xALIx wrote:

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

1) When x is divided by 2y, the remainder is 4

2) When x + y is divided by y, the remainder is 4

Pls explain your answer

Responding to a pm:

Before I analyze this question for you, you must understand the method I use for divisibility (making groups). If you haven't come across this method, check out this post:

http://www.veritasprep.com/blog/2011/04 ... unraveled/Statement 1 alone is not sufficient. Here is the reason:

1) When x is divided by 2y, the remainder is 4

This means that when you split x balls into groups of 2y balls each, you are left with 4 balls out of which you cannot make any more groups. (So 2y must be greater than 4 and y must be greater than 2)

What if instead, you had to split those balls into groups of y balls each. You made groups of 2y balls each above. Now you can easily split each oen of those groups into two groups of y balls each. But what about the 4 leftover balls? Can you make another group of x balls out of it? Depends on the value of x. Say if x is 3, you can make another group and the remainder will be 1. If x is 5, you cannot make another group and remainder will still be 4. Hence this statement is not sufficient to say what the remainder is when x is divided by 2y.

Statement 2 alone is sufficient.

2) When x + y is divided by y, the remainder is 4

You have x+y balls and you have to make groups out of them containing y balls each. The y balls make one group and the x balls make more groups with 4 balls remaining. Hence when you make groups of y balls each out of x balls, you get a remainder of 4. This means that when you divide x by y, you get remainder 4.

Answer (B)

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