Bunuel wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S less than 4?
(1) x > w + 4
(2) y – 5 > z
Target question: Is the range of the numbers in S less than 4?ASIDE: Range = (greatest value) - (least value)
KEY CONCEPT: If the range of a set containing 2 values = k, then adding additional values to the set cannot decrease the range.
For example, the set {3, 10} has a range of 7
If we add more values to the set, we cannot make the range less than 7
Statement 1: x > w + 4 Subtract w from both sides to get: x - w > 4
This us tells us that the range of the set {x, w} is already greater than 4
So, if we add y and z, the range of the set {w, x, y, z} MUST be greater than 4
So, the answer to the target question is
NO, the range is NOT less than 4Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: y – 5 > zAdd 5 to both sides to get: y > z + 5
Subtract z from both sides to get: y - z > 5
This us tells us that the range of the set {y, z} is already greater than 5
So, if we add w and x, the range of the set {w, x, y, z} MUST be greater than 5
So, the answer to the target question is
NO, the range is NOT less than 4Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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