Data Sufficiency

manasgoswami1 wrote:Is a^3 > 20?

(1) a^4 > 80
(2) a^5 > 200

answer

B.

Here's another question that is looking for a yes or no answer. Statement (1) allows for both
positive and negative values of a, so it is not sufficient, and we can cross off A and D.
Statement (2), on the other hand, tells us that a is positive and must be a value of at least 3.
If a > 3, then the answer to the question stem must always be yes. Therefore, statement (2) is suffi-
cient, and our answer is B.

My question is on statement 2

how can we assume that the value at least 3? it could be a fraction too like 2.9

Dear manasgoswami1,
I'm happy to help.
You are 100% right. Since no restriction is given, a could be anywhere on the continuous infinity of the number line. On a real GMAT problem, it would be a big mistake to assume, without justification, that a variable must have an integer value. See:
https://magoosh.com/gmat/2012/number-sense-for-the-gmat/

Given that, if we are given a^5 > 200, how do we know that a^3 > 20? I don't believe there's anyway to do this without a calculator, which of course is not accessible on the GMAT Quant section.

With a calculator, it turns out: the fifth root of 200 is approximately 2.885399812, and that number cubed is more than 20, so (B) really is sufficient.

I don't know where you found this question, but it appears not to be a good GMAT question. Don't assume every question you find is a high-quality question.

Mike