Bunuel wrote:
w, x and y are positive integers such that w ≤ x ≤ y. If the average (arithmetic mean) of w, x and y is 20, is w > 15 ?
(1) y = 28
(2) One of the three numbers is 17
Given: w, x and y are positive integers such that w ≤ x ≤ y. The average (arithmetic mean) of w, x and y is 20 We can write: (w+x+y)/3 =20
Multiply both sides of the equation by 3 to get:
w + x + y = 60Target question: Is w > 15 ? Statement 1: y = 28 Substitute to get:
w + x + 28 = 60Subtract 28 from both sides:
w + x = 32Consider these two conflicting cases:
Case a: w = 16 and x = 16, in which case the answer to the target question is
YES, x is greater than 15Case b: w = 10 and x = 22, in which case the answer to the target question is
NO, x is NOT greater than 15Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: One of the three numbers is 17Consider these two conflicting cases:
Case a: w = 17, x = 20 and y = 23. In this case, the answer to the target question is
YES, x is greater than 15Case b: w = 10, x = 17 and y = 33. In this case, the answer to the target question is
NO, x is NOT greater than 15Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that y = 28
Statement 2 tells us that one of the TWO REMAINING numbers is 17
So, EITHER x = 17 OR w = 17
Let's examine both cases:
Case a: x = 17 and z = 28. Since we know that
w + x + y = 60, we can substitute to get
w + 17 + 28 = 60 and when we solve this we get w = 15
In this case, the answer to the target question is
NO, x is NOT greater than 15Case b: w = 17 and z = 28. Since we know that
w + x + y = 60, we can substitute to get
17 + x + 28 = 60 and when we solve this we get x = 15
This means w = 17, x = 15 and z = 28
Since this breaks the given restriction that
w ≤ x ≤ y, it CAN'T be the case that w = 17
Since case a is the only possible case, it must be the true that
x is NOT greater than 15Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent