Data Sufficiency Problem

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nickhar130: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Nov 03, 2010 10:07 am; Thanked: 1 times

by nickhar130 » Fri Nov 05, 2010 10:55 am

In the quadrilateral CDEF, CD//EF and DE//CF. Do all sides CDEF have the same length?

1) CE = DF

2) All angles of triangle CDF are the same.

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Source: Beat The GMAT — Problem Solving | Fri Nov 05, 2010 10:55 am

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Fri Nov 05, 2010 5:13 pm

nickhar130 wrote:

In the quadrilateral CDEF, CD//EF and DE//CF. Do all sides CDEF have the same length?

1) CE = DF

2) All angles of triangle CDF are the same.

Statement (1) is not sufficient as CE=DF is a general condition for all quadrilaterals;
Statement (2) assumes all angles in triangle CDF are equal; all sides must be equal then. The opposite angles are equal in quadrilateral. We have got all sides being equal in this case.

Pick (B), statement (2)

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nickhar130: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Nov 03, 2010 10:07 am; Thanked: 1 times

by nickhar130 » Sat Nov 06, 2010 10:36 am

I'm understanding condition 1, but for condition 2 if angle CDF are the same, then the opposite angle perhaps angle CFE are same and therefore we assume all sides are same? Can you please elaborate more on this because I lack the knowledge of what is given and which opposite angles are assumed to be the same.

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