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The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog.  Today, they have followed up with the answer:

The first thing to do is rephrase the question, setting up cases that are based on the value of x.

If x > 60, then Max(x, 60) = x, and Min(40, x) = 40. So then, with x in this range, the average we are asked for equals (x + 40)/2.
If 40 < x < 60, then Max(x, 60) = 60 and Min(40, x) = 40. So then, with x in this range, the average we are asked for equals (60 + 40)/2 = 50.
If x < 40, then Max(x, 60) = 60 and Min(40, x) = x. So then, with x in this range, the average we are asked for equals (x + 60)/2.

Statement (1): INSUFFICIENT. If Min(x, 60) = x, then x < 60. However, the average we are asked for does not have a fixed value. If x is between 40 and 60, then the average is 50, but if x is below 40, the average is (x + 60)/2, which does not equal 50.

Statement (2): INSUFFICIENT. If Max(40, x) = x, then x > 40. By similar reasoning as we used for Statement (1), we know that the average does not have a fixed value.

Statements (1) and (2) together: SUFFICIENT. We know that x < 60 AND x > 40. Thus, x is in the range in which the average we are asked for equals 50.

The correct answer is C: BOTH statements TOGETHER are sufficient to answer the question, but neither statement alone is sufficient.




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