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.

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