Ratio problem

jessicamuniz wrote:Hi guys,
Here is quick and silly question, but I would like to know the possible ways to get the answer....thanks in advance....

Is a positive?
1) 15a > 16a
2) a+15 > 0

Hope to hear from you soon!

Statement 2 can be rewritten (by subtracting 15 from both sides) as:

a > -15

Of course a could still be negative or still could be positive here, so insufficient.

Statement 1, on the other hand, is sufficient:

15a > 16a

If a were positive, we could divide by a on both sides, and we would not need to reverse the inequality. If we did divide by a without reversing the inequality, we'd find that 15 > 16, which is clearly nonsense. So a cannot be positive (and cannot be zero), so a must be negative. Because we know with absolute certainty that the answer to the question "Is a positive?" is "no", we have sufficient information.

I'd add that it's very rare on the current GMAT to see a yes/no DS question like this, where you have sufficient information to know that the answer is 'no'. In the OG, there are 55 yes/no DS questions with sufficient information; for only one of them is the answer 'no', while for the remaining 54, the answer is 'yes'. I've yet to see a single GMATPrep question or real GMAT question for which there is sufficient information to know that the answer is 'no'. So while some books make a big deal about this 'trap', you'll likely never need to worry about it.