Is this a pattern in GMAT?

Hi samirabrahao1,

Data Sufficiency questions test a number of skills that are not, strictly speaking, "math" skills. Those skills include attention-to-detail, organization, accuracy, thoroughness, the ability to prove that your thinking is correct, etc. Many DS questions can be solved by TESTing VALUES, but you have to be thorough with your work. In real life, there are more than just positive integers, so you have to think about more than just positive integers when you're dealing with those types of questions (and in certain PS questions too).

Every question that you'll face on the Official GMAT is meticulously designed, and sometimes the specific wording involved can help you to choose which values to Test. For example, if we're told that X is an integer, then it would make sense to TEST any/all of the following: positive integers, negative integers, 0, odd integers, even integers. If a prompt tells us that X > 0, then you should look to TEST at least one integer and, in certain cases, a fraction.

If you have specific questions that you're interested in, then you should post them in the appropriate Forums here. As long as they're not questions that you've seen on an Official GMAT, then you can post whatever questions you like.

GMAT assassins aren't born, they're made,
Rich

Thanks for your reply. All thats been said here has further strengthened my opinion that some answer explanations are greatly misleading. Do you have any specific thoughts on the answer explanations contained in the GMATPrep software?

I don't think anyone here would call the OEs "misleading". Have you seen any explanations that are misleading (by the way, do you mean inefficient, as in "there's a better way")?

Hi samirabrahao1,

By their design, many text-based explanations are going to be 'technical' in nature (since there is always a technical reason for why the correct answer is correct). Those explanations can sometimes be remarkably 'thick' and even confusing, even if they are correct. To that end, if you're working with materials that you think are too technical in nature, then you would likely find it beneficial to invest in some new resources. By extension, if you're focusing on approaching GMAT questions in overly technical ways, then you are likely missing out on faster, "easier" approaches that focus on Tactics.

GMAT assassins aren't born, they're made,
Rich

I mean when the question tells you that 0 < X < 2 and you presume X could be a fraction, but the answer explanation tells you that X = 1. Or maybe when they tell you that the square root of 2X² is 2√x. The questions themselves may be thoroughly revised and tested, but does the same apply for the AEs??

Yep, I totally agree with you. I mainly use the explanations to help me find errors while solving equations and the like. I'm only trying to address what I think could be a pattern regarding number property questions, and I used some of the answer explanations to support this idea, but people don't seem share the same feeling so nevermind. I just want to make clear that I'm not putting GMAT's quality into question here, that would be insane.

Do not abandon fraction numbers in DS, ever. If you assume values to be integer when nothing is specified then you will assume that 1/x is always less than or equal to 1. This approach will surely land you in one of the trap answers laid out specifically for people not thinking about x not being an integer value.

Sure, there are questions where assuming different number type is not important but that is for you to decide, no question will ever tell you that this question can be solved without bothering about the number types.

Thanks for the information.

Even though what you said makes a lot of sense, my main point here is that I have yet to come across any of said traps during my studies. Let's see how things stand in a week, when I've actually taken the real test for a change.

Dear samirabrahao1,
I see you have gotten many good responses and I am also happy to respond.

I think you are confusing the issue of categories of numbers with the delicate issue of picking numbers. You see, it's one issue to say: what kinds of numbers are allowed in the problem? In the question you cited, that would be all numbers, every number on the number line between zero and two. It's an entirely separate issue to say: what numbers would be strategically sound choices to pick as counterexamples that would allow us to eliminate choices quickly. It's extremely important not to confuse these two things. In this problem, every fraction & decimal between 0 and 2 is allowed, but it may be that the integer 1 is highly strategic choice to make a quick determination. Again, those are two very different issues.

The question you cited was really a question about number sense. Here's how I would think about it.

Adding 2 to a number makes every number on the number line bigger. Therefore, x + 2 is greater than x always.

Multiplying by 2 makes positive numbers more positive and negative numbers more negative. Therefore, 2x is greater than x.

Squaring is the wild card. Positive numbers greater than 1 get bigger when squared, but positive fractions between 0 and 1 get smaller.

I am a little unclear on the exact question you are citing, and what the answer choices might be. I would say that if this is a Magoosh question or the question of any other private prep company, or if it is an official question, then it is 100% legal to post the exact question, as long as you cite your source.

Mike

Mike, I bought a lot of questions from the official website and I have not bookmarked this particular one, but I will make sure to post an example the next time I have a subject to bring to this forum.

I'd like to highlight a particular topic you brought up:

"...what numbers would be strategically sound choices to pick as counterexamples that would allow us to eliminate choices quickly. (...) In this problem, every fraction & decimal between 0 and 2 is allowed, but it may be that the integer 1 is highly strategic choice to make a quick determination."

