If x

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

That is,

If $x < \frac{8}{5}$ , 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 $x = \frac{8}{5}$ . 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 $x = \frac{8}{5}$ , then our maximum value (exclusive) will be 60% of this or…

$\frac{3}{5}\frac{8}{5} = \frac{24}{25}$ , 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 $0.125 = \frac{1}{8}$ .

Therefore, the maximum value here is $\frac{1}{8} \times 2x = \frac{1}{8} \times 2(\frac{8}{5}) = \frac{1}{8} \times \frac{16}{5} = \frac{2}{5}$ .

Therefore, the maximum value here is $\frac{2}{5}$ , 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 $\frac{1}{x}$ percent, the easiest first step will be simply to invert our original $x$ :

$\frac{1}{x} = \frac{1}{\frac{8}{5}} \frac{5}{8}$

So we know that we need $\frac{5}{8}$ percent, or $\frac{\frac{5}{8}}{100} = \frac{5}{800}$ . Therefore, we simply need to multiply $\frac{5}{800}$ by $16x$ .

$16x = 16 \times \frac{8}{5} = \frac{16(8)}{5}$ .

Therefore, we have $\frac{5}{800} \times \frac{16(8)}{5}$ . By cross-canceling, we see:

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

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?