Do both sufficient statements provide the same answer in a DS question

Hi,

As far as I think GMAT "might" not give you any such question inw hich both Stat1 and Sta2 are giving you different answers individually.
If i get a question like this then i will still be going and marking option "D" and not option "E"

Bunuel, this is a very interesting observation you have mentioned. But I have seen in some yes/no DS questions to provide a "no" for 1 statement and "yes" for the other statement and as both statements still give an unambiguous yes or no , the correct answer happens to be D.

Such kind of DS questions would be considered flawed as per GMAT standards.

amritrungta

Here are some tacit rules that are followed by GMAT test writers when it comes to Data Sufficiency:

1) The two statements in data sufficiency will never contradict each other.

2) If each statement alone is sufficient, then the outcome will be consistent. This means that if it is a Yes/No data sufficiency question, then both statement will answer the question in the main stem as Yes, or both will answer them as No. If it is a value question, then the outcome will be identical in both cases.

3) If you find that your outcome to the question is different for both the statements, while each statement is sufficient, then you can be guaranteed that either you made some computational error in a value question or you are misinterpreting the statements. This is a valuable tool and I use it to gain further confidence that I did indeed get the data sufficiency question right.

Cheers,
Dabral

Absolutely! The two statements will not contradict so if you get different answers, you must recheck your logic/calculations.
In fact, I have discussed an advanced DS strategy based on this property of GMAT DS questions here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/07 ... t-part-ii/

I like to explain this concept in this way:

A DS question is a puzzle.

For example: Given that x > 0, what is the value of x?

Now, from the question stem alone, you will not be able to get a unique value of x. So you cannot answer the puzzle.
x could be 1 or 5 or 1000 or 674828.45 etc.

So, to help you get to the answer, you have two hint statements given to you.

Statement 1: x^2 + x - 2 = 0
On solving, this statement tells you that x is either -2 or 1.
Now can you answer the puzzle? Yes. We are given that x is positive and this statement tells us that x is either -2 or 1 so x must be 1. That is the only possible value. In this case, we say that statement 1 alone is sufficient to answer the question and hence answer would be either (A) or (D).

Now, think about it: can statement 2 tell you that x is either -4 or 5? No! Both statements are hints which may/may not help you find the answer to the SAME puzzle. x has one value and that is what you need to find. So statement 2 can tell you that x is 1 or 2. It can tell you that x is 1. It can tell you that x is 1, 5 or 7 etc. But is it possible that it does not include that value 1 for x? No! The actual value of x is 1 (which we found from statement 1). Since statement 2 is a hint to the same puzzle, it must include that value 1. Otherwise, it would be an incorrect hint and hence, an incorrect DS question.

Hope it helps.

I don't have too much to add to the good posts above, but I did want to point out why the two statements must be consistent (in other words, it always needs to be possible that both statements are true at the same time). The question always needs to make logical sense if you use both statements, even when one statement is sufficient alone, because some test takers will combine the statements, because some test takers won't notice that one statement is sufficient. And when you use both statements, and they contradict each other, there is no logically correct answer to a DS question. For example, if you had this DS question:

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

Note that this is a terrible quality question. Clearly neither statement is sufficient alone, but when you combine them, no value of x is even possible. In that case, most mathematicians would probably say the information is sufficient - you know that no value for x exists. But it's also perfectly logical to say this is insufficient, because you can't find x using the two statements. So there's no good answer to a question like this - you can justify C, and you can justify E. That's why the real GMAT can never include questions where the two statements are contradictory.

That said, I've seen dozens of prep company questions which do not observe this design principle. If you ever come across questions like that, you're not studying from realistic material, so find better resources to work with.

And Karishma, in the blog post she linked to above, described how you can sometimes take advantage of the consistency of the two statements when solving DS questions. I wanted to offer another example. Say you had this DS question:

What is the value of the positive integer k?

1. 110 < k^2 < 135
2. 1202 < k^3 < 1402

If k is a positive integer, Statement 1 is sufficient - 11^2 = 121 is the only perfect square in that range, so k = 11.

