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Stendulkar wrote:If x is positive integer, is x greater than 3
1) (x-1)^2 is greater than 4.
2) (x-2)^2 is greater than 9.
Statement 1
If
something^2 > 4, we know that that
something is either greater than 2 or less than -2.
So, if
(x-1)^2 > 4, we know that
(x-1)>2 or
(x-1)< -2
Since we're told that x is positive, we can rule out (x-1)< -2 and conclude that (x-1)>2.
If x-1 > 2, we can add 1 to both sides of the inequality to get x>3
SUFFICIENT
Statement 2
If something^2 is greater than 9, we know that that something is either greater than 3 or less than -3.
So, if (x-2)^2 > 9, we know that (x-2)>3 or (x-2)< -3
Since we're told that x is positive, we can rule out (x-2)< -3 and conclude that (x-2)>3.
If x-2 > 3, we can add 2 to both sides of the inequality to get x>5
If x>5, then x is certainly greater than 3
SUFFICIENT
So, the answer is
DBrent Hanneson - Creator of GMATPrepNow.com
