Find the values of A and B on basis of two statements given below I The ratio of A amp B is 3 5 and ...........

Math and Mental Ability Data Sufficiency

Find the values of A and B on basis of two statements given below?

I. The ratio of A & B is 3 : 5, and B is positive.

II. The ratio of 2A & B is 12 : 10, and A is positive.

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

if the question can be answered by using either statement alone.

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

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

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Explanation:

Alright, let’s break it down:

- Statement I: Says A/B = 3/5, B is positive. That means A = 3k, B = 5k for some positive k. But k could be any positive number—so A and B aren't uniquely determined. Not enough by itself.

- Statement II: Says (2A)/B = 12/10 ? 2A/B = 6/5 ? A/B = 3/5. Also, A is positive. This is exactly the same ratio as in Statement I. Again, you get A = 3m, B = 5m for some positive m—still not unique.

- Both together: Still only tell you the ratio is 3:5. No new information pops up; you're just restating the same thing two ways. Multiple value pairs possible.

Here’s what this really means:

- Neither statement alone gives you unique values for A and B.

- Even combining them doesn’t solve it—ratios don’t fix actual numbers.

- So the correct answer is Option 4: The question cannot be answered, even when you use both statements.

Option 4 is the answer.