If S is a data set of three numbers x, y and z, is the range

[BTGmoderatorDC]

If S is a data set of three numbers x, y and z, is the range of the numbers in S less than 2?

(1) x - y < 1
(2) y - z < 2

[ceilidh.erickson]

If S is a data set of three numbers x, y and z, is the range of the numbers in S less than 2?

(1) x - y < 1
(2) y - z < 2

You can solve this problem by testing numbers.

(1) x - y < 1
This tell us that the distance between x and y is less than 1, but it gives us no information about z, so we can't know anything about the range of the set. Insufficient.

(2) y - z < 2
This tells us that the distance between y and z is less than 2, but tells us nothing about x, so again we can't make any inferences about the range. Insufficient.

(1) & (2) together
Try testing values that fit both statements: the distance between x and y is less than 1, and the distance between y and z is less than 2.

Case 1: values close together
x = 0.5
y = 0.4
z = 0.3
The range = 0.2, so the answer to the question is "yes".

Case 2: try to pick values that are further apart to see if you can get a range greater than 2:
x = 2.9
y = 2
z = 0.1
The range = 2.8, so the answer to the question is "no."

If we can sometimes get a "yes" and sometimes a "no," then the statements together are still insufficient.

The answer is E.