Hi j_shreyans,

This DS question is based on "symbolism" - you're given information about what a symbol means, then you're asked to do some basic calculations using that symbol. It's also perfect for TESTing Values:

Here, we're given 2 symbols:
Max(X,Y) = the bigger value of X or Y
Min(X,Y) = the smaller value of X or Y

We're asked to figure out the average of Max(X,60) and Min(40,X).

*Note: The Max(X,60) = 60 or X (if X is >= 60) and the Min(40,X) = 40 or X (if X <= 40).

Fact 1: Min(X,60) = X

This tells us that X is <= 60

If X = 60, then Max(60,60) = 60 and Min(40,60) = 40. The answer to the question is (60+40)/2 = 50
If X = 0, then Max(0,60) = 60 and Min(40,0) = 0. The answer to the question is (60+0)/2 = 30
Fact 1 is INSUFFICIENT

Fact 2: Max(40,X) = X

This tells us that X is >= 40

If X = 40, then Max(40,60) = 60 and Min(40,40) = 40. The answer to the question is (60+40)/2 = 50
If X = 100, then Max(100,60) = 100 and Min(40,100) = 40. The answer to the question is (100+40)/2 = 70
Fact 2 is INSUFFICIENT

Combined, we know:
40 <= X <= 60

From our prior work (above), we know....
If X = 60, then the answer to the question is 50
If X = 40, then the answer to the question is 50

The answer will ALWAYS be 50; here's why:

Since X has a range of 40 to 60 inclusive, the Max(X,60) will ALWAYS = 60 and the Min(40,X) will ALWAYS = 40. Thus, the average of those 2 values will ALWAYS = 50.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

j_shreyans 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

Target question: What is the average of Max(x,60) and Min(40,x)?

Statement 1: Min(x,60) = x
So, when we compare x and 60, the smaller value is x.
This tells us that x < 60
This alone is not enough information to answer the target question. Consider these two CONFLICTING cases:
Case a: x = 50, in which case Max(x,60) = 60 and Min(40,x) = 40. So, the average of Max(x,60) and Min(40,x) = (60 + 40)/2 = 50
Case b: x = 10, in which case Max(x,60) = 60 and Min(40,x) = 10. So, the average of Max(x,60) and Min(40,x) = (60 + 10)/2 = 35
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Max(40,x) = x
So, when we compare x and 40, the larger value is x.
This tells us that x > 40
This alone is not enough information to answer the target question. Consider these two CONFLICTING cases:
Case a: x = 50, in which case Max(x,60) = 60 and Min(40,x) = 40. So, the average of Max(x,60) and Min(40,x) = (60 + 40)/2 = 50
Case b: x = 70, in which case Max(x,60) = 70 and Min(40,x) = 40. So, the average of Max(x,60) and Min(40,x) = (70 + 40)/2 = 55
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x < 60
Statement 2 tells us that x > 40
Combined, we know that 40 < x < 60
This means that Max(x,60) = 60 and Min(40,x) = 40.
So, it MUST BE THE CASE that the average of Max(x,60) and Min(40,x) = (60 + 40)/2 = 50
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent