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# Data Sufficiency: different answers but both correct

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Joined: 22 May 2016
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20 Jan 2019, 08:43
Can a data sufficiency question have different answers from statement 1 and statement 2?
Example (hypothetical question):
Find x?
(1) x - 9 = 10
(2) x - 9 = 15

As you can see, each statement is sufficient but we get different answers from each. Is this a possible GMAT question?

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20 Jan 2019, 23:26
1
jasmitkalra wrote:
Can a data sufficiency question have different answers from statement 1 and statement 2?
Example (hypothetical question):
Find x?
(1) x - 9 = 10
(2) x - 9 = 15

As you can see, each statement is sufficient but we get different answers from each. Is this a possible GMAT question?

Posted from my mobile device

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. So, for example, you cannot have x > 0 from one statement and x <=0 from another. Such a question would be considered flawed by GMAT standards.

The same for your example. From (1) x = 19 and from (2) x = 24. The statements clearly contradict each other. You own't see such questions on the test.

Strategies and Tactics for DS Section

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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26 Jan 2019, 14:43
1
jasmitkalra wrote:
Can a data sufficiency question have different answers from statement 1 and statement 2?
Example (hypothetical question):
Find x?
(1) x - 9 = 10
(2) x - 9 = 15

As you can see, each statement is sufficient but we get different answers from each. Is this a possible GMAT question?

Posted from my mobile device

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).
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18 Feb 2019, 14:03
1
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.
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18 Feb 2019, 15:24
1

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.
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18 Feb 2019, 15:49
1
fskilnik wrote:

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.

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.
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18 Feb 2019, 17:45
1
IanStewart wrote:
fskilnik wrote:

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.

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?

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).

IanStewart wrote:
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.

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.

IanStewart wrote:
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.

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.

IanStewart wrote:
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.

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.
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18 Feb 2019, 18:28
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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.
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05 Mar 2019, 02:30
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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..........

Responding to a PM:

Yes, I agree that if one statement gives me a definite YES, I will ONLY look for a NO from the other to get a may be. The other statement cannot give me a definite NO.

I do understand that GMAC reps don't necessarily take a definitive stand on this but what I think is that they might be playing the "don't say anything that you could be proven wrong on" game. Since some experimental questions that do not make the cut go into the OG, GMAC reps seems to be ensuring that something like that doesn't catch them unaware.

If contradictory information were possible on two statements, option (C) would make no sense (say the two stmnts are n = 1 and n = 0) and options (A), (B) and (D) would be questionable too (so what if n = 1, apparently it could be something else too such as 0 or for that matter 100 too so stmnt 1 is not sufficient).
Hence, there is no way a valid, scored GMAT question would offer contradictory data, in my opinion.
If option (C) exists, I should be able to consider it - whether I need to or not is beside the point.
For me, every question has to be a complete logical whole. Seeing that GMAT spends a lot of time and money on every question, I am sure that that is what they want too. Also, since GMAT's scoring and item-validating algorithms are extremely data driven, I would be surprised if they let unexplainable data go through (since options (A), (B) and (D) may be chosen randomly)
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20 Jan 2019, 15:47
Hi jasmitkalra ..... welcome to the community.

The answer is no. You are definitely not going to see such Qs in any GMAT real test.
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26 Jan 2019, 16:26
Hi ccooley,
Thanks for your nice tips. But how do you be sure that x could be negative too in statement 2? Thanks__

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26 Jan 2019, 16:34
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
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30 Jan 2019, 13:08
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__

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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.
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30 Jan 2019, 21:42
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__

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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.
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Updated on: 18 Feb 2019, 13:09
Bunuel wrote:
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..........
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Originally posted by Asad on 30 Jan 2019, 22:04.
Last edited by Asad on 18 Feb 2019, 13:09, edited 1 time in total.
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09 Feb 2019, 08:56
jk11 wrote:
Can a data sufficiency question have different answers from statement 1 and statement 2?
Example (hypothetical question):
Find x?
(1) x - 9 = 10
(2) x - 9 = 15

As you can see, each statement is sufficient but we get different answers from each. Is this a possible GMAT question?

Posted from my mobile device

The two statements never contradict each other in official questions. This question seems to be poorly written. What's the source?
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09 Feb 2019, 09:04
CAMANISHPARMAR wrote:
jk11 wrote:
Can a data sufficiency question have different answers from statement 1 and statement 2?
Example (hypothetical question):
Find x?
(1) x - 9 = 10
(2) x - 9 = 15

As you can see, each statement is sufficient but we get different answers from each. Is this a possible GMAT question?

Posted from my mobile device

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.
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18 Feb 2019, 13:01
Bunuel wrote:
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

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_

Hi Bunuel,
did you miss my question?
or, is my question weird?
I think, my question is a pertinent point for knowing DS!
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18 Feb 2019, 16:15
IanStewart wrote:
fskilnik wrote:

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.

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?

So, what is the answer of this DS according to GMAC?
Thanks__
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18 Feb 2019, 17:11
So, what is the answer of this DS according to GMAC?

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.
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Re: Data Sufficiency: different answers but both correct   [#permalink] 18 Feb 2019, 17:11

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