Polygon X

[logitech]

If has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.

[kris610]

A says that 180(n-2) is evenly divisible by 16, which would mean n has to be 6 (less than 9).

For B, n could be any value less than 9 and satisfy as 15 would divide 180.

[pbanavara]

I think it's C .. not sure - Combining the 2 the only option is n=6

Because from A n can be 4 as well.

- pradeep

[earth@work]

I think it's C .. not sure - Combining the 2 the only option is n=6

Because from A n can be 4 as well.

- pradeep

same as kris610, answer A
n cannot be 4, 180(n-2)/16=45(n-2)/4 now n-2 shud be divisible by 4 so smallest value of n=6 <9

[pbanavara]

I think it's C .. not sure - Combining the 2 the only option is n=6

Because from A n can be 4 as well.

- pradeep

same as kris610, answer A
n cannot be 4, 180(n-2)/16=45(n-2)/4 now n-2 shud be divisible by 4 so smallest value of n=6 <9

Agree - my bad .. calculation mistake

[anayeri]

Is there a quicker way to do this rather than have to actually go through each calculation?

[4meonly]

My attempt:
sum of angles = 180*(n-2)
I factorized 180 = 2^2 * 3^2 * 5 *(n-2)
n<9

(1) The sum of the interior angles of Polygon X is divisible by 16.
16 = 2^4
The only way to make 2^2*3^2*5*(n-2) divisible by 16 (n-2) should give additional 2^2. because n<9 the only n is 6, because (6-2)=2^2
So the only sum is 2^2*3^2*5*(6-2) = 2^4*3^2*5 that is div by 16
SUFF


(2) The sum of the interior angles of Polygon X is divisible by 15.
With the same logic 180 is already divisible by 15 so ANY n will give thesum that is divisible by 15
INSUFF

A

[logitech]

A

Dude, go relax for a week or two and come back to GMAT field again.

[Stuart@KaplanGMAT]

If has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.

First, let's jot down the key formula:

# of interior degrees of an n sided polygon = 180(n-2)

In DS, we can start with whichever statement is easier. In this case, that's certainly (2).

(2) Well, 180 is divisible by 15. Therefore, all polygons will have interior angles divisible by 15.

Not only is this insufficient, it's completely useless information. Therefore, we can eliminate (b), (c) and (d). (Remember, (c) is only correct if each statement adds something that you need.)

(1) 180(n-2)/16 is an integer.

Factoring out:

45(n-2)/4 is an integer. Well, we can't get "4" out of "45", so 4 MUST be a factor of (n-2). The only integer between 3 and 8 that gives us what we need is 6: sufficient.

(1) is sufficient, (2) isn't: choose (A).

[4meonly]

A

Dude, go relax for a week or two and come back to GMAT field again.

No, I cant. I am very angry!!! ))))

[cramya]

No, I cant. I am very angry!!! ))))

4meonly,

Persistence is a good thing! Hope u can crack the Verbal this time along wiht maintaining or improving quant.

Wish u good luck in the prep!