BTGmoderatorLU wrote:In a carnival game, players try to toss marbles into a milk jug. One point is awarded when a marble hits the jug without going in, two points are awarded when a marble goes into the jug, and no points are awarded when a marble misses the jug completely. If Maurice scored m points while playing the game, is m odd?

1) Exactly three of Maurice's marbles hit the jug without going in.
2) Exactly five of Maurice's marbles went into the jug.

The OA is A

Say the number of marbles that hit the jug without going in is p and the number of marbles that went into the jug is q. Thus,

m = 1*p + 2*q
m = p + 2q

Since 2q is an even number irrespective of whether q is even or odd, whether m is even of odd would depend on whether p is odd.

Question rephrased: Is p odd?

Let's take each statement one by one.

1) Exactly three of Maurice's marbles hit the jug without going in.

=> p = 3, an odd number. The answer is Yes. Sufficient.

2) Exactly five of Maurice's marbles went into the jug.

=> q = 5. There is no information about p. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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