Pre-think
a + b + c = 6
And all three numbers are positive integers.

(1) Only
a = b +1
If b=1, then a=2, c=3
If b=2, then a=3, c=1
There are no other possible combinations.
In either case, range is 2.
We can answer "No" to the question "Is the range of the three numbers greater than 2".
Sufficient.

(2) Only
We already know the range can be 2.
If c=4, then a=b=1. The range is 3.
We cannot answer the question with certainty.
Insufficient.

The answer is thus (A).

Average is 2 .. so sum must be 6 ..

a+b+c = 6

Constraint .. a,b, c are all positive integer


(1) \(a - b=1\)
a = b+1
the numbers are b+1, b, c
2b+c = 5
b, c can be (1,3) or (2, 1)
corresponding values for (a, b, c ) = (2, 1,3) or (3, 2, 1)

both have range 2. So we can definitely answer that range is not greater than 2.

Sufficient



(2) \(c\) is the largest of the three numbers.
if c is greatest, a and b minimum can be 1 and so c will be 4. range =3
if a = 1 and b = 2, c = 3.. range = 2
Insufficient.

Ans A