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

[BTGModeratorVI]

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

Answer: B
Source: Official guide

[Jay@ManhattanReview]

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

Answer: B
Source: Official guide

Let's take each statement one by one.

(1) x = 5

With x = 5, we have 10^x + y = 10^5 + y = 100,000 + y. The remainder when 10^x + y is divided by y will depend on the value of y. Insufficient.

(2) y = 2

Since whatever be the value of x, 10^x must be a positive number with its units digit equal to 0. When y = 2, and an even no. is added to it, 10^x + y would be an even no.

So, even no. divided by 2 will render the remainder equal to 0. Sufficient.

Correct answer: B

Hope this helps!

-Jay
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