Katrina draws a regular n-sided polygon. What is the value o

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[GMAT math practice question]

Katrina draws a regular n-sided polygon. What is the value of n?

1) One internal angle of the polygon is 108o
2) The sum of all the side lengths is 120

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by KCTester » Tue May 15, 2018 8:39 am

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In a regular polygon, all sides and angles are equal.
We can use the rule that the total sum of all angles in an n-sided polygon is equal to ( n - 2 ) * 180.

Statement #1:
Using the rule above, we can create an quation:
108n = (180 - 2)n
This equation, basically says, that the measure of one angle multiplied by the number of angles is the total sum of interior angles, which is also equal to (180 - 2)n
Solving the equation:
108n = 180n - 360
72n = 360
n = 5 sides.
SUFFICIENT!

Statement #2:
The length of sides say nothing about the number of sides or angles in a polygon. You could have a 12-sided polygon with each side equal to 10, or you could have a square with each side equal 30.
NOT SUFFICIENT!

Answer: A
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by Jeff@TargetTestPrep » Wed May 16, 2018 10:12 am

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Max@Math Revolution wrote:
Katrina draws a regular n-sided polygon. What is the value of n?

1) One internal angle of the polygon is 108o
2) The sum of all the side lengths is 120
We need to determine the value of n in a regular n-sided polygon, that is, we need to determine the number of sides of this regular polygon.

Statement One Alone:

One internal angle of the polygon is 108 degrees.

Since we have a formula for the sum of the measures of all the interior angles of a polygon, and since all the angles of a regular polygon are equal, knowing the measure of one interior angle of a regular polygon is sufficed to determine the number of sides of the polygon. Statement one alone is sufficient. (Note: here n = 5, but we will leave the readers to verify it.)

Statement Two Alone:

The sum of all the side lengths is 120.

This means the perimeter is 120. However, without any further information, knowing the perimeter of a regular polygon doesn't allow us to determine the number of sides of the polygon. Statement two alone is not sufficient.

Answer: A

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by Max@Math Revolution » Thu May 17, 2018 12:24 am

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
The angle sum of the n-sided polygon is ( n - 2 ) * 180 o = n * 108 o.
So, 72*n = 360 o or n = 5.
Condition 1) is sufficient.

Condition 2)
If the length of each side is 24, then n = 120/24 = 5.
If the length of each side is 20, then n = 120/20 = 6.
Since we don't have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A