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How to best guess on this gmat-prep problem ?

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How to best guess on this gmat-prep problem ?

by shailendra.sharma » Wed Jun 26, 2013 6:33 am
See the following Data Sufficiency problem

Image

This was the last problem for me on recent GMAT Prep test: for lack of time I needed to guess it (I know how to solve it). But I ended up guessing D instead of correct answer 'C', because --

1) Both statements are similar / symmetric.
2) With right triangle information (from the statement), I ended up thinking I might have enough information with single statement.
3) I was sure A and B are not the option - as statements were symmetric.
4) I was also sure that problem is solvable - so E is not the option.

Any suggestions on how I could have put my bets on C, instead of D. Note: I was left with 1 minute for this problem ?

May be I should have thought required x is in a quadrilateral and I might need more information ? Please suggest.
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by srcc25anu » Wed Jun 26, 2013 11:00 am
ST1: QR = RS
from this condition, visualize an image where points S and Q are fixed. Now if you move Point U to left or right from its current position, the angle X will change.
hence Insufficient

St2: ST = TU
from this condition, visualize an image where points S and U are fixed. Now if you move Point Q to left or right from its current position, the angle X will change.
hence Insufficient

both statements together: we have fixed both U and Q points. hence we can only have a fixed x angle.
Hence Sufficient
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by shailendra.sharma » Thu Jun 27, 2013 12:57 am
Excellent strategy srcc25anu !

I am sure I will be able to apply similar strategy on other problems.
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by luckypiscian » Thu Jun 27, 2013 1:19 am
x = 180 - angle RSQ - angle TSU

i.e. it is dependent on angle RSQ and angle TSU.
Lets equate RSQ and TSU

RSQ = 180 - SQR - QRS
TSU = 180 - SUT - UTS

so now to determine TSU and RSQ there are 4 unknowns

Hence
x = 180 - (180 - SQR - QRS) - (180 - SUT - UTS)
or
x = SQR + SUT + QRS + UTS - 180

we also know that
QRS + UTS = 90
since PTR is a right angled triangle

so x = SQR + SUT - 90

so now to determine x there are 2 unknowns i.e. angles SQR, SUT

only if both the conditions are applied RSQ and TSU will both become isosceles triangles
which will enable us equate (SQR + SUT) in terms of (QRS + UTS)

SQR will be (180 - QRS)/2
and SUT will be (180 - UTS)/2
and
x will be
(180 - QRS)/2 + (180 - UTS)/2 - 90
= 180 - QRS + 180 - UTS - 180
= 180 - (QRS + UTS)
= 180 - 90
= 90
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by GMATGuruNY » Thu Jun 27, 2013 3:13 am
shailendra.sharma wrote: Image
An alternate approach:
Plug in for the angles, being sure to satisfy the rules of geometry and any given constraints.

Statement 1:
Since QR=RS, ∠RQS = ∠RSQ.
Here, the following two cases are possible:
Image
Since x can be different values, INSUFFICIENT.


Statement 2:
Since ST=TU, ∠UST = ∠SUT.
Here, the following two cases are possible:
Image
Since x can be different values, INSUFFICIENT.


Statements combined:
Since QR=RS, ∠RQS = ∠RSQ.
Since ST=TU, ∠UST = ∠SUT.
Image
Here, two random combinations for ∠RQS = ∠RSQ and ∠UST = ∠SUT yield the same result:
x = 45.
SUFFICIENT.

The correct answer is C.
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by lunarpower » Fri Jun 28, 2013 6:22 am
i received a private message about this thread.

most of the replies in this thread -- while perfectly correct and respectable solution methods to the problem -- don't really seem to address the original request, which was for guessing hints.

so ...

i hate to say this, but i don't see any "easy guessing hints" here. (even with perfectly symmetric statements, like these, the correct answer could still be any of C/D/E.)

more to the point -- you shouldn't put too much stock in "guessing hints" anyway -- because the entire point of Data Sufficiency, especially at higher levels, is for "gut feelings" to be wrong.
think about the way these things work. for instance, on virtually every mid- or higher-level DS problem on which it seems "obvious" that the answer is C, choice C turns out to be a trap. (in OG12, this happens in problems 105, 107, 108, 117, 123, 136, 144, 149, 150, 154, 168, and 173, among others!)

the best answer i can give here is a non-answer: you should manage time well enough so that you don't end up in this situation in the first place.

see, the mistake that lots of people make here is to think that they should have a "guessing plan", in the same way they'd have an earthquake plan (or other emergency plan).
there's a difference, though: an earthquake (or similar disaster) is something that just happens. it just befalls you; there's nothing you did to cause it, and there's nothing you can do to prevent it from happening. so, in that case, you need a plan.
running out of time on the GMAT, on the other hand, is not something that just happens. it only occurs if you neglect good time management (by sitting there, rather than quickly guessing and moving on, when you get stuck on a problem).

so, although it might be annoying, the best possible answer to this question is, "don't let your time management slip, and then you won't have to worry about this."
the second-best answer is that there's no easy guessing method (remember, that's the whole point); you'll have to try either algebra or plugging, as suggested by the other posters in this thread.

--

also, you said you had 1 minute to solve the problem.

maybe i am missing something here, but, if you already realized that the statements were symmetrical, then 1 minute should definitely have been enough time to try the "plugging" method.
i.e., to tell whether the answer is (d), just test statement 1 or statement 2 alone; you should figure out pretty quickly that neither individual statement is sufficient. boom, not (d).
why didn't you try to do that with the minute that you had?
should have been plenty of time, given what you'd already deduced about the situation in the problem.

(the "visualization" method -- in which you realize that each individual statement still allows you to "wiggle around" one of the segments that make up angle x -- is also, of course, doable within 1 minute. heck, that is doable in a few seconds. but not everyone is going to think of that, especially under pressure.)
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by shailendra.sharma » Fri Jun 28, 2013 9:34 pm
1) Ideally I should not be coming in a situation for need of guessing. I scored 51 on this test - probably test tried to stumped be with tough question in last one minute.

2) The visualization trick that srcc25anu suggested could have been savior if I could come across. And until GMATGuruNY post I did not know I could even do smart number picking in geometry questions too.

3) When I posed the question on guessing, I intended to know some trick out of Manhattan Advanced GMAT book.

In summary, I can take away lot of learning from this whole post.
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by lunarpower » Fri Jun 28, 2013 11:42 pm
shailendra.sharma wrote:1) Ideally I should not be coming in a situation for need of guessing. I scored 51 on this test - probably test tried to stumped be with tough question in last one minute.
well, there you go. see, you don't need to be perfect to get a perfect score.
nice!
2) The visualization trick that srcc25anu suggested could have been savior if I could come across. And until GMATGuruNY post I did not know I could even do smart number picking in geometry questions too.
testing cases (= "smart number picking") on DS problems in particular is THE single most important strategy/technique you can adopt for solving math problems.
you may get the chance to test cases / "plug numbers" on as many as 10 different DS problems on the same exam (!). there's just no other strategy or technique that can even come close, in terms of raw productivity.

there's also the following 3 techniques for multiple-choice problems:
* backsolving (= start from an answer choice; do whatever you can with the given information; if everything agrees with everything else, you have the correct answer)
* "smart numbers" (= choose your own values for undetermined quantities; solve the problem with those values; check ALL the choices for your answer)
* estimation (including the use of visualization and/or common sense to produce your estimate)

for all of the above techniques, the most important thing to know is that the techniques are general -- i.e., they do not fall within the boundaries of any subject or topic.
in other words, that you'd even make a statement such as "i didn't know i could do xxxxxx technique on geometry problems" is not ideal; you shouldn't associate these techniques with particular problem topics.
instead, whenever you get stuck, just think about whether you can use any of these alternative methods -- regardless of the subject/topic area of the problem.

it may be true that the techniques work more often in certain areas. (for instance, backsolving generally works on at least half of all multiple-choice word problems, and "pick numbers" solves virtually all remainder problems, especially in DS). however, the techniques are universal, so it's important that you not impose artificial limits on your ability (or willingness) to use them.

3) When I posed the question on guessing, I intended to know some trick out of Manhattan Advanced GMAT book.
when you look through that book, one main impression that you should get is that most of the things in there are NOT "tricks". i.e., they are not little rules/facts/shortcuts that you can memorize.
instead, they are mentalities that you can adopt in order to become a better problem solver across the board.
among the most important is the notion of pattern recognition. in fact, i would say that at least half of the stuff in that book can be characterized as "recognizing patterns", which is pretty much the opposite of what anyone might reasonably describe as a "trick".
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