GMAT Set30 Question

[Man_of_Honour]

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.
A. Statement (1)

ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Kindly give reasons for ur answers

[DWarrior]

Interior angles of a quadrilateral add up to 360 degrees.

St1: two are 90 degrees, that means there's 180 left for the other two. Insuff.

St2: insuff

St1+2: we have 180 degrees remaining for the two non-right angles. Our choices are:
BCD=90 and ABC=180, impossible (other angle would need to be 0)

BCD=60 and ABC=120, possible

BCD=45, ABC=90, also possible and would mean two 90 deg angles, one 45 deg angle, and another 135 deg angle.

So now there are two possibilities, and either there is a 60 deg angle or there isn't, so combined statements are insufficient. E.

[bose]

imo E, pretty well explained by dwarrior

Agreed, E, it's tricky, though, because it would be easy to say 'the 4 angles are 90, 90, 60, 120' which would give C as the answer.

[SeanCaralho]

I'm pretty sure the answer is A. If a four-sided figure has two right degree angles, then the other two angles also must be right angles. Try drawing a quadrilateral with two right angles, and you'll see it's impossible for the other angles to be anything other than 90 degrees.

Therefore no interior angle can be 60 degrees, so we have sufficient information to answer the question.

[DMoney]

^^Check this out... On the last shape, make those two angles right angles, and you have a quadrilateral w/two right angles & two other angles that are not right but do equal 180 degrees. Answer is E.