Well, actually "just 2" isn't right either. And the question is indeed asking for the value of n.
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It is important to have a good technique for DS in order to avoid common pitfalls, and to be efficient. Here is the Kaplan method in a nutshell:
All DS questions are either "value" or "yes/no" question. The first thing you should do in a DS question is determine what kind it is. The next thing you should do is take stock of all the information given (and not given) in the question stem. Finally, and perhaps most importantly, you should think about what kind of information you would need in order to answer the question.
Only after doing all that should you approach the statements.
Evaluate the first statement first unless the second statement is clearly easier. Analyze the statements seperately from each other; for example, if you looked at the first statement first, when looking at the second one you should "forget" the first. Evaluate the statements in combination only if necessary.
Applied here:
The question stem's wording was most likely: "If n is an integer, what is the value of n?"
From this question stem, we know that n is an integer; we don't know anything else. We are asked for the value of n. What kind of info would we need in order to answer this question? In a value question, a statement has to lead to just one and only one value in order to be sufficient. Anything else (no value, multiple values, undefined values is insufficient). So, any information that allows us to detrermine one and only one value for n would be sufficient. On to the statements.
(1):
n being divisible by 2^n-1 means that n is a multiple of 2^n-1: n/(2^n-1) We can rearrange this expression to 2n/2^n. But in order to satisfy this expression n can be multiple values. Insufficient.
From (2), we have absolutely no idea what the value of n is. Insufficient.
Because the statements are insufficient by themselves, it is necessary to combine them.
(1) + (2):
From (2), we know that n must be greater than (but cannot be) 1. Now, looking at (1) more closely we can determine that the only positive values n can take in (1) are 1 and 2. But because (2) tells us us that n cannot be 1, n must equal 2, and the statements are sufficient when combined. Choose C.
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Develping your procedure for DS is at least as (and maybe more) important than knowing content. It is important to develop a procedure that is efficient. Here, because a Kaplan-trained student would have identified this as a value question, the moment she saw that (1) allowed for multiple values, she knows (1) is insufficent; it doesn't matter how she saw this. That is, as soon as you saw n could be 1 or 2, it is insufficient. Alternatively, because 0 is an integer and 0 divided by any non-zero number is 0 if you saw that n could be 0 or 1, you know it is insufficient. Or, if you saw that n could be any negative integer, it is insufficient. That is, as a matter of test-taking procedure, you didn't have to determine ALL of those things to see that (1) is insufficient; you just needed to determine ANY of those things.
The Kaplan method for Data Sufficiency:
Step 1: Focus on the question stem.
Step 2: Evaluate each statement in conjunction with the question stem but separately from each other.
Step 3: Combine the statements only if necessary.
Sangeet, because reading the question stem threw you here, here's a tip for teling apart yes/no from value: if the question clause starts with "is", "does", or "are" it is a yes/no question. Here, the question clause is "what is the value of n?"
Kaplan Teacher in Toronto
