Lines & Angle problem

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omair_bba: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Fri Sep 24, 2010 12:26 pm

by omair_bba » Thu Aug 30, 2012 10:53 am

Hi, Below Q is not from any OG.

Q: Concerning the figure below, if a=b, which of the following statements must be true?

(I) c=d , (II) f & k are parallel. , (III) m & f are perpendicular.

A) None
B) I only
C) I & II only
D) I & III only
E) I,II & III

Please explain answer too !

Thankx...

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Source: Beat The GMAT — Quantitative Reasoning | Thu Aug 30, 2012 10:53 am

vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Thu Aug 30, 2012 11:29 am

omair_bba wrote:Hi, Below Q is not from any OG.

Q: Concerning the figure below, if a=b, which of the following statements must be true?

(I) c=d , (II) f & k are parallel. , (III) m & f are perpendicular.

A) None
B) I only
C) I & II only
D) I & III only
E) I,II & III

Please explain answer too !

Thankx...

From the figure given a+c=180 and b+d=180. Since a=b, we can say that c=d. I'm not sure if the II and III MUST BE TRUE. IMO B

- VK

I will (Learn. Recognize. Apply)

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omair_bba: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Fri Sep 24, 2010 12:26 pm

by omair_bba » Thu Aug 30, 2012 12:03 pm

@vk_vinayak

From the figure given a+c=180 and b+d=180. Since a=b, we can say that c=d. I'm not sure if the II and III MUST BE TRUE. IMO B

Yup the answer is B

I solved it the same way !

But what else I should know to eliminate II & III with surety ?

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adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pmFollowed by: 3 members; Thanked: 39 times

by adthedaddy » Thu Aug 30, 2012 12:21 pm

But what else I should know to eliminate II & III with surety ?

Dear Omair,

I have redrawn the figure you posted in such a way that it satisfies the given condition of a=b.

You need to imagine possibilities to prove option (II) and Option (III) wrong.

You can see in the following figure, 'f' & 'k' are neither parallel nor 'm' & 'f' are perpendicular.
It also satisfies all the given conditions.

So, we can conclude that, only condition (I) is true as a,c & b,d form a linear pair. Thus, a=b => c=d

Ans: Option B

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