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Manager  Joined: 10 Nov 2010
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Max (x,y) is defined as the maximum of x and y, and min(x,y)  [#permalink]

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Question Stats: 72% (01:24) correct 28% (01:32) wrong based on 671 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

guys my question is how to rephrase this question and consider the possible values of x
i have considered the possible values of x
if x>60 then max(x,60)=x and min(40,x)=40
if x<40 then max(x,60)=60 and min(40,x)=x
if 40<x<60 then max(x,60)= 60 and min(40,x) =x

i have doubt in last two considered values.

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Math Expert V
Joined: 02 Sep 2009
Posts: 59086
Re: Max (x,y) is defined as the maximum of x and y, and min(x,y)  [#permalink]

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GMATD11 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

guys my question is how to rephrase this question and consider the possible values of x
i have considered the possible values of x
if x>60 then max(x,60)=x and min(40,x)=40
if x<40 then max(x,60)=60 and min(40,x)=x
if 40<x<60 then max(x,60)= 60 and min(40,x) =x

i have doubt in last two considered values.

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.

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) ?

Question is: $$average=\frac{min(40,x)+max(x,60)}{2}=?$$. Consider the following three cases:

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.

Hope it helps.

P.S. You could just plug some different values of x to get the three cases, for example: x=30<40, 40<(x=50)<60 and x=70>60.
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Math Expert V
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Re: Max (x,y) is defined as the maximum of x and y, and min(x,y)  [#permalink]

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

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GMATD11 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

Stem : To have a definite average (independent of x) : 40< x < 60

A)x < 60 : Says nothing about 40
B) x > 40 : Says nothing about 60

Combining together;

40 < x < 60 (the stem)

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

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________ Re: Max (x,y) is defined as the maximum of x and y, and min(x,y)   [#permalink] 04 Jan 2019, 02:41
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