The part I underlined above is exactly what I wanted to put into question, and I offered some arguments to support this. However, with all thats been said, it seems pretty clear that we cannot replace the word "may" in your sentence with a word that offers a little more "assurance", which is unfortunate :D

Maybe this is a stupid question if taken out of context, who knows? But I wanna make it very clear that the answer explanation for the question we've been using as an example states that "because 0 < X < 2, then X = 1", but the question did not contain the information that X was an integer, which makes the answer explanation highly dubious from my point of view.

It was an easy question that could have been answered in less than 20 seconds if they had provided that info, but they made me spend almost a minute trying to find any "traps", ONLY to state that X is an integer in the answer explanation.

Dear samirabrahao1,
I'm happy to respond.

I think it's extremely important to continue to distinguish mathematical necessity from strategic choice.

If the question specifies some condition and asks whether this condition is true for all x such that 0 < x < 2, then in order for it to be true, it would have to work for every single x in that range. We may be able to figure out whether it works purely with number sense, without plugging anything in. If we have to plug something in, then of all the infinite numbers on the number line greater than zero and less than two, probably the single most convenient choice is x = 1. It's not a matter of mathematical necessity that x be an integer, but for the purposes of a strategic choice, x = 1 might be extremely quick choice to verify or eliminate some option.

I don't know what your original question was, but I will make up this similar question. This is probably a much simpler question.

For all x such that 0 < x < 2, which of the following is always greater than x?
I. 2x
II. x + 2
III. x^2
Then, the answer choices would be various combinations of I, II, and III. As I explained in my previous post, x + 2 is greater than x for all numbers on the number line, so II is always true. For all positive numbers, 2x > x, so I is always true. Suppose we were stuck on III. Is III always true? Well, if I plug in x = 1, I get 1^2 = 1, so x is equal to x^2 for that value. Equal to is not greater than. At that one value, we know option III is not true, so it can't possibly be always true. One counterexample is enough to establish that something isn't always true. That single plug-in is enough to determine that the full answer could only be I and II.

Once again, it was not necessary at all that x be an integer. We could have plug in any value of x. You certainly could have plugged in 1.9999 or 1.3875 if you wanted to. Have fun squaring those without a calculator! The best strategic choice by far was x = 1, because that immediately led to a very clear answer. If you can do the math quickly in your head, that's always a better strategic choice: as it happens, that occurs far more frequently with integers.

If x = 1 or x = 0 is in the allowed range, these often would be a very simple choice. You see, there's an art to picking numbers. I think you want some clear guidelines, and this is a matter of intuition and creativity. It's not a science---it's an art.

I think before we go too much further in this conversation, we should have some other example problems. Math happens in the details. I think you are getting confused between points of necessity and points of strategy. Many mathematical folks who write solutions are not hyper-clear on making this distinction explicit to their readers.

Does all this make sense?
Mike

Mike,

I think the whole point is trying to come up with the strategy you speak of. It would be useful if I could safely establish that, when the number type isn't specificied, the variables are most likely integers, and work through the test with that taken for granted. Indeed, there could be exceptions, but how far would I get by thinking in a more simple, straightforward way? I am aiming at only 600, 630 at most, not 700+, so I'd happily walk into a trap if that meant saving precious time and if this was a hard question. Do you think my line of thought is correct, or do you think I should make adjustments? It goes without saying that I'm taking the test next week. I've only had a month to prepare.

Dear samirabrahao1,
I'm happy to respond.

My friend, I still don't think you fully understand the distinction I drawing. The strategy of which I speak does NOT involve making blanket assumptions about the variables. You always have to keep in mind all possibilities for the variables.

The strategy of which I am speaking applies only in "must be true" problems, a small subclass of problems with variables. In such a problem, you can eliminate something if you find a counterexamples. As I have said, integers can make simple counterexamples, only because they are very quick to test. We are not assuming that, for example, x = 1 is the only possibility, or that only integers are possible. We are just taking a moment to see what happens at that one value, because what happens at that one value might be enough to eliminate a case, as it did in the problem I proposed above.

Again, I think you have having trouble understanding this, because we are having a discussion at a very high level of abstraction. I think in order to understand it, we need to discuss individual problems. You could link to problems, or find other problems posted on GC and invite me to respond to your queries.

Also, I would caution you against aiming for a 630, even if that's all you need. Aim for the very best you can do: that is one of the habits of excellence. Do not underestimate the GMAT in any way. Do not set any upper limits to your efforts or aspirations. Commit yourself to doing your best and give 110% in your GMAT preparation between now and your test. The GMAT is very tough, and it has a way of clobbering the folks who set their sights and their ambitions low.

Does all this make sense?
Mike