*This series is designed to help you step up your Data Sufficiency practice while we all spend a little extra time at home during the coronavirus situation; I’m going to publish one practice Data Sufficiency question each day! You can choose to do all of them, or none of them. *

*Click on the tag “Social Distancing DS Challenge” at the bottom of this post to see all of the questions in this series! *

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #18**

Is the number *x* between .5 and .9 ?

(1) 800*x* < 620

(2) 1200*x* > 620

**Explanation**

Let’s solve for *x* in each inequality statement.

Statement (1): 800*x* < 620* … x* < .775 … That alone is not sufficient to say that *x* is in the presented range, since we can’t be sure *x* isn’t less than .5

Note: The easier way to think about this without using a calculator is to think about fractions and decimals you know well. Reduce this fraction first by ten (80*x* < 62), then cut it in half (40*x* < 31), and finally isolate the *x*: *x* < ^{31}/_{40}. What’s really close to ^{31}/_{40} that you know well? Let’s use ^{3}/_{4}, which equals .75.

Statement (2) = 1200*x* > 620 … *x* > .517 … Statement (2) is also not sufficient alone.

Suggestion: Handle this calculation the same way as you did statement (1). 1200*x* > 620 … reduce by ten: 120*x* > 62 … cut in half: 60*x* > 31 … isolate *x*: *x* > ^{31}/_{60} which is just barely more than .5 … no lengthy calculation needed!

But combined with statement (1), we know that *x* is in the range: .517 < *x* < .775, which is within the range presented of .5 < *x* < .9

The correct answer is (C).

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