Hi All,
One of the rarer rules that can appear on the GMAT is "add a side, add 180 degrees"
For example
A triangle = 180 degrees
A 4-sided shape = 360 degrees
A 5-sided shape = 540 degrees
A 6-sided shape = 720 degrees
Etc.
In this prompt, we can use a combination of Geometry rules and the Answer choices to TEST THE ANSWERS.
To start, we have to figure out the values of X and Y. Since those two angles form a line (thus, X+Y = 180) and Y = 5X, then X+5X = 180.... X=30 and Y=150
We're told that each of the angles in this unknown polygon is the SAME. We're asked for the number of sides that this polygon has.
Using the above math rule, and the answer choices, we can work our way through the list until we find the polygon with equal 150 degree angles. Let's start with Answer B...
Answer B: 6-sided
A 6-sided shape = 720 degrees
720/(6 sides) = 120 degrees per side
This is TOO SMALL (it's supposed to be 150 degrees), so we clearly need more sides/more degrees.
Answer D: 12-sided
A 12-sided shape = 180 + 9(180) = (10)180 = 1800 degrees
1800/(12 sides) = 150 degrees per side
This is an exact MATCH for what we were told, so this must be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★