Testluv wrote:... and sometimes we need to use that fact to correctly answer a question. For example, consider:
What is the value of x?
(1) x is positive or zero
(2) x is negative or zero
Obviously, (1) and (2) by themselves are not sufficient. What about in combination? Because on the GMAT the statements can't contradict each other, x must be zero, and the correct answer is (C). However, if you argue that the statements can properly contradict each other, then you would have to choose (E).
Dear Testluv,
I said I would not come to this anymore, but I will make an exception because you are a teacher (so am I) therefore I think this could be of real use to you.
Ian and yourself mention explicitly that all official GMAT´s DS problems are "coherent" (in the sense already understood from all above) and I tried to explain that this could not be true (only) in a very special case: when the problem has (or, better said, should have been) already finished before the student must consider the statements together. In other words, when at least one of the statements is sufficient to answer the question asked.
More than that, I said that I have already seen that occuring, but it is true that the official guides (or paper-based tests) in which this occurs are really old, because I´ve started to give private classes in year 2000 and from the very beginning I created a special database (now) with more than 3,800 exercises divided into PS/DS type, level of difficulty, time expected to be solved, subject involved AND BIBLIOGRAPHY.
Anyway, your example does not refute any of my arguments, because when we really need to study both statements together, which is the case, I said the statements cannot be contradictory. And you agree. We all agree.
There are somethings nice in Ian´s last reply, one of them is NOT to consider official guides and GMAT rules as absolutely perfect. I show to my students problems related to bad-created problems almost daily, one easy example that you find in many GMAT official questions is like:
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If y is not zero, what is the value of x/y ?
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Although this is not "wrong", when we ask "what is the value of x/y ?" we MAY (and therefore we SHOULD) consider that the fraction is well-defined, that is, y is not zero FOR SURE, nobody needs to say to us at the beginning of the question!
Another typical example is:
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What is the percentage of ...
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And the choices should be
First Option
(A) 0.2
(B) 0.3
etc
Second Option
(A) 20%
(B) 30%
etc
GMAT usually puts the options (choices) as
(A) 20
(B) 30
etc
and this is really annoying, because the answer to the question: what is the probability that a fair coin turns out to get a "head" face is 0.5 or 50%, it is not 50.
I know the GMAT "thinks" that when he asks what is the percentage... he considers the answer 20 AS 20 PERCENT, but it is "ugly", much more ugly than creating a chart flow that makes someone VERY carefull as magnus to believe that A and B are not symmetrical. The answer is (A) and (B) ARE symmetrical, because if it wasn´t, the Data Sufficiency would be flawed in the sense that there would not be the same "probability" to each alternative choice and this would be at least very non-elegant. The fact is that the "chart flow" was not made by someone as careful to details as magnus and he is suffering because he is far above-average, even considering people who wrote the official guides, for sure. I can be certain of that because when I read the solution to many GMAT problems in the official guides, I see that some answers are really weak, they are right but they are the "stupid" way of looking into things/concepts. That´s why I don´t give them the credit that magnus does but, of course, I have much more experience than he has (I guess), therefore I understand he does not have any reason to believe that he should put his belief in me "versus" on the almighty official guides. I respect that but I must say, not being humble at all, that my students believe in me much more than in the official guides, from the simple fact that I show them frequently better ways of looking into the whole game: strategy, concepts, solutions, etc.
Let me show you a small smart stuff that I will use to "prove" to you that I am that alert to using rigour/care to help my students:
In the DS problem where the question stem is "Is a < = b ?" , if you would like to prove that the (say) first statement is not sufficient, you have to bifurcate the statement, that is, you have to show that there is a possible a such that it is less or equal to b AND another a such that a is greater than b, right?
BUT in the DS problem where the question stem is "Which is greater, a or b?" , if you would like to prove that the (say) first statement is not sufficient, you MAY (if possible) take JUST one example of a and b EQUAL. Why? Because then you cannot say which one is greater, you can say ONLY that "no one is greater than the other" but this does not answer the question asked, because the question asked "which is greater" meaning, "you have to choose between a and b", and you can´t. In other words, if you find a (possible) example of equality, for the exercise to be well-created, it is NECESSARY to be able to bifurcate in the common sense (that is, with an example of a greater or equal and another example of b greater) but if the student, in the especific question mentioned in this paragraph, finds an equality, he may (and should) spare time because the bifurcation is guaranteed even if he used just one example to get the equality.
This is the sort of care that I have and, please, do not try to refute my points, ok? I took my time here to try to put my positions clearer to you all, not because I want to check if they are right. That means that I cannot be wrong? No, I can be. But I have been asking and explaining this sort of thing to my students, many of them got from 96% to 98% in their real quant section of GMAT, many of them studied at the best engineering/science schools in Brazil, many of them were/are as careful as magnus and they were always trying to see me "in trouble" with their questions, not because they would like to see that I am not perfect, but because they would really want to receive an answer that they could trust and that they could use, for their advantage, during the "D day" at the "D moment" of doing the real test. And that all means really a lot. I had no 20 students with average-capacity in the class, I am used (10 years) to private lessons with students that are probably much more intelligent than I am, and I LEARNED with them not only through good math solutions, but also through great insights into the whole test environment.
I hope I do not pass as an arrogant guy, really. I am writing all this because I believe it is a contribution of someone who looks carefully to the GMAT for very many years, and I am as careful to what GMAT official guides say as to what I myself say. In my online course, if a student sees something wrong or imprecise in what I wrote or explain (and I am the sole writer and creator of my website, my online course, really everything I put/write there), I change it as soon as he/she writes me about it, and I give bonuses of credit questions to them, because my sense of "perfection" is always increasing and I count on people to help me avoid misunderstandings.
In that sense, if you read some posts I put here (why not, please do!) and you find something wrong, please tell me. Even a small detail, and I will publicly thank you for that. I will be happy to do that because if I know people are reading what I explain with full attention, that means that I am really able to "deserve" this attention, and if, after your correction, my (our) solution is perfect, than we all benefit, even the other readers, for sure.
Well, please do not try to find flaws in what I wrote, because I am really not willing to come back at this post again trying to make my rebuttals, but if you like something that I wrote, please say so because I am a human being, and that means that I love to be seen as someone who makes a difference. I am trying (also) here.
Regards to you all,
Fabio.
