Advice

If x<8/5, which of the following could be greater than 1? GMAT

If x<8/5, which of the following could be greater than 1?

That is,

If , which of the following could be greater than 1?

I. 60 percent of x

II. 0.125 times 2x

III. 1/x percent of 16x

A. None

B. I only

C. II only

D. III only

E. I and III

This type of question is actually fairly easy to deal with.

The first step is just to assume that . Generally speaking, when you have a maximum or minimum value (exclusive) like this, just set equal. A boundary is a boundary for a reason.

Therefore, testing the boundary will show us specifically why that boundary exists. We will likely be able to address most if not all of the statements from this.

Statement I:

If we assume , then our maximum value (exclusive) will be 60% of this or…

, which is obviously less than 1.

Given that we find that our maximum value is less than 1, this statement will never give us a value greater than 1. This statement is FALSE.

If x<8/5, then I’m just writing it here again for SEO.

Statement II:

The first thing to note here is that .

Therefore, the maximum value here is .

Therefore, the maximum value here is , so we will never get a value greater than 1. This statement is FALSE.

Statement III:

The key point here is to read as clearly as possible.

If you are looking at percent, the easiest first step will be simply to invert our original :

So we know that we need percent, or . Therefore, we simply need to multiply by .

Therefore, we have . By cross-canceling, we see:

What you’ll notice here is that even though the 1/x term will increase as x decreases, the 16x term will decrease at a much faster rate. In short, making x smaller will make the value smaller, so 0.16 is our maximum value here.

The answer is (A) NONE.

This is where I just blather on about more rubbish like if x<8/5, which of the following could be greater than 1?

Rowan