Social Distancing with Data Sufficiency Challenge! – Day 27

assorted ceramics on wooden shelves

Photo by Daria Shevtsova on

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 #27

Jeff wants to organize the first 15 marbles of his marble collection on a shelf that is x centimeters wide. The marbles vary in diameter. Will the 15 marbles fit on the shelf space if they are arranged side-by-side?

(1) x = 30 centimeters

(2) The first 20 marbles in the collection have an average diameter of 2 centimeters.


Statement (1) tells us nothing about the marbles, so it can’t be sufficient, and statement (2) doesn’t mention the width of the shelf (value of x), so it can’t be sufficient, either.

But what about combining them? Not so fast: even though the average in statement (2) would accommodate the 15 marbles on the 30cm shelf, the average applies to the first 20 marbles rather than the first 15.  It’s possible that the first ten marbles each have a diameter of 3cm, but the second ten each have a diameter of 1cm. The first ten alone would take up the full 30cm, leaving no room for marbles 11-15.

Thus, we cannot be sure the first 15 have an average diameter of 2 or less. The correct answer is (E).