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

[BTGmoderatorDC]

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



OA C

Source: Manhattan Prep

[Jay@ManhattanReview]

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

OA C

Source: Manhattan Prep

To get the average of Max(x, 60) and Min(40, x), we must know the values of Max(x, 60) and Min(40, x).

Let's take each statement one by one.

(1) Min(x, 60) = x

=> x < 60

=> Max(x, 60) = 60 and Min(40, x) = Indeterminable: if x < 40, then Min(40, x) = x, no unique value!

(2) Max(40, x) = x

=> x > 40

=> Max(x, 60) = Indeterminable: if x > 60, then Max(x, 60) = x, no unique value!

(1) and (2) together

From both the statements, we get 40 < x < 60

=> Max(x, 60) = 60 and Min(40, x) = 40

Thus, the average of Max(x, 60) and Min(40, x) = (60 + 40)/2 = 50. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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