Hi All,
We're told that P, R and S are CONSECUTIVE integers in ASCENDING order and X is the AVERAGE (arithmetic mean) of the three integers. We're asked for the value of X.
To start, it's worth noting that since we're dealing with 3 CONSECUTIVE integers, the sum will always be '3 times' the value of the 'middle' numbers, so the average of those 3 numbers will be the value of the "middle" number - in this case, "R" will be the average. This means that X = R, so if we find the value of X or R, then we have answered the question. We can also set up the 'Average Formula': (P + R + S)/3 = X. This can be rewritten into any of the following:
P + R + S = 3X
P + R + S = 3R
P + S = 2R
This question can be approached in a couple of different ways; here's a way to use a mix of Algebra and Number Properties.
(1) Twice X is equal to the sum of P, R and S.
With the information in Fact 1, we can create the following equation:
2X = P + R + S
Comparing this equation to the initial equations we wrote, something interesting should stand out: How can (P + R + S) be equal to 3X AND 2X. Those appear to be 2 different results... and there's only one situation in which they are NOT.... when X = 0. Thus, the 3 values would be -1, 0 and 1 and the average is 0.
Fact 1 is SUFFICIENT
(2) The sum of P, R and S is zero.
Fact 2 gives us the SUM of the three terms, so we can easily calculate the average... X = (0)/3 = 0.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
