Inequality

[abhirup1711]

If x is positive, is x > 3 ?
(1) (x - 1)^2 > 4
(2) (x - 2)^2 > 9

[Bill@VeritasPrep]

1. Take the square root of both sides: x - 1 > 2 or x - 1 < -2. Since x must be positive, we can disregard the second one. If x - 1 > 2, then x > 3. Sufficient

2. Again, take the square root of both sides (and we can again disregard the negative root): x - 2 > 3, so x > 5. Sufficient.

[GMATGuruNY]

If x is positive, is x > 3 ?
(1) (x - 1)^2 > 4
(2) (x - 2)^2 > 9

Test the THRESHOLD.
Here, the threshold is x=3.

Statement 1: (x-1)² > 4
If x=3, then (x-1)² = 4.
Implication:
To satisfy the constraint that (x-1)² > 4, x>3.
SUFFICIENT.

Statement 2: (x-2)² > 9
If x=3, then (x-2)² = 1.
Implication:
To satisfy the constraint that (x-2)² > 9, x>3.
SUFFICIENT.

The correct answer is D.

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Hi abhirup1711,

When facing these types of situations, sometimes its best to just "step back" and ask "what fits?"

We're told that X is POSITIVE, which is a great "restriction" (it means that we don't have to think about 0 or negatives). We're asked "is X > 3?" This is a YES/NO question.

Fact 1: (X-1)^2 > 4

With the squared term, I'd normally be thinking about positives AND negatives; remember though that negatives are NOT an option on this question.

Think of it in this way:

(Number)^2 > 4

The Number in the parentheses has to be greater than 2.

X - 1 > 2
X > 3
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

Fact 2: (X-2)^2 > 9

Here we have:

(Number)^2 > 9

The Number in parentheses has to be greater than 3

X - 2 > 3
X > 5
The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[sanju09]

If x is positive, is x > 3 ?
(1) (x - 1)^2 > 4
(2) (x - 2)^2 > 9

(1) If x > 0 and (x - 1)^2 > 4, then 1, 2, 3 doesn't fit into it, any number greater than 3 would make it true, hence YES, x > 3. Sufficient

(2) If x > 0 and (x - 2)^2 > 9, then 1, 2, 3, 4, or 5 doesn't fit into it, any number greater than 5 would make it true, hence [spoiler]YES, x > 3. Sufficient

Pick D[/spoiler]