permalink]  09 May 2012, 13:57
Expert's post
nmartelo wrote:
So the question should be ((10^x)+y)/3?

Posted from GMAT ToolKit

Yes, it's: $$\frac{10^x+y}{3}$$.
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Re: If x and y are positive integers, what is the remainder when [#permalink]  05 Sep 2012, 02:17
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The OG explanations sometimes really baffle me; I reached the solution simply by realizing that it did not matter what power the 10 was to be elevated to, and to know the value of y was sufficient; just like Bunuel explained above. The OG explanation should not be the primary route, in my opinion.
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Re: If x and y are positive integers, what is the remainder when [#permalink]  20 Jun 2014, 01:03
The question is not really understandable. Please post it either in the "formula form" or like this (10^x)+y.
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Re: If x and y are positive integers, what is the remainder when [#permalink]  20 Jun 2014, 01:14
Expert's post
unceldolan wrote:
The question is not really understandable. Please post it either in the "formula form" or like this (10^x)+y.

10^x +y means $$10^x +y$$, so no ambiguity there. If it were 10^(x +y) it would be written that way. Still edited the original post to avoid further confusions.
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Re: If x and y are positive integers, what is the remainder when   [#permalink] 20 Jun 2014, 01:14
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