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Senior Manager  S
Status: No dream is too large, no dreamer is too small
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If x and y are positive intergers, what is the remainder  [#permalink]

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Question Stats: 74% (00:58) correct 26% (00:58) wrong based on 308 sessions

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If x and y are positive intergers, what is the remainder when 10^x+y is divided by y?

(1) x=5
(2) y=2

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Joined: 02 Sep 2009
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Baten80 wrote:
If x and y are positive intergers, what is the remainder when 10^x+y is divided by y?

(1) x=5
(2) y=2

$$\frac{10^x+y}{y}=\frac{10^x}{y}+1$$ --> so we basically need the remainder upon division 10^x by y (as in 10^x+y the second term y is divisible by y itself then only the first term matters for remainder).

(1) x=5 --> need the value of y. Not sufficient.
(2) y=2 --> as x is a positive integer then 10^x is an even number and 10^x=even divided by 2 yields the remainder of zero. Sufficient.

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Re: If x and y are positive intergers, what is the remainder  [#permalink]

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REM[10^(x+y)]/y

(1) x=5

REM[10^(5+y)]/y no information about y so REM is not consistent hence INSUFFICIENT.

(2) y=2

REM[10^(x+2)]/2

Any power of 10 is even => Divisible by 2 => REM =0

Hence SUFFICIENT

Hence (B) !
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Re: If x and y are positive intergers, what is the remainder  [#permalink]

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Top Contributor
Baten80 wrote:
If x and y are positive integers, what is the remainder when $$10^x + y$$ is divided by y?

(1) x = 5
(2) y = 2

Given: x and y are positive integers

Target question: What is the remainder when $$10^x + y$$ is divided by y?

Statement 1: x = 5
Since we have no information about y, we cannot answer the target question with certainty
Statement 1 is NOT SUFFICIENT

Statement 2: y = 2
Important: When we divide an integer by 2, the remainder will be EITHER 1 OR 0, depending on whether the integer is odd or even.
If the number is ODD, then we get a remainder of 1 after dividing by 2
If the number is EVEN, then we get a remainder of 0 after dividing by 2

Now that we know the value of y, our target question becomes, "What is the remainder when $$10^x + 2$$ is divided by 2?"
Since $$10^x$$ is EVEN for all positive integer values of x, we know that $$10^x + 2$$ must be EVEN

So, our target question becomes, "What is the remainder when SOME EVEN NUMBER is divided by 2?"
The answer to this new target question is the remainder will be 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

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_________________ Re: If x and y are positive intergers, what is the remainder   [#permalink] 12 Mar 2020, 07:00

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