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# Data Sufficiency: different answers but both correct

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02 Mar 2019, 10:09
As I mentioned above, the question doesn't make any sense. So it is pointless to debate what the "right" answer should be, because it's like debating "what colour is the number 5?" For the question I posted, you could argue "I cannot find a unique value of x, therefore the answer is E". That is a good argument. I think most mathematicians would instead argue "no value of x exists, therefore I have answered the question using both statements, and the answer is C". That is also a good argument. That is why you can simply never see a DS question like this on the GMAT.
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02 Mar 2019, 11:23
IanStewart wrote:
As I mentioned above, the question doesn't make any sense. So it is pointless to debate what the "right" answer should be, because it's like debating "what colour is the number 5?" For the question I posted, you could argue "I cannot find a unique value of x, therefore the answer is E". That is a good argument.I think most mathematicians would instead argue "no value of x exists, therefore I have answered the question using both statements, and the answer is C".That is also a good argument. That is why you can simply never see a DS question like this on the GMAT.

But the highlighted part can't be happen in DS because of my above explanation. We all know that there are 2 types of DS. They are:
1/ value types question (what is the value of x?)
2/ yes/no question (Is x positive?)

You example is value types question. So, our goal is to find the specific value. But, you are going to say no value , which implies "value types question". So, should I correlate the yes/no question with value types question?
It seems that i am going to argue with you, but i am very excited/curious to know this types of problem.
Thanks___
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02 Mar 2019, 11:42
But the highlighted part can't be happen in DS

Yes, that is my point. This kind of question cannot show up on the GMAT, because it is not clear what the right answer to such a question should be. And there isn't any reason for either of us to spend time discussing what the right answer is to a question that has no right answer, nor is there any reason to spend time discussing the right answer to a question that can never appear on the GMAT.
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02 Mar 2019, 12:11
IanStewart wrote:
But the highlighted part can't be happen in DS

Yes, that is my point. This kind of question cannot show up on the GMAT, because it is not clear what the right answer to such a question should be. And there isn't any reason for either of us to spend time discussing what the right answer is to a question that has no right answer, nor is there any reason to spend time discussing the right answer to a question that can never appear on the GMAT.

Thank you so much for your feedback in the debatable question!
I'm really sorry to bother you! I'm writing here because it seems that the correct choice is E. But, someone may establish the most prominent mathematicians' thinking in this types of question. What I've written in this link is what the GMAC actually says. I should not care about what the prominent mathematicians say, should I?
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02 Mar 2019, 14:49
Top Contributor
IanStewart wrote:
...because it's like debating "what colour is the number 5?"

If you ask me, that 5 looks black
QED

*drops microphone, and then smartly inserts folder bologna into tuxedo breast pocket.

Nice to see you back on the forums, Ian!!
You always provide valuable insights.

Cheers,
Brent
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02 Mar 2019, 23:21
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

It is IMPOSSIBLE to have contradictory information between the two statements OR between the question stem and statements. Hence this question does NOT qualify to be a GMAT Like question

Question : Find x?

Statement 1: x - 9 = 10

i.e. x = 10+9 = 19

SUFFICIENT

Statement 1: x - 9 = 15

i.e. x = 15+9 = 24

SUFFICIENT

As per the logic of DS questions the answer to this question should Be

Option D

But since this question has different values of x obtained from the two statements therefore it is a BAD question to practice.

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05 Mar 2019, 02:30
1
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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05 Mar 2019, 02:50
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..........

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.

Could you explain me the above by giving an authentic example, please? Thnaks__
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05 Mar 2019, 06:11
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..........

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.

Could you explain me the above by giving an authentic example, please? Thnaks__

That is the whole point. We can't have an "authentic" example of this kind. It is hypothetical only.

What is n?
Stmnt 1: n = 1
Stmnt 2: n = 0

If stmnt 1 gives n is 1, and we take it at face value and say that stmnt 1 is sufficient to give the answer, then suddenly, how can stmnt 2 say that n = 0? If another value of n were possible (n = 0), how did we conclude that n is indeed 1 using stmnt 1? This just means we don't have sufficient data and hence neither statement should be enough to answer. What then stops n from being 100 or 345? We probably don't have information about that too. When we say that the value of a variable is 1, it has to be just that.
Hence, with contradictory data, options (A), (B) and (D) all become questionable.
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09 Mar 2019, 01:14
A DS question is answered in such a way that everybody should logically agree on the same answer. But the instructions for DS does not be exactly interpreted in this way. It only asks whether the statements are independently or together sufficient to answer the question or are insufficient independently or together.

Consider this:

stmt 1: n=4, stmt 2: n=-4

Some may dismiss this as contradictory.

They do not contradict if n is a square root of 16. So "D" is an "authentic" answer. . In addition to "authentically" saying that D is the right answer we can also "authentically" say that E is the answer as some others may say that information is not sufficient.

Some may say that C is the answer assuming common sense for the missing info.

Some may be able to reason that A alone is sufficient or B alone is sufficient.

