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# S99-08

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:53
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35% (medium)

Question Stats:

67% (00:58) correct 33% (00:55) wrong based on 45 sessions

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$$Max(x, y)$$ is defined as the maximum of $$x$$ and $$y$$, and $$Min(x, y)$$ is defined as the minimum of $$x$$ and $$y$$. What is the average of $$Max(x, 60)$$ and $$Min(40, x)$$?

(1) $$Min(x, 60) = x$$

(2) $$Max(40, x) = x$$
[Reveal] Spoiler: OA

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16 Sep 2014, 00:53
Official Solution:

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

If $$x \gt 60$$, then $$Max(x, 60) = x$$, and $$Min(40, x) = 40$$. So then, with $$x$$ in this range, the average we are asked for equals $$\frac{x + 40}{2}$$.

If $$40 \le x \le 60$$, then $$Max(x, 60) = 60$$ and $$Min(40, x) = 40$$. So then, with $$x$$ in this range, the average we are asked for equals $$\frac{60 + 40}{2} = 50$$.

If $$x \le 40$$, then $$Max(x, 60) = 60$$ and $$Min(40, x) = x$$. So then, with $$x$$ in this range, the average we are asked for equals $$\frac{x + 60}{2}$$.

Statement (1): INSUFFICIENT. If $$Min(x, 60) = x$$, then $$x \le 60$$. 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 $$\frac{x + 60}{2}$$, which does not equal 50.

Statement (2): INSUFFICIENT. If $$Max(40, x) = x$$, then $$x \gt 40$$. 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 $$x \le 60$$ AND $$x \ge 40$$. Thus, $$x$$ is in the range in which the average we are asked for equals 50.

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24 Mar 2017, 21:04
Don't we need a specific value for X? here we are getting a range for X. Is that enough?
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25 Mar 2017, 01:42
AARONRAMSEY wrote:
Don't we need a specific value for X? here we are getting a range for X. Is that enough?

This is explained in the solution: If $$40 \le x \le 60$$, then $$Max(x, 60) = 60$$ and $$Min(40, x) = 40$$. So then, with $$x$$ in this range, the average we are asked for equals $$\frac{60 + 40}{2} = 50$$.

When considering the statements together we goth that $$40 \le x \le 60$$, thus the average = $$\frac{60 + 40}{2} = 50$$.

Hope it's clear.
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Re: S99-08   [#permalink] 25 Mar 2017, 01:42
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# S99-08

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