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

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