Data Sufficiency

Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

I narrowed it down to C and E...i believe its C...can ny1 provide a detailed explanation?

zagcollins wrote:Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

I narrowed it down to C and E...i believe its C...can ny1 provide a detailed explanation?

(C) is very tempting, but ignores a tricky possibility. The answer is actually (E).

(1) by itself tells us that the two remaining angles sum to 180, but we have no idea if they're 120/60 or some other combination, so it's insufficient.

(2) just tells us that one angle is twice another. We might have a 60 degree angle, but again we might not, so it's insufficient.

Combined, it's very tempting to say that the angles have to be 90/90/120/60. However, the angles also could be 90/90/45/135, since 90 is twice as much as 45, so statement (2) is still satisfied. Therefore, we may or may not have a 60 degree angle: choose (E).

As it is a quadrilateral the some of its interior angles should be 360 degrees.

Statement 1 provides the information that the sum of two angles of the quadrilateral is 180. But there is no clue about other two. So insufficient.

Statement 2 provides the information that 1 certain angle is double to other one. Nothing about other. So insufficient.

But if we combine two statements, we can get that in the ABCD quadrilateral where A=90 , B=120, C=60, D= 90. So both Are sufficient.

Thanks.

saeed wrote:As it is a quadrilateral the some of its interior angles should be 360 degrees.

Statement 1 provides the information that the sum of two angles of the quadrilateral is 180. But there is no clue about other two. So insufficient.

Statement 2 provides the information that 1 certain angle is double to other one. Nothing about other. So insufficient.

But if we combine two statements, we can get that in the ABCD quadrilateral where A=90 , B=120, C=60, D= 90. So both Are sufficient.

Thanks.

See my solution above - combined, the angles could be 90, 90, 45 and 135 as well.

Thanks Stuart. Its really a tricky question.

A really difficult question

I believe the answer to this question should be A.

If a quadrilateral has two 90 degree angles, the other two have to be 90 degrees as well. I could not think of any quadrilateral shape with two 90 degree angles that is not a square or a rectangle. I could be wrong, but I don't think I am...

What do you guys think?

Nihilist wrote:I believe the answer to this question should be A.

If a quadrilateral has two 90 degree angles, the other two have to be 90 degrees as well. I could not think of any quadrilateral shape with two 90 degree angles that is not a square or a rectangle. I could be wrong, but I don't think I am...

What do you guys think?

Hi!

No matter which two angles are 90 degrees, it's still possible that the other two aren't 90.

Look at your computer screen (probably a rectangle). Imagine that the top left corner was 1 foot higher, but the top right corner remained the same. You'd still have a quadrilateral (it still has 4 corners, after all), and the bottom two angles would still be 90 degrees each, but the top two are no longer 90 degrees.

Even if opposite angles are 90 degrees the other two angles could be non-90s (picture two right triangles with the same hypotenuse, but different legs, glued along the hypotenuse - the two right angles from the triangles are corners of the quadrilateral, but the other two corners won't be 90 degrees).

ah yes, you're right. Thanks!

This is a GMATPrep, test 2 question. Alas got it wrong!!

Thanks Stuart for the explanation.