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orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; Thanked: 2 times; GMAT Score:660

by orel » Tue Dec 09, 2008 9:47 am

sos!

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Source: Beat The GMAT — Data Sufficiency | Tue Dec 09, 2008 9:47 am

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

by Stuart@KaplanGMAT » Tue Dec 09, 2008 2:10 pm

Q: does quadrilateral ABCD have a 60 degree angle?

(1) ABCD has two right angles.

Well, there's 180 degrees left, but we have no idea how it's split up: insufficient.

(2) One angle is double another angle.

We could have 120/60, or we could have 100/50: insufficient.

Together:

It's very temping to say that once we remove our two 90 degree angles we're left with 180 and that, building in rule (2), the two remaining angles have to be 120/60, giving us a "YES" answer.

However, there's another possibility. Instead of our double values being 120/60, our double values could be 90/45. A quadrilateral with angles of 135/90/90/45 satisfies both statements and gives us a "NO" answer.

So, even after combining, we can get both a "YES" and a "NO": choose (E), not enough information.

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orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; Thanked: 2 times; GMAT Score:660

by orel » Tue Dec 09, 2008 2:44 pm

thanks, Stuart!

First, I chose C, but didn't understand what was wrong with that. But after your explanation, everything is clear!
Thank you
Feruza

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Fri Dec 12, 2008 12:44 am

IMO E

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Mon Feb 09, 2009 9:08 am

Stuart Can you please show me how to construct an quadrilateral with two 90 degree and other two are not 90 each? I am asking for a real construction.

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BuckeyeT: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Jan 24, 2009 3:00 pm; Thanked: 11 times; GMAT Score:730

by BuckeyeT » Mon Feb 09, 2009 10:59 am

Quad ABCD
Angle ABC = 90; Angle BCD = 45; Angle CDA = 90; Angle DAB = 135.

Sketch this one out, and you see why the answer is E.

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mrsmarthi: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Nov 30, 2008 8:41 pm; Thanked: 4 times

by mrsmarthi » Mon Feb 09, 2009 5:29 pm

Stuart Kovinsky wrote:Q: does quadrilateral ABCD have a 60 degree angle?

(1) ABCD has two right angles.

Well, there's 180 degrees left, but we have no idea how it's split up: insufficient.

(2) One angle is double another angle.

We could have 120/60, or we could have 100/50: insufficient.

Together:

It's very temping to say that once we remove our two 90 degree angles we're left with 180 and that, building in rule (2), the two remaining angles have to be 120/60, giving us a "YES" answer.

However, there's another possibility. Instead of our double values being 120/60, our double values could be 90/45. A quadrilateral with angles of 135/90/90/45 satisfies both statements and gives us a "NO" answer.

So, even after combining, we can get both a "YES" and a "NO": choose (E), not enough information.

Staurt,

Didn't mean to question your solution.

I would like to go with B as the ans.

Stmt 2 states - The degree measure of ABC is twice the measure of BCD.

It is clearly stating the sum of the angles on the straight line on one side of the quadrilateral.

This gives x + 2x = 180 ==> x = 60.

This is sufficient to say that one angle of the quadrilateral is 60.

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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

by Stuart@KaplanGMAT » Tue Feb 10, 2009 1:15 am

mrsmarthi wrote:
Stuart Kovinsky wrote:Q: does quadrilateral ABCD have a 60 degree angle?

(1) ABCD has two right angles.

Well, there's 180 degrees left, but we have no idea how it's split up: insufficient.

(2) One angle is double another angle.

We could have 120/60, or we could have 100/50: insufficient.

Together:

It's very temping to say that once we remove our two 90 degree angles we're left with 180 and that, building in rule (2), the two remaining angles have to be 120/60, giving us a "YES" answer.

However, there's another possibility. Instead of our double values being 120/60, our double values could be 90/45. A quadrilateral with angles of 135/90/90/45 satisfies both statements and gives us a "NO" answer.

So, even after combining, we can get both a "YES" and a "NO": choose (E), not enough information.
Staurt,

Didn't mean to question your solution.

I would like to go with B as the ans.

Stmt 2 states - The degree measure of ABC is twice the measure of BCD.

It is clearly stating the sum of the angles on the straight line on one side of the quadrilateral.

This gives x + 2x = 180 ==> x = 60.

This is sufficient to say that one angle of the quadrilateral is 60.

Hi! Questioning is good!

You have made the assumption that our shape is a parallelogram - that each adjoining pair of angles must add up to 180 degrees. However, nowhere in the question are we given that information. In data sufficiency, if we're not told something explicitly, we cannot make any assumptions.

A quadrilateral can be any enclosed 4 sided shape (with straight sides, of course, in 2-dimensional space). So, your equation does not have to apply to this question.

Based on statement (2) alone, the angles in our shape could be 60/60/120/120, but they could also easily be 1/2/3/354 or 45/90/90/135.

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