Hi All,
One of my friend had asked me to solve the DS question attached in the picture, I wasn't able to solve it. can somebody help me understand how this one has to be tackled.
Regards
Naren
Data Sufficiency
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 10
- Joined: Sat Jun 27, 2015 6:51 pm
- Location: London
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
This is a GMATPrep question. There are several ways to solve, but if you can label an unknown angle with a letter in a question like this, and then use the basic angles facts to express every other angle in terms of that letter, you'll be able to answer any similar question, so that's the approach I'll use:
Statement 1 alone is not sufficient, because you can freely move point U around, and that changes the size of x. Similarly Statement 2 alone is not sufficient, because you can move point Q around and change x.
Using both Statements, say the angle at point R is y degrees. Then the angle at point T must be 90-y degrees, because in the big right triangle, the angles sum to 180.
Now Statement 1 tells us RQS is isosceles, so the angles at Q and S are equal. If the third angle in that triangle is y, then the two equal must sum to 180-y (because the sum of angles in a triangle is 180), so each angle is (180-y)/2 = 90 - (y/2)
Similarly, we know from Statement 2 that triangle TUS is isosceles. If the angle at T is 90-y degrees, the two equal angles must sum to 90+y degrees (because the sum of the three angles is 180). So each of the two equal angles is (90+y)/2 = 45 + (y/2)
Now we have labeled all three of the angles around point S -- they are 90 - (y/2), x, and 45 + (y/2). These angles form a straight line, so must add to 180. But notice what happens when we sum the three angles - the terms containing 'y' cancel out, and we get 135+x. So x must be 45 degrees, and the statements together are sufficient. The answer is C.
Statement 1 alone is not sufficient, because you can freely move point U around, and that changes the size of x. Similarly Statement 2 alone is not sufficient, because you can move point Q around and change x.
Using both Statements, say the angle at point R is y degrees. Then the angle at point T must be 90-y degrees, because in the big right triangle, the angles sum to 180.
Now Statement 1 tells us RQS is isosceles, so the angles at Q and S are equal. If the third angle in that triangle is y, then the two equal must sum to 180-y (because the sum of angles in a triangle is 180), so each angle is (180-y)/2 = 90 - (y/2)
Similarly, we know from Statement 2 that triangle TUS is isosceles. If the angle at T is 90-y degrees, the two equal angles must sum to 90+y degrees (because the sum of the three angles is 180). So each of the two equal angles is (90+y)/2 = 45 + (y/2)
Now we have labeled all three of the angles around point S -- they are 90 - (y/2), x, and 45 + (y/2). These angles form a straight line, so must add to 180. But notice what happens when we sum the three angles - the terms containing 'y' cancel out, and we get 135+x. So x must be 45 degrees, and the statements together are sufficient. The answer is C.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
-
- Junior | Next Rank: 30 Posts
- Posts: 10
- Joined: Sat Jun 27, 2015 6:51 pm
- Location: London
Hi Ian,
That helps a lot, thanks for explaining, I was doing it completely opposite, I took y = (180-2z), and hasn't considered t = 90-y.
once again thanks for the great reply.
Regards
Naren
That helps a lot, thanks for explaining, I was doing it completely opposite, I took y = (180-2z), and hasn't considered t = 90-y.
once again thanks for the great reply.
Regards
Naren
-
- Legendary Member
- Posts: 518
- Joined: Tue May 12, 2015 8:25 pm
- Thanked: 10 times