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From statement 1 x is even. Insufficient. You don't know anything about y.

From statement 2 y is a factor of x, you don't know anything about x if x=5 then y=0, 1 or 5 x/y=0, 5 or 1 if x=6 then y=0, 1, 2, 3, 6 x/y= 0, 6, 3, 2 or 1 Insufficient

Combining, x= even and y is a factor of x x=6 then y can be 0, 1, 2, 3, 6 x/y can be 0 or even or odd Insufficient

Nice Question Here we need to get whether x/y is even or not. Statement 1 using test cases 4/2=> yes its even 2/2 => no its not even

Statement 2 It just says that x/y = integer. eg=> 4/2= Yes its even 2/2 => no its not even Combining the two statements again 4/2 => yes its even 2/2 => no its not even

Statement 1: x is even Since there's no information about y, this statement is NOT SUFFICIENT However, to be 100% certain, some students may choose to TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 6 and y = 1, in which case x/y = 6/1 = 6. So, x/y is EVEN Case b: x = 6 and y = 2, in which case x/y = 6/2 = 3. So, x/y is NOT even Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is a factor of x There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 6 and y = 1, in which case x/y = 6/1 = 6. So, x/y is EVEN Case b: x = 6 and y = 2, in which case x/y = 6/2 = 3. So, x/y is NOT even Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined NOTICE that, for statement 1 and 2 above, I was able to use the same values for x and y to show why each statement on its own is NOT SUFFICIENT. So, when we examine the statements COMBINED, the same values for x and y will apply. That is.... Case a: x = 6 and y = 1, in which case x/y = 6/1 = 6. So, x/y is EVEN Case b: x = 6 and y = 2, in which case x/y = 6/2 = 3. So, x/y is NOT even Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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