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Jayden draws a regular n-gon. What is the value of n?

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by Max@Math Revolution » Mon May 21, 2018 2:41 am

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[GMAT math practice question]

Jayden draws a regular n-gon. What is the value of n?

1) Each interior angle of the n-gon is greater than 115.
2) Each interior angle of the n-gon is less than 125.
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Source: — Data Sufficiency |
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n-gon

by GMATGuruNY » Mon May 21, 2018 3:23 am
Max@Math Revolution wrote:[GMAT math practice question]

Jayden draws a regular n-gon. What is the value of n?

1) Each interior angle of the n-gon is greater than 115.
2) Each interior angle of the n-gon is less than 125.
Sum of the interior angles of a quadrilateral = 360, with the result that each angle of a square = 360/4 = 90.
For each additional side, the sum of the interior angles increases by 180:
Sum of the interior angles of a pentagon = 360+180 = 540, with the result that each angle of a regular pentagon = 540/5 = 108.
Sum of the interior angles of a hexagon =540+180 = 720, with the result that each angle of a regular hexagon = 720/6 = 120.
If the number of sides is more than 6, the degree measurement of each interior angle will be greater than 120.

Statement 1:
As shown above, the n-gon must have 6 or more sides.
Since n could be different values, INSUFFICIENT.

Statement 2:
As shown above, the n-gon must have 6 or fewer sides.
Since n could be different values, INSUFFICIENT.

Statements combined:
For each interior angle to have a degree measurement between 115 and 125, the n-gon must have 6 sides.
Thus, n=6.
SUFFICIENT.

The correct answer is C.
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by Max@Math Revolution » Wed May 23, 2018 5:02 pm
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Each interior angle of a regular n-gon measures (n-2)*180o / n.

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)
(n-2)*180o / n > 115o
=> n*180° - 360° > n*115°
=> n*65° > 360°
=> n > 360° / 65°.
So, we must have
n > 5
=> n ≥ 6, since n is an integer.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
(n-2)*180° / n < 125°
=> n*180° - 360° < n*125°
=> n*55° < 360°
=> n < 360° / 55°
So, we must have
n < 7, since n is an integer
Since we don't have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
When we consider both conditions together, we have n ≥ 6 and n ≤ 6.
Thus, n = 6.
Both conditions together are sufficient.

Therefore, C is the answer.

Answer: C

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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