BTGmoderatorDC wrote:If x is a positive integer, is x < 16?

1) x is less than the average (arithmetic mean) of the first ten positive integers
2) x is the square of an integer.

Target question: Is x < 16?

Statement 1: x is less than the average (arithmetic mean) of the first ten positive integers
Since the first ten positive integers are EQUALLY SPACED, the average = (smallest number + biggest number)/2 = (1 + 10)/2 = 5.5
So, x < 5.5
Since 5.5 < 16, we can also write: x < 5.5 < 16
From here, we can see that the answer to the target question is YES, x IS less than 16
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is the square of an integer.
There are infinitely many values of x that satisfy statement 2. Here are two:
Case a: x = 4 (4 is a square of an integer, since 4 = 2²). In this case, the answer to the target question is YES, x IS less than 16
Case b: x = 25 (25 is a square of an integer, since 25 = 5²). In this case, the answer to the target question is NO, x is NOT less than 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent