Data Sufficiency

faraz_jeddah wrote:What is the area of the quadrilateral ABCD?

1) Each diagonal bisects the other diagonal into two pieces that equal √ 2
2) Each side is equal and has a length of 2

EDIT: Answer I picked was C but OA is A

by the way, guys, this "spoiler" stuff messes up the forum experience for people who use tablets (ipad, etc.) if someone is using a tablet, then it's actually impossible for him/her to see what's behind the "blackouts". just fyi, probably shouldn't do that.

if the official answer to this question is (a), then the official answer is wrong.
as Matt has pointed out, "diagonals bisect each other into equal parts" is true of ANY rectangle. (if you don't see why, just draw a bunch of rectangles.)
so, under condition #1, the rectangle can range anywhere from a square to a long and skinny rectangle with almost no area. that's not sufficient.

so you are correct, and the answer key is incorrect. the answer to this problem (as transcribed here, at least) is (c).

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random nitpick:
the wording of statement 2 is funky here, too. "each side is equal" is a nonsense statement, since "equal" is not something that can apply to a singular thing. if this fact were on the official exam, it would say something like "all side lengths are equal" or "any 2 sides have the same length".

statement 1 has a bigger issue: "two pieces that equal √2" is ambiguous. when i see that statement, i don't know whether that means (a) each piece measures √2 units, or (b) the sum of the pieces is √2 units.

so, yes, there are problems with this problem.

Matt@VeritasPrep wrote: if you're currently at the 50th percentile in math, the questions you need to sweat are the ones from the 45th percentile to the 60th, not the ones above the 85th.

this is a dangerous game to play, because it's pretty much impossible to detect the "percentile" of a question (and, more importantly, because thinking about that kind of thing at all is nothing but a distraction from the things that actually matter).

in fact, it's often hard even to tell whether a question is in the top or bottom half of the difficulty spectrum, let alone which approximate "percentile" it's in.
e.g., the DS problems labeled #53 and #58 in OG13 were labeled #165 and #171, respectively, in OG12. Quick! Are they in percentile 50-99 (as the OG12 rankings would seem to indicate) or in percentile 1-49 (as the OG13 rankings would)?
ummmm.... yeah.

and there's also, simply put, the fact that there's no such thing as an "Nth percentile test taker" on a micro level. on a macro level obviously that concept exists, but it's just not a thing when it comes to individual problems.

i.e., almost every student i've ever taught has distinct strengths and weaknesses. so, even if you knew the "percentiles" of the problems, that still wouldn't be a useful guide for any individual student, since there would be some subjects/topics in which (s)he would nail the top-level questions but others in which (s)he would founder on much (supposedly) "easier" questions.
it would be absurd to think that any given test taker would be best served by doing the "Nth percentile questions" across the board and ignoring the others -- even if you knew those rankings exactly (which, of course, you don't).

it's best simply not to think about "percentiles" at all. who cares?
just try to solve the problems.

as for judging whether a problem is too easy or too hard for you, well, that's where the "three hints" protocol (mentioned earlier) comes in.
i.e., if you still don't understand something after a fair amount of hand-holding/spoon-feeding, then it's best to leave it for the moment and come back to it later.

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matt wrote:

That does lead me to one issue I have with the boards -- probably a case of "When in Rome ..." for all of us -- and that's that our answers are too thorough and direct.

i mean, i feel what you're saying here, but i'm on the other side of this particular fence (= i'm on the "thorough and direct = good" side of the fence).

see, if i knew that this was most people's first encounter with the question at hand, i'd probably be more indirect myself. but i usually assume that, if someone has taken the time and trouble to post about a problem on a public forum, then (s)he has been puzzling over that problem for a good long time already.
if that's the case, then, i would imagine, this student would get really annoyed if i only "dropped hints" as to how to solve the problem. at that point, if i were him/her, i would just be like "i've had it with this problem, someone tell me where i'm going wrong".
but that's just me.

^^^ the above is also why i don't generally answer threads without specific questions about a problem. if a student just posts a problem and says "explain this problem", then i'd prefer that they think it over enough to formulate some specific questions first.
but (in my opinion anyway) if a student has already thought about the problem enough to produce a specific question(s), then it's time to ... well, just answer the questions.

Matt@VeritasPrep wrote:EDIT: Looking at how long my response is, I took it to PM; otherwise this thread may quickly bloviate out of control.

i was going to suggest that, yeah.

(remember, though, everyone who's subscribed to the thread will see the first version of your post... lol)