Now, when we look at Statement 2, we know the two statements are consistent. If the only possible value for k, using Statement 1, is 11, then it absolutely must be true that k = 11 is one solution for Statement 2. So even if you don't know what 11^3 is, there's no need to calculate it when you look at Statement 2. You can be completely sure 11^3 is somewhere between 1202 and 1402. Since 10^3 clearly is not in that range (10^3 = 1000), the only question we need to answer is whether k could be 12. It's easy to see that k cannot be 12 just by estimation (12*12*10 = 1440 is already larger than 1402, and 12*12*12 is bigger than 12*12*10), so 11 is the only solution to Statement 2 as well, and the answer is D.

And as mentioned above, you can use statement consistency to check your work - if you get contradictory solutions when analyzing each statement separately, you've done something wrong, or you're studying from low quality material.

Hi,

So in that case, If I arrived at different solutions for the same DS question, Can we say I went wrong somewhere and need to recheck my calculations???

This can actually help in confirming a particular DS question, given that Number proporties (like odd/even) are pretty tricky.

Thanks

Hi All,

Some of the 'language' in this discussion might be misinterpreted, so I'm going to add some clarification to the discussion.

In DS questions, the two Facts CANNOT BOTH be Sufficient with different answers. If you come across this type of situation in a DS question, then the likely reason for it is that your work is INCOMPLETE (so you didn't do enough to prove that one of the Facts was actually Insufficient).

Here's a simple example:

X is an integer. Is X greater than 0?

1) -3 < X < 0

In this Fact, there are a couple of possible values for X....
IF....
X = -1, then the answer to the question is NO
X = -2, then the answer to the question is NO
The answer is ALWAYS NO, so....
Fact 1 is SUFFICIENT

2) X^2 = 4

In this Fact, there are a coupe of possible values for X....
IF....
X = 2, then the answer to the question is YES
X = -2, then the answer to the question is NO
Fact 2 is INSUFFICIENT

In this situation, if your work was 'incomplete' in Fact 2 (and you thought that X = 2 was the only solution), then you might think that it's SUFFICIENT (but it's actually NOT - there's another possible value for X that leads to a different answer to the question).

Hi Engr2012,

If you can 'dig up' any DS questions that match what you describe, then you should post them here. It's possible that the question wasn't properly 'designed' or it's possible that you might have missed something when you attempted to solve it.

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

I just read for 'calculate value questions' like 1/(x + 4)? that you should not overthink and just check if statement 1 and 2 are sufficient to calculate x and I agree.
However, I was wondering if both statements alone are sufficient, if it is always D, or can the answers be dissimilar (so you have to calculate exactly)?

Post scriptum: Apologies if this is frequently asked

Dear neenpaques,
I'm happy to respond.

Here's a blog article with some DS tips.
https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/

If the DS question is a "find the value of the expression" question, and if you have enough information to calculate the solution from each statement, then the answer always will be (D). In a real GMAT DS or in a high quality practice question, the two statements always will lead to the same value for the expression in the prompt. If you stumble upon a DS practice question in which the two statements lead to different values of the prompt, then that's something that should make you question the validity of that particular source of questions.

As I am sure you are aware, not every car company that says, "We sell the best car on the road!" is actually selling the best car on the road. Much in the same way, not every GMAT prep company that says "We have high quality questions that are GMAT-like" actually has high quality, GMAT-like practice questions. Be a thoughtful and discerning consumer of GMAT practice questions.

Does all this make sense?
Mike

That is a very good question and a question that has been answered by experts above.

As for your question, for official GMAT questions, if both statements are sufficient individually, then you must get the same unique value.

This is actually a fun way of checking when you do end up with D for a question asking you a particular value of 'x'. So if you see that you are getting 2 different values of x individually, then recheck your solution.

Hope this helps.

Hi neenpaques,

This is a question that has troubled many test takers. But the bottom line is - If you encounter an official question or a question that has high standards as those of the official questions, then you will always find the values to be same from both the statements.

The answer will be D always.

This is how I remember it, a la Johnny Cochran:

"If the answer is D, then the numbers must agree."

If you're getting D, but with two different answers, then you did something wrong on either condition #1 or condition #2.

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