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How many sides does polygon P have? (1) All sides of P have equal len

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18 May 2018, 04:13
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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 $$1,440^{\circ}$$
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18 May 2018, 04:35
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alanforde800Maximus wrote:
How many sides does polygon P have?

(1) All sides of P have equal lengths. - Clearly Not Sufficient.

(2) The sum of the measures of the interior angles of P is $$1,440^{\circ}$$ - Sufficient.

Sum of Interior angles of a polygon = $$(n-2)$$ * $$180^{\circ}$$=$$1440^{\circ}$$ $$-> n=10.$$

As its a DS question so, if we know the formula, we know that B will be sufficient. We don't have to do the entire calculation.

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Re: How many sides does polygon P have? (1) All sides of P have equal len  [#permalink]

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18 May 2018, 08:24
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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 $$1,440^{\circ}$$

Target question: How many sides does polygon P have?

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

Cheers,
Brent
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Re: How many sides does polygon P have? (1) All sides of P have equal len  [#permalink]

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18 May 2018, 08:40
the sum of the angles in an n-sided polygon = (n - 2)(180º)
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How many sides does polygon P have? (1) All sides of P have equal len  [#permalink]

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07 Jul 2018, 10:37
For those wondering whether it matters if the polygon is regular or irregular, in this question it does not:

The sum of the interior angles of an n-sided polygon is always = (n-2) * 180

The sum of each of the angles is [(n-2) * 180]/n, if the polygon is regular.

Here they are just asking for the number of sides ('n'), not each of the interior angles of polygon.
How many sides does polygon P have? (1) All sides of P have equal len &nbs [#permalink] 07 Jul 2018, 10:37
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