Triangles

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joefreddy: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sat Aug 04, 2007 2:58 am

by joefreddy » Mon Apr 14, 2008 5:51 pm

Pls help

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Source: Beat The GMAT — Data Sufficiency | Mon Apr 14, 2008 5:51 pm

codesnooker: Legendary Member; Posts: 543; Joined: Fri Jan 18, 2008 1:01 am; Thanked: 43 times; GMAT Score:580

by codesnooker » Mon Apr 14, 2008 10:48 pm

Okay this is very simple problem.

If you can prove it with first statement, then is automatically proves with second statement.

I have drawn an image and show the angles with various alphabets, as we can not draw angle symbol over here.

Now according to statement 1, angle QPR = 30 degree.

According to the property of triangle,

x + angle QPR + m + angle QSP = 180 degree

i.e. x + 30 + m + 90 = 180
i.e. x + m + 120 = 180

and also,

x + y + angle PSR = 180 degree.
i.e. x + y + 90 = 180

equating both statements,

x + m + 120 = x + y + 90

x will cancel out from both sides...

therefore, y - m = 30

So it clearly states that angle PRS is 30 degree greater than angle PQR

So, statement 1 is alone to derive the answer.

Now, according to second statement,

angle PQR + angle PRQ = 150 degree,

it means, angle QPR = 30 degree (by the property of triangle).
So, now the situation becomes again as statement 1, and it can be proved again.

So, both statement are alone sufficient.

PS: Please hide the answers through spoliers....

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