How many sides does polygon P have?
(1) All sides of P have equal lengths.
(2) The sum of the measures of the interior angles of P is 1,440 degree.
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How many sides does polygon P have? (1) All sides of P have
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alanforde800Maximus
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Brent@GMATPrepNow
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Target question: How many sides does polygon P have?alanforde800Maximus wrote:How many sides does polygon P have?
(1) All sides of P have equal lengths.
(2) The sum of the measures of the interior angles of P is 1440º
Statement 1: All sides of P have equal lengths.
There are infinitely many polygons that satisfy statement 1. Here are two:
Case a: Polygon P is an equilateral triangle. In this case, the answer to the target question is polygon P has 3 sides
Case b: Polygon P is a square. In this case, the answer to the target question is polygon P has 4 sides
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The sum of the measures of the interior angles of P is 1440º
Useful rule: the sum of the angles in an n-sided polygon = (n - 2)(180º)
So, we can write the equation: (n - 2)(180º) = 1440º
STOP: We need not solve this equation for n.
We need only recognize that we COULD solve it for n (but we won't, because that would be a waste of valuable time)
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
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Jeff@TargetTestPrep
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Statement One Alone:alanforde800Maximus wrote:How many sides does polygon P have?
(1) All sides of P have equal lengths.
(2) The sum of the measures of the interior angles of P is 1,440 degree.
All sides of P have equal lengths.
Knowing that all sides of P have equal lengths does not allow us to determine the number of sides P has. Statement one is not sufficient.
Statement Two Alone:
The sum of the measures of the interior angles of P is 1,440 degrees.
Since we have a formula S = 180(n - 2) where S is the sum of the measures of the interior angles of an n-sided polygon, we can determine the number of sides P has by substituting 1,440 for S. Without actually solving for n, we see that statement two is sufficient.
Answer: B
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