it has to be C
coz with st 1 we can have polygon of side 4 or 5 or 7 so on so forth
but with 2nd st we know that it is quadrilateral
If p is a polygon and x is a prime number, is p a quadrila
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aditya8062
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srcc25anu
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Given p = polygon and x = prime
Polygon can be 3-sided (triangle), 4-sided (square / rectangle), 5-sided (pentagon) and so on ...
quadrilateral is a 4 sided polygon
so essentially the question is asking whether the polygon has 4 sides or their interior angles sum to 360 degrees.
1. polygon's interior angles sum to 180 x
sum of interior angles = (no. of sides - 2) * 180
given X = prime
if x = 2, Sum of angles = 180 * 2 = 360 degrees (hence no of sides = 4) Yes a quadrilateral
but if x = 3, sum of angles = 180 * 3 = 540 (number of sides = 5) NOT a quadrilateral.
Hence insufficient
2. polygon has 2x sides
if x = 2, no of sides = 4 (YES a quadrilateral)
if x = 3, no of sides = 6 (NOT a quadrilateral)
Hence insufficient
Taking 1+2 together, still insufficient
hence E
What's the OA?
Polygon can be 3-sided (triangle), 4-sided (square / rectangle), 5-sided (pentagon) and so on ...
quadrilateral is a 4 sided polygon
so essentially the question is asking whether the polygon has 4 sides or their interior angles sum to 360 degrees.
1. polygon's interior angles sum to 180 x
sum of interior angles = (no. of sides - 2) * 180
given X = prime
if x = 2, Sum of angles = 180 * 2 = 360 degrees (hence no of sides = 4) Yes a quadrilateral
but if x = 3, sum of angles = 180 * 3 = 540 (number of sides = 5) NOT a quadrilateral.
Hence insufficient
2. polygon has 2x sides
if x = 2, no of sides = 4 (YES a quadrilateral)
if x = 3, no of sides = 6 (NOT a quadrilateral)
Hence insufficient
Taking 1+2 together, still insufficient
hence E
What's the OA?
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aditya8062
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it has to be C .from st1 we are getting the sides as 4 ,5 ,7,9Taking 1+2 together, still insufficient
hence E
and from st 2 we know that sides are even hence sides have to be 4
hence C
make sense ?
1) n-2 = x 180x
4-2= 2
5-2= 3
6-2= 4 no good , not prime
7-2= 5
number of sides can vary so not suff
2) 2*x = sides
2 * 2= 4
2 * 3= 6
2 * 5= 10
2 * 7= 14
again number of sides can vary so not suff
together
4 sides when x=2 is only consistent answer.
suff. answer c
4-2= 2
5-2= 3
6-2= 4 no good , not prime
7-2= 5
number of sides can vary so not suff
2) 2*x = sides
2 * 2= 4
2 * 3= 6
2 * 5= 10
2 * 7= 14
again number of sides can vary so not suff
together
4 sides when x=2 is only consistent answer.
suff. answer c
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Anju@Gurome
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Let us assume p has n sides.varun289 wrote:If p is a polygon and x is a prime number, is p a quadrilateral?
p's interior angles sum to 180x
p has 2x sides
So, we need to determine whether n = 4 or not.
Statement 1: Sum of interior angles of p = (n - 2)×180°
Hence, n = (x + 2)
For x = 2, n = 4
For x = 3, n = 5
Not sufficient.
Statement 2: n = 2x
For x = 2, n = 4
For x = 3, n = 6
Not sufficient
1 & 2 Together: (x + 2) = 2x ---> x = 2 ---> n = 4
Sufficient
The correct answer is C.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
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Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
