Social Distancing with Data Sufficiency Challenge! – Day 18

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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) 800x < 620

(2) 1200x > 620


Let’s solve for x in each inequality statement.

Statement (1): 800x < 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 (80x < 62), then cut it in half (40x < 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) = 1200x > 620 … x > .517 … Statement (2) is also not sufficient alone.
Suggestion: Handle this calculation the same way as you did statement (1). 1200x > 620 … reduce by ten: 120x > 62 … cut in half: 60x > 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).