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

Question

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

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

u1983 · Answer

1) One internal angle of the polygon is  108^o ................................ Sufficient

As for a regular polygon, all the internal angles are same and the value of a internal angle of a polygon is defined as 180(n-2)/n
Thus  108=180(n-2)/n  or  108n=180n-360  or  72n=360  or  n=5

2) The sum of all the side lengths is  120 ........................................ .In sufficient  
No way we can determine the # sides.
As if the each side length is 30, n=4
As if the each side length is 24, n=5
As if the each side length is 20, n=6
As if the each side length is 12, n=10

Hence I would go for  option A .

GMATBusters · Answer

1) One internal angle of the polygon is 108 deg
The Internal angle of a regular polygon = (n-2)*180/n. Hence n can be determined.
 SUFFICIENT 
2) The sum of all the side lengths is 120
The length of sides has no relation to the number of sides.
 NOT SUFFICIENT

Answer A

JeffTargetTestPrep · Answer

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

MathRevolution · Answer

=>

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 ) *  180^0  = n *  108^0 .
So, 72*n =  360^0  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

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

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