Each question is followed by two statements I and II 1 If the question can be answered by any one of...........

Math and Mental Ability Data Sufficiency

Each question is followed by two statements, I and II.

1.If the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.

2.If the question can be answered by using either statement alone.

3.If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

4.If the question cannot be answered even by using both statements together.

O is the centre of two concentric circles, AE is a chord of the outer circle and it intersects the inner circle at points b and D. C is a point on the chord in between B and D. What is the value of AC / CE?

I. BC/CD = 1

III.A third circle intersects the inner circle at B and D and the point C is on the line joining the centres of the third circle and the inner circle.

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Explanation:

Let’s break down the statements and the options so we can really see what’s going on.

Statement I:

- You’re told that BC/CD = 1.

- That means BC = CD.

- But without knowing anything else about the chord’s full length or where C sits between B and D relative to the whole chord AE, you can’t say what AC/CE is (unless C were the midpoint, but you don’t have the full context).

- So, statement I alone isn’t enough.

Statement II:

- This one introduces a third circle and says the point C is on the line joining centers of the third and inner circles, but we don’t get enough specific metrics or constraints for AC/CE—just more information about positioning, not ratios.

- On its own, still not enough to nail down AC/CE on a number line.

Both Together:

- Now, if you use the facts together: BC = CD *and* C lies symmetrically with respect to two centers along the chord line, it still doesn’t nail things down for AC/CE unless there’s something really specific about how that third circle interacts—but you’re missing concrete measurements.

- Even together, the data is sketchy for what’s being asked.

Here’s what the options mean:

- Option 1: Either one, but not both, solves it. (Nope)

- Option 2: Either alone is enough. (Nope, neither is alone)

- Option 3: Only *both* statements together solve it. (Also doesn’t fit—combining them doesn’t guarantee the ratio, as above)

- Option 4: Even both together aren’t enough. (That’s what’s going on.)

Correct Answer:

Option:4, 4

If you want AC/CE, you just don’t have enough detail from either statement, or even putting both together. Neither one nor both can pin down the ratio for you. Option 4, 4 is the answer that holds up under scrutiny.