Each of the following questions is followed by two statements 1 If either of the statements I or II ...........

Math and Mental Ability Data Sufficiency

Each of the following questions is followed by two statements.

1.If either of the statements I or II alone but not the other is sufficient to answer the question.

2.If both the statements I or II alone are sufficient to answer the question.

3.If questions can be answered with the help of both statements together, but not with the help of either statement alone.

4.If question cannot be answered unless more information is provided.

What is the probability of drawing a green ball from a box containing red, blue and green balls, if 1 ball is drawn at random?

I. The odds against drawing a red ball are 3:4 and the odds against a green ball are 9:11.

II.The odds against drawing a blue ball are 2:3.

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Explanation:

Let’s break it down and look at what the statements really give us:

- Statement I: The odds against red are 3:4, so for every 3 reds, there are 4 non-reds. The odds against green are 9:11, so for every 9 greens, there are 11 non-greens. That’s already a ton of info—we can set up equations for red, green, and the rest (blue), and solve for the probability of green alone.

- Statement II: Odds against blue are 2:3. So, for every 2 blues, there are 3 non-blues. But that's the only direct info we get—if we try building equations just from this, we can’t pin down the exact number of greens (since we don’t have either red or green separated out). So it’s not enough alone.

- Option 1: Says either I or II alone, but not the other, is sufficient. That fits, since I alone is enough, but II alone isn’t.

- The rest of the options don’t fit. We don’t need both together (Option 3), and we definitely have enough information from just I, so Option 4’s out.

So, here’s what this really means: Statement I is enough to answer the question on its own, but Statement II isn’t. So Option:1 (1) is right.