Q1: Is "m" a multiple of 6?

1) More than 2 of the first 5 positive integer multiples of m are multiples of 3

2) Fewer than 2 of the first 5 positive integer multiples of m are multiples of 12

Plugging in numbers should give it to you.

1) If more than 2 of the first 5 positive integer multiples of m are multiples of 3, then the number itself must be a multiple of 3. However, this does not mean it is a multiple of 6. Insufficient.

e.g. m = 9, then first 5 integer multiples are 9, 18, 27, 36, 45.

or m = 6, then we have 6, 12, 18, 24, 30. Both satisfy the criteria, but 9 is not a multiple of 6.

2) If you take m=6, then 2 of the first 5 integer multiples are multiples of 12. Not so if you take any other number. Sufficient.

Hence B.

Q2: What is the sum of positive integers x and y?

1) x^2 + 2xy + y^2 = 16

2) x^2 - y^2 = 8

Exactly as Fig has explained.

Q3: If x is an integer, is x even?

1) x^2 - y^2 = 0

2) x^2 + y^2 = 18

Also exactly as Fig has explained.

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Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?