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x and y are positive integers. When x is divided by 2y, the remainder is y. What is the value of y?

(1) x is even

(2) y is a prime number

*kudos for all correct solutions

Target question: What is the value of y? Given: x and y are positive integers. When x is divided by 2y, the remainder is y --------ASIDE------------------------------------

When it comes to remainders, we have a nice rule that says:

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

---------------BACK TO THE QUESTION------------

From the given information, we can say that the possible values of x are: y, y + 2y, y + 4y, 6 + 6y, . . . etc.

In other words,

the possible values of x are: y, 3y, 5y, 7y, . . . etc. Statement 1: x is even We already know that

the possible values of x are: y, 3y, 5y, 7y, . . . etc All of these possible x-values are in the form x = (ODD)(y)

So, if x is EVEN, it must be the case that

y is EVENThere are several values of x and y that satisfy statement 1. Here are two:

Case a: x = 12 and y = 4. In this case, the answer to the target question is

y = 4Case b: x = 6 and y = 2. In this case, the answer to the target question is

y = 2Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is a prime number We already know that

the possible values of x are: y, 3y, 5y, 7y, . . . etc So, there are several values of x and y that satisfy statement 2. Here are two:

Case a: x = 2 and y = 2. In this case, the answer to the target question is

y = 2Case b: x = 3 and y = 3. In this case, the answer to the target question is

y = 3Since we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 told us that

y is EVENStatement 2 told us that y is a prime number

Since 2 is the ONLY even prime number, the answer to the target question is

y = 2Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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