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.
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