I wonder what is the position of GMAC on this.
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09 Mar 2019, 03:43
SravnaTestPrep wrote:
Consider this:

stmt 1: n=4, stmt 2: n=-4

Some may dismiss this as contradictory.

They do not contradict if n is a square root of 16.

Those statements do contradict each other no matter what you know about n. n cannot be equal to two different numbers simultaneously; if n is a square root of 16, then n is equal either to 4 or to -4, not to both at the same time.
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09 Mar 2019, 04:34
IanStewart wrote:
SravnaTestPrep wrote:
Consider this:

stmt 1: n=4, stmt 2: n=-4

Some may dismiss this as contradictory.

They do not contradict if n is a square root of 16.

Those statements do contradict each other no matter what you know about n. n cannot be equal to two different numbers simultaneously; if n is a square root of 16, then n is equal either to 4 or to -4, not to both at the same time.

Two equally objective persons may deduce logically the value of the same variable in a different way. It may later be resolved. In this sense, there is no precise value for a variable even simultaneously. So you may take the value of n arrived by 2 independent persons which an be resolved and both be used in a consistent way using a single formulation. In other words they produce exactly the same effects.
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09 Mar 2019, 09:28
SravnaTestPrep wrote:
IanStewart wrote:
SravnaTestPrep wrote:
Consider this:

stmt 1: n=4, stmt 2: n=-4

Some may dismiss this as contradictory.

They do not contradict if n is a square root of 16.

Those statements do contradict each other no matter what you know about n. n cannot be equal to two different numbers simultaneously; if n is a square root of 16, then n is equal either to 4 or to -4, not to both at the same time.

Two equally objective persons may deduce logically the value of the same variable in a different way. It may later be resolved. In this sense, there is no precise value for a variable even simultaneously. So you may take the value of n arrived by 2 independent persons which an be resolved and both be used in a consistent way using a single formulation. In other words they produce exactly the same effects.

But, how do you come up with 2 different values simultaneously?
Are you talking about the following example?
What is the value of n?
1) $$n=4$$
2) $$n^2=16$$
Here statement 2 gives 2 values (e.g., 4,-4). Statement 1 directly says n=4. So, Why different people takes the value of n=-4 in statement 2?
Thanks__
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09 Mar 2019, 10:14
SravnaTestPrep wrote:

Two equally objective persons may deduce logically the value of the same variable in a different way. It may later be resolved. In this sense, there is no precise value for a variable even simultaneously. So you may take the value of n arrived by 2 independent persons which an be resolved and both be used in a consistent way using a single formulation. In other words they produce exactly the same effects.

I don't understand your post, but letters in GMAT DS questions are not 'variables' (except on rare occasions when they define a function f(x), or similar situations). Letters in GMAT DS questions stand for single unknown values. If you see an equation like n^2 = 16 in a GMAT DS question, then we can be certain that the value of n is either 4 or to -4, we just don't know which. But it's not equal to both values simultaneously; n can only have one value.

I'll agree that two objective people can arrive at two different solutions to an equation. But if that happens, at least one of them is wrong. We aren't talking about literary criticism or philosophy where there can be many 'right' answers. In math there are right answers and wrong answers.

And I'll reiterate what I said earlier: you can never see a real GMAT DS question where one statement leads you to conclude that n = 4, and the other leads you to conclude that n = -4, because those two things cannot both be true, and it is always possible in GMAT DS for both statements to be true simultaneously. Some (badly designed) prep company questions do not observe that principle, but every real GMAT question does.
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09 Mar 2019, 16:59
Can you definitively say that something cannot have two values simultaneously ? The gist of my post was that we can have a real life situation where n can have two values at the same time and math should be able to reflect that reality.

Instructions for the DS questions do not foreclose the possibility of n with two different values simultaneously.
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09 Mar 2019, 17:34
Consider this point also. We use some fundamental information to solve a problem. Why not use it to fill in the missing info? When it is given that n=4 and n=-4 we use our common sense math knowledge that n^2 =16 and this leads to the bizarre situation that I elaborated in my earlier post. My question is whether DS instructions rule out a" letter" representing more than one value.
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09 Mar 2019, 17:56
SravnaTestPrep wrote:
IanStewart wrote:
Those statements do contradict each other no matter what you know about n. n cannot be equal to two different numbers simultaneously; if n is a square root of 16, then n is equal either to 4 or to -4, not to both at the same time.

Two equally objective persons may deduce logically the value of the same variable in a different way. It may later be resolved. In this sense, there is no precise value for a variable even simultaneously. So you may take the value of n arrived by 2 independent persons which an be resolved and both be used in a consistent way using a single formulation. In other words they produce exactly the same effects.

But, how do you come up with 2 different values simultaneously?
Are you talking about the following example?
What is the value of n?
1) $$n=4$$
2) $$n^2=16$$
Here statement 2 gives 2 values (e.g., 4,-4). Statement 1 directly says n=4. So, Why different people take the value of n=-4 in statement 2?
Thanks__

Hi SravnaTestPrep,
Did you miss my question?
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09 Mar 2019, 18:02

I definitely think you raised a very valid point. The DS instructions are not properly framed and it is possible to interpret them differently from what GMAC wants them to be.
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