GregMAT 2 Month Plan - Quant Misc - Difficult Geometry [Week 3 Day 6]

GRE Quant Problem Solving
1

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I wanted to check if the method I used to solve this question is right, or if I just got lucky with the answer. Greg solved this using triangles and the property that the 3rd side should be less than the sum of the other 2 sides.

What I used is -

  • Any figure has the most efficient (maximum) perimeter and area when it’s a regular figure.
  • In the given figure, the maximum side given is 5.
  • This means, that when the pentagon is regular, all sides would be 5 and the perimeter is 25.
  • Since the sides are different in the given figure, it’s not a regular pentagon. Hence, the perimeter should be less than 25.
  • The sum of the given sides is 14, so the unknown side should be 5 or 10, since 15 would result in a perimeter of 14+15 = 29 which is greater than the perimeter of the regular pentagon, which is 25.

So I went with option C. Is this the right logic to apply to this problem?

2

you got lucky in this one since a regular pentagon must have all sides of equal length and not of exact 5 unit. it can be of 6 7 8 or any number of units but all sides must have same length. It is as if saying that a equilateral triangle can be of only 3 unit length in each side.

3

Yeah, that makes sense. Also, selecting 10 as one of my solutions would contradict my previous assumption of having a maximum of 5 as the side.

Thanks for confirming!