sarimzahid2395 wrote:

How can you do this quickly? Without testing cases?

sarimzahid2395 - The point here is that testing cases

is a time-efficient method of solving the question. I like to say that being a good

reader is what helps boost your Quant scores, and this problem is a case in point. Remember,

it is analytical reasoning that lies at the heart of the test, not necessarily mathematical prowess. Here, the keywords about the unknown are

positive and

integer. Statement (1) restricts those infinite possible positive integers to just two: 1 or 2, since 0 is not considered positive. The 1 breaks the square root down without performing any complicated analysis. The problem then reads, "is 1 < 2.5(1) - 5?"

Reminder: whenever the square root symbol appears on the GMAT™, as

Bunuel pointed out above in another response, only the positive root is considered. Getting back to the reformed question, it is clear that 1 is

not, in fact, less than -2.5, but we have a definitive answer. The only way to overturn (A) as an answer is if 2 leads to a different scenario. In the question, "is √2 < 2.5(2) - 5," the answer will again come to

no, since √2 is greater than 0. A "no" response to both 1 and 2, the only possible

x values, provides a consistent picture, so the answer for now is that (A), Statement (1), is SUFFICIENT.

Looking at Statement (2), our

prime positive integers, combining the information in the statement with that of the problem, will be 2, 3, 5, 7, 11, and so on, once again stretching to infinity. We have already tested 2, so we can test

any other valid number in the list of primes and see whether we also get a consistent picture:

is √3 < 2.5(3) - 5?

Just by focusing on the right-hand side, we can quickly determine that 2.5(3) - 5 = 2.5, and the question thus becomes,

is √3 < 2.5?

You do not have to be a math genius to see that √3

must be less than 2.5, since √4 would give us 2. Hence, we now have a

yes answer to the same question we had a

no to before, with 2, from this very statement. We can say goodbye to (D), then, and choose (A) as the answer.

I am no Quant maven, even if I aspire to be one. But with a little number sense, I cracked this one in 1:16 without writing down a thing. The concepts and vocabulary that are brought to bear in the question are simple enough. It is a mistake to think that you have to figure out everything all the time when you just need to answer the question that is being asked.

Good luck in your studies.

- Andrew