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X is a mode of [3, 0, 1, -1, 0, 5, 1] X is neither positive nor negative

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficient

(1) has 1,0 as mods INSUFFI (2) 0 is the only number neither +ve nor -ve SUFFFI IMO B
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That would never be a question because both statements 1 and 2 MUST be true. In your case, that is not possible.

Agreed, this is not a 'legal' question. One of the basic principles of DS is that the two statements CANNOT contradict one another. In this case, both statements provide a unique answer (stmt one = 1 and stmt two = 0) which contradict.

With that said, if on the GMAT you find yourself where the statements contradict, you have done something wrong.

HTHs, Martin.
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I appreciate the kudos if you find this post helpful! +1

stmt 1: using the formula: mode = ( 3 * median ) - ( 2 * mean) u can calculate mode....

hence A is sufficient ...

stmt 2: using this also v can say mode = 0 as its neither positive nor negative...

so ans has to D...

but y its B ??? ani one plz explain

Not sure where you are getthing this calculation of mode from. But here is the definition of mode: The number which appears most often in a set of numbers. Therefore it could be either 0 or 1. A is INSUFFICIENT.

Did not really find this one that hard to solve. Looking at A and then B, I did tend to think that C screamed at me but then B does give the value as 0. So B it is.
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My attempt to capture my B-School Journey in a Blog : tranquilnomadgmat.blogspot.com

The mode is the number that occurs the most frequently in a data set. For example the mode of {2, 3, 4, 4} is 4. A set can have more than one mode, for example set {2, 2, 3, 3, 5} has 2 modes 2 and 3. If every number in a set occurs an equal number of times, then the set has no mode. For example set {1, 2, 3} has no mode.

So, according to above {3, 0, 1, -1, 0, 5, 1} has two modes 0 and 1, which means that \(x\) can be either of these two values. Not sufficient.

(2) \(x\) is the median of {-4, 4, 2, -2} --> the median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order. So, the median of {-4, -2, 2, 4} is (-2+2)/2=0 --> \(x=0\). Sufficient.