Data Sufficiency: different answers but both correct

This will never happen on the GMAT. You might see unofficial questions that behave like this - if so, that question is poorly written!

Since you know that this will never happen on the real GMAT, you can actually take advantage of that knowledge on certain problems. For instance, suppose that you're solving this problem:

Is x positive?
(1) x = 2
(2) |x|-x/2 > 0

The first statement is easy - you know x is positive. So that's sufficient. The second statement, you might notice right away that x could be negative. You actually don't have to keep testing cases at this point! Once you know that x could be negative, you know that this statement is insufficient. That's because the statements won't contradict each other: it'll never be the case that (1) says x is always positive, but (2) says x is always negative. The only possibility is that (1) says x is always positive, but (2) says that it could go either way. So the answer would be (A).

Hi ccooley,
Thanks for your nice tips. But how do you be sure that x could be negative too in statement 2? Thanks__

Posted from my mobile device

One important question to Bunuel, ccooley,
Here is an example:

Is x positive?
1) definite yes
2) i have no idea
My question: statement 2 may give us only "yes" (but not "no" alone) or both yes and no simultaneously. As far we know that statement 1 and statement 2 can't contradict each other. So, why do we try to find out "yes" from statement 2 since we already know that statement 1 gives only "yes"?
Thanks__

Posted from my mobile device

Hi Bunuel, hope you are well. Did you miss my question?
I think, this question is too much important to know to solve the DS in quickest way.

If you have a definite YES from (1), it means that it's sufficient. Now, (2) can give YES too, which would mean answer D, OR sometimes YES, sometimes NO, which would mean answer A. (2) cannot give a NO answer in this case because it would mean that (1) and (2) contradict each other.

Hi Bunuel,
Thanks for your feedback. Actually, my question is somewhat different to your feedback! My question is why do we try to find out YES in statement 2 in this example? Finding YES in statement 2, in this case, is just waste of time, isn't it? Because we have an automatic YES in statement 2 in case of statement 1 (since statement 1 is only YES)!

Here is my logic again: Statement 2 can't give ONLY NO in this case, because, then, both statement will contradict each other. So, if we are 100% sure that there is no NO value in statement 2 (specifically in this example), then we must not try for finding YES value in statement 2 !!! It'll be just waste of time finding YES value in statement 2. Without finding YES, I can definitely say: it is D (Correct option). Am I right?
Thanks_

Edited..........

The two statements never contradict each other in official questions. This question seems to be poorly written. What's the source?

Yes, this is not possible. I just wanted to confirm. This question does not have any source, i made up this hypothetical problem to ask my question. Thanks.

Hi Bunuel,
did you miss my question?
or, is my question weird?
I think, my question is a pertinent point for knowing DS!

Asad - if I understand your question correctly, you are correct. I think ccooley gave a good example above, but just to be clear: if you see, say, this question:

Is x < 0?

1. x < |x|
2. |x - 0.5| + |x + 2.5| = 3

then Statement 1 tells us that x is negative (since x = |x| is true any time x is 0 or greater). Now when we look at Statement 2, since we know the two statements can never contradict each other, it absolutely must be possible for x to be negative in the equation in Statement 2. There is no need to spend any time proving that. All you care about now, when looking at Statement 2, is whether x can be positive (or zero). That is, if Statement 1 gives us a definite "yes" answer, then when looking at Statement 2, a "yes" answer must be possible for sure -- we only need to check if a "no" answer is also possible. And here, Statement 2 is not sufficient, since x can be equal to any positive value less than or equal to 0.5 (Statement 2 means that -2.5 < x < 0.5), so the answer is A.

Dear AsadAbu ,

You have asked (through a private message) our position on this matter.

This is a delicate issue (I have already exchanged posts with other experts on this matter) because "each statement alone is sufficient to answer the question asked" does NOT guarantee, by itself, that the unique answers obtained in each statement must be the same. I mean, logically speaking, there is not such a restriction. (The consideration of a "unique universe for both statements and the question stem pre-statements" is not explicitly mentioned in the Data Sufficiency official rules. In other words, this is not a "law" to be obeyed, it is one possible interpretation that one may decide to follow.)

On the other hand, it´s highly improbable that you will find any OFFICIAL GMAT quantitative section question in which the correct answer is D and in which each statement does not have the same unique answer as the other statement unique answer. The expression in bold was used by an official GMAT representative when I (myself!) made exactly the same question to her many years ago.

