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Max (x,y) is defined as the maximum of x and y , and

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Max (x,y) is defined as the maximum of x and y , and [#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


I read the explanation given by MGMAT, ill post below so as not to spoil. However, after reading, I am still confused about what this means. Perhaps someone could give a more clear and consice explanation? thanks for the help.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/max-x-y-is-d ... 28330.html
[Reveal] Spoiler: OA

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Re: Max (x,y) is defined as the maximum of x and y , and [#permalink]

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New post 06 Dec 2010, 04:57
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mmcooley33 wrote:
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


I read the explanation given by MGMAT, ill post below so as not to spoil. However, after reading, I am still confused about what this means. Perhaps someone could give a more clear and consice explanation? thanks for the help.


First of all: max(x,y) and min(x,y) are just some functions defined as: max(x,y)=the maximum of x and y and min(x,y)=the minimum of x and y.

Question is: \(average=\frac{min(40,x)+max(x,60)}{2}=?\)
If \(x<{40}\) then \(min(40,x)=x\), \(max(x,60)=60\) and \(average=\frac{x+60}{2}=?\);
If \(40<x<60\) then \(min(40,x)=40\), \(max(x,60)=60\) and \(average=\frac{40+60}{2}=50\);
If \(x>{60}\) then \(min(40,x)=40\), \(max(x,60)=x\) and \(average=\frac{40+x}{2}=?\).

(1) Min(x,60)=x --> just says that \(x<60\), so we have either the first or the second case. Not sufficient.
(2) Max(40,x)=x --> just says that \(x>40\), so we have either the second or the third case. Not sufficient.

(1)+(2) \(40<x<60\) so we have the second case: \(min(40,x)=40\), \(max(x,60)=60\) and \(average=\frac{40+60}{2}=50\). Sufficient.

Answer: C.
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Re: Max (x,y) is defined as the maximum of x and y , and [#permalink]

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New post 06 Dec 2010, 21:06
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mmcooley33 wrote:
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


I read the explanation given by MGMAT, ill post below so as not to spoil. However, after reading, I am still confused about what this means. Perhaps someone could give a more clear and consice explanation? thanks for the help.


Simply put, to get an average of two numbers you need both of 'em; Just one would not do. Here we need to find out the average of Max(x,60) and Min(40,x), so wee need both the numbers. Lets analyze S1 and S2 now:

S1. Min(x,60)=x => Max(x,60) = 60. But what is the value of Min(40,x)? We dont know. Not Sufficient.
S2. Max(40,x)=x => Min(40,x) = 40. But what is the value of Max(x,60)? We dont know. Not Sufficient.

Taking both statements: Max(x,60) = 60 and Min(40,x) = 40, so the average (60+40)/2. Sufficient

Answer: C
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Kudos [?]: 127 [1], given: 9

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Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128493 [0], given: 12179

Re: Max (x,y) is defined as the maximum of x and y , and [#permalink]

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New post 21 Aug 2017, 08:32
mmcooley33 wrote:
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


I read the explanation given by MGMAT, ill post below so as not to spoil. However, after reading, I am still confused about what this means. Perhaps someone could give a more clear and consice explanation? thanks for the help.



OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/max-x-y-is-d ... 28330.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128493 [0], given: 12179

Re: Max (x,y) is defined as the maximum of x and y , and   [#permalink] 21 Aug 2017, 08:32
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