At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses Q at the restaurant? (Assume that all boxes are filled to capacity.)  Select
A) 96  B) 240  C) Q=256  D) Q=384  E) Q=480
Most Test Takers would recognize the system of equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....   We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.   This means, at the minimum, we have...   1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272= 
<gadget id="calculator">12 + 272</gadget>
<output>284</output>
284 glasses at the MINIMUM   Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....   The difference in the number of boxes MUST be 16 though, so we could have....   2 small boxes and 18 large boxes   3 small boxes and 19 large boxes   etc.   With every additional small box + large box that we add, we add   12+16= 
<gadget id="calculator">  12+16</gadget>
<output>28</output>
28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....   284+28= 
<gadget id="calculator">284+28</gadget>
<output>312</output>
312   312+28= 
<gadget id="calculator">312+28</gadget>
<output>340</output>
340   340+28= 
<gadget id="calculator">340+28</gadget>
<output>368</output>
368   368+28= 
<gadget id="calculator">368+28</gadget>
<output>396</output>
396   At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....   396+28= 
<gadget id="calculator">396+28</gadget>
<output>424</output>
424   424+28= 
<gadget id="calculator">424+28</gadget>
<output>452</output>
452   452+28= 
<gadget id="calculator">452+28</gadget>
<output>480</output>
480   Final Answer:   Q=480
<result>E</result>
At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses Q at the restaurant? (Assume that all boxes are filled to capacity.)