In short: in the official exam (i.e., where it matters), you may expect the same answers when each statement alone is sufficient to answer the question asked.

Regards,
Fabio.

P.S.: in my PERSONAL opinion, "same answers" (when (D) is correct) is much more elegant. I do NOT want to go into this any further. Please respect that.

There is such a restriction, and for a good logical reason. Imagine the following DS question:

What is the value of x?
1. Either x=3 or x=4
2. Either x=5 or x=6

What is the answer to this DS question? It would be perfectly reasonable to say "using both statements, no value of x exists, so I've answered the question and the answer is C". But it would be just as reasonable to say "using both statements, I can't solve the question because no value of x exists, so the answer is E". There is no logically correct answer to this question.

So it always must be true in any DS question that the two statements are logically consistent - it needs to be possible for both statements to be true simultaneously, since sometimes test takers will combine the statements. If the statements are not consistent, then you can have situations where a question has two perfectly justifiable 'correct' answers, which is obviously something that can't happen on the GMAT.

So, what is the answer of this DS according to GMAC?
Thanks__

If my post above wasn't clear, I was explaining why this kind of question is illogical. It does not have a correct answer. So it could never be a real GMAT DS question.

The example shown does not apply. All the issue is related to a DS question in which the right answer is (D). It´s not the case here, because each statement alone is NOT sufficient to answer the question asked (in a unique way).


According to DS rules, when it is questioned "what is the value of x?" , we must consider a statement sufficient if, and only if, the statement gives us only one answer, in this case, a unique numerical answer.
If each one alone is not sufficient, THEN AND ONLY THEN we must consider both statements together and, in your scenario, the fact that there is no value of x that satisfies both statements together implies that the problem must be considered wrong, in other words, it is not well-stated, in other words, there is no answer. Not C, Not E, Not A, Not B and Not D.


Yes, this is a nice argument for the "elegancy" I mentioned. Unfortunately it is a strong argument but, IN MY OPINION, not a "smocking gun". Please respect that.
I repeat: I wish I had a conclusive remark to save the day or, of course, I would like YOU to have one. Till now, I couldn´t have one that would close the matter according to MY level of rigor, so to speak.


In the case in which (D) is the right answer, we would have finished the problem before any logical trouble starts. But, again, I agree your vision is the nicer, because if we agree on your terms, alternative choice (D) does not have a "special treatment". In terms of "symmetry beauty", the Oscar goes to your argument. No doubt!

Well, nice discussion Ian. It´s a pleasure to see you are still active!

Kind Regards,
Fabio.

Thank you for the kind words, Fabio. Even when one statement is sufficient alone, it still always needs to be true in GMAT DS that the statements make sense when taken together, because test takers who do not recognize that one statement is sufficient still must logically be able to think about the two statements simultaneously. They can't arrive at a logically nonsensical situation when they combine Statement 1 and Statement 2. If you look over every official GMAT DS question ever published, I guarantee you'll see that the two statements are consistent in every case. For test takers, one consequence of that is they can take advantage of the DS shortcut ccooley and I described in separate posts above.

Hi IanStewart,
Thanks for your creative example, but I have still some confusion in your explanation. I'll be really grateful if you eradicate my confusion.
In the highlighted part, could you tell me how did you get C, please? No value doesn't mean that it is sufficient, because sufficient means I've enough information to narrow THE QUESTION down to ONE ANSWER!. So, did you find one specific value/ONE ANSWER by combining both statements?


• When statement 1 sufficient then it is A
• When statement 2 sufficient then it is B
• When statement 1 & 2 Separately sufficient then it is D
• When statement 1 & 2 (after combining) sufficient then it is C
• But, E doesn't mean something is sufficient; actually E means C is insufficient/not sufficient!
So, in your example, C is insufficient/not sufficient (meaning we can't get one specific value for this question stem). So, the answer of your example is E to me.

One most important thing about the definition of insufficient/not sufficient is: So far I know insufficient/not sufficient doesn't mean the following :
• not good enough
• I can't solve
• need more info
• I don't know
Insufficient/not sufficient means: There are TWO OR MORE POSSIBLE ANSWERS to THE QUESTION.
So, what is your thinking in my explanation?
Thanks__