Let say angle SUT=a then equation will be:-
2(x+a)-180+180-2a+90=180
2x=90
x=45
Answer should be "C".

first off, note that the conditions given in statements (1) and (2), individually, are identical. (i.e., if you flip the triangle around, statement 1 becomes statement 2, and vice versa.) that's a humble observation, but it serves to eliminate choices a and b in a hurry: if statement (1) is sufficient then statement (2) must be as well, and vice versa.

that leaves us with the last 3 choices.

you can visualize the fact that one of the two statements alone won't do the job:
imagine that statement (1) alone is true, making triangle QRS isosceles. that means segment QS is fixed in place.
however, there are no restrictions on triangle STU. that means, in effect, that we can move point U wherever we feel like moving it.
as we 'slide' point U along the bottom of the triangle, the value of x changes; therefore, statement (1) alone (and hence statement (2) alone) is insufficient.

if you don't buy the above argument, or if it's just something you'd never possibly think of within the time limit, then you could always try plugging in numbers and seeing that x can have different values.

--

statements (1) and (2) together:
since the triangle is a right triangle, we know that angles R and T must add to 90 degrees. let angle R be y degrees, and let angle T be (90 - y) degrees.
then
each of angles RQS and RSQ is (180 - y)/2 = 90 - y/2 degrees; and
each of angles TSU and TUS is (180 - (90 - y))/2 = 45 + y/2 degrees.
therefore, since angle RSQ, x, and angle TSU make a straight line together,
x = 180 - RSQ - TSU
= 180 - (90 - y/2) - (45 + y/2)
= 45 degrees.
sufficient
answer = c

Thanks, Ron. Can you please take a stab at walking me through the second post I made "GMAT Prep - Geometry (2)."

Thanks!

not sure exactly what you're asking... you're an anonymous poster, so i of course have no idea which is your second post.

do check out the post i made to that thread tonight, though - it's a pretty sweet shortcut.

Hello all,

Can anybody explain the above formula?

I guess the formula is suggesting the sum of angle in triangle RTP=180. But this is what i dun understand, and what i figured:

2(x+a)-180 => Is this suppose to be angle R? If so, how so??
+180-2a => From triangle SUT, this gives u angle T
+90 => Right angle P

Am i correct so far?

You are right.

see angle QST = x + a (if statement 2 is correct)

Then angle RSQ = 180 -(x+a)

Now angle RQS = angle RSQ (if statement 1 is correct)

Thus angle PRT = 180 - [2 x {180-(x+a)}]


This will give desired result.

............................................................

Pls do not insist on above step as a must.

Alternatively (C) can be explained thus:

From (1)

Say angle RSQ = a
Then angle RQS also = a
Thus angle PRT = 180-2a

From (2)

Say angle TSU = b
Then angle SUT also = b
Thus angle RTP = 180-2b

Combining (1) and (2)

(180-2a) + (180-2b) = 90 [ in Triangle PRT]

a+b is known

Now straight Line RST

x + a + b = 180

x is known.

Does that answer your questions, vanquish1984?