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
