alex.gellatly wrote:If x and y are positive integers and y = srt[9-x], what is the value of y?

1) x is less than 8
2) y is greater than 1

Thanks in advanced

Target question: what is the value of y?

To begin, notice that y = sqrt(something). For y to be an integer, that something must equal 1, 4, 9, 16, . . . etc.
In other words, 9-x must equal 1, 4, 9, 16, . . . etc.
Since the value of x is restricted to positive integers, we should recognize that x cannot be greater than 8, otherwise the square root of 9-x cannot be a positive integer.

From all of this, we can see that the only possible values for x are 5 and 8
When x=5, we get y = sqrt(9-5) = sqrt(4) = 2
When x=8, we get y = sqrt(9-8) = sqrt(4) = 1
Also notice that y can have only two values. y must equal either 1 or 2

Statement 1: x is less than 8
Since there were only two possible values of x to begin with (x = 5 or 8), statement 1 tells us that x must equal 5, which means y must equal 2.
Statement 1 is SUFFICIENT

Statement 2: y is greater than 1
Since there were only two possible values of y to begin with (y = 1 or 2), statement 2 tells us that y must equal 2.
Statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent