interior angle
This topic has expert replies
- Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
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.
(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.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
- ronniecoleman
- Legendary Member
- Posts: 546
- Joined: Sun Nov 16, 2008 11:00 pm
- Location: New Delhi , India
- Thanked: 13 times
Staurt,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.
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.
- Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
Hi! Questioning is good!mrsmarthi wrote:Staurt,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.
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.
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.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course