Seven pieces of rope have an average

Seven pieces of rope have an average (arithmetic mean) length if 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

2 Explanations

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Rukhsora Rakhmatova

Looking at answer choices makes this problem easier: 1. Start with max number E.152 shortest=(longest-14)/4 so, (152-14)/4 = not integer, next check D. 134 (134-14)/4=Integer, Correct answer is D!

Oct 22, 2017 • Comment

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Mike McGarry, Magoosh Tutor

Aug 17, 2015 • Comment

Krishan Agarwal

If you stop at 1:07, and just take [7x+3(84)+14]/7=68 you will see that you can just divide the numerator by 7. You get x + 3(12) + 2=68, then x+38=68, and finally x=30. No need to do advanced multiplication or subtraction.

Sep 18, 2017 • Reply

Sam Kinsman

You're absolutely right Krishan - you've spotted an EXCELLENT shortcut!! Thanks for sharing it with us here :D

Sep 20, 2017 • Reply