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S99-08

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S99-08 [#permalink]

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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) \(Max(40, x) = x\)
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New post 16 Sep 2014, 01:53
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.


Answer: C
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Re: S99-08 [#permalink]

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New post 24 Mar 2017, 22:04
Don't we need a specific value for X? here we are getting a range for X. Is that enough?
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New post 25 Mar 2017, 02:42
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: S99-08   [#permalink] 25 Mar 2017, 02:42
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