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

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Intern
Joined: 31 Oct 2010
Posts: 31

Kudos [?]: 76 [0], given: 25

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

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06 Dec 2010, 03:29
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Difficulty:

35% (medium)

Question Stats:

92% (00:56) correct 8% (00:00) wrong based on 13 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

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

Kudos [?]: 76 [0], given: 25

Math Expert
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128493 [1], given: 12179

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

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06 Dec 2010, 04:57
1
KUDOS
Expert's post
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.

_________________

Kudos [?]: 128493 [1], given: 12179

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Status: I rest, I rust.
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Kudos [?]: 127 [1], given: 9

Schools: ISB - Co 2013
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Re: Max (x,y) is defined as the maximum of x and y , and [#permalink]

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06 Dec 2010, 21:06
1
KUDOS
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

_________________

Respect,
Vaibhav

PS: Correct me if I am wrong.

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

Math Expert
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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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
_________________

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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