Polygon X

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sun Dec 07, 2008 11:54 am

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.

LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"

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Source: Beat The GMAT — Data Sufficiency | Sun Dec 07, 2008 11:54 am

kris610: Master | Next Rank: 500 Posts; Posts: 198; Joined: Fri Mar 09, 2007 8:40 pm; Thanked: 7 times

by kris610 » Sun Dec 07, 2008 3:43 pm

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.

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pbanavara: Master | Next Rank: 500 Posts; Posts: 279; Joined: Wed Sep 24, 2008 8:26 am; Location: Portland, OR; Thanked: 6 times

by pbanavara » Mon Dec 08, 2008 6:49 pm

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

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earth@work: Master | Next Rank: 500 Posts; Posts: 248; Joined: Mon Aug 11, 2008 9:51 am; Thanked: 13 times

by earth@work » Mon Dec 08, 2008 8:15 pm

pbanavara wrote: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

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pbanavara: Master | Next Rank: 500 Posts; Posts: 279; Joined: Wed Sep 24, 2008 8:26 am; Location: Portland, OR; Thanked: 6 times

by pbanavara » Mon Dec 08, 2008 8:18 pm

earth@work wrote:
pbanavara wrote: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

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anayeri: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Oct 08, 2008 11:29 am; Location: Toronto, Ontario; Thanked: 5 times

by anayeri » Mon Dec 08, 2008 8:19 pm

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

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Tue Dec 09, 2008 8:11 am

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

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Tue Dec 09, 2008 11:21 am

4meonly wrote:
A

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

LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: Polygon X

by Stuart@KaplanGMAT » Tue Dec 09, 2008 2:04 pm

logitech wrote: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).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Wed Dec 10, 2008 5:36 am

logitech wrote:
4meonly wrote:
A
Dude, go relax for a week or two and come back to GMAT field again.

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

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 10, 2008 5:39 am

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!

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