Data Sufficiency

Hi kamalakarthi,

This question combines some basic algebra skills with some Number Properties. Since we're dealing with inequalities (instead of equations), chances are that we'll have to do a little more work than normal to answer this question.

We're told that X is an INTEGER. We're asked for the value of X.

Fact 1: X^2 - 4X + 3 < 0

You can factor this quadratic into 2 pieces:

(X-1)(X-3) < 0

Now comes the Number Property....

For the above product to be LESS than 0, ONE of the pieces must be POSTIVE and the OTHER must be NEGATIVE. That's the ONLY way to get a result that is less than 0. So let's talk about the possibilities....remember that X must be an INTEGER

X can't be 3, 4, 5, 6, etc. because then you'll either have two positives or a 0.
X CAN be 2, since (1)(-1) is less than 0
X can't be 1, because then you'd have a 0.
X can't be 0, -1, -2, -3, -4 etc. because then you'd have two negatives.
The only answer is 2.
Fact 1 is SUFFICIENT.

Fact 2: X^2 + 4X + 3 > 0

From here, we don't have to do nearly as much work. X could be ANY POSITIVE INTEGER, so there are an infinite number of answers.
Fact 2 is INSUFFICIENT

Final Answer: A

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

kamalakarthi wrote:If x is an integer, what is the value of x?

(1) x² - 4x + 3 < 0

(2) x² + 4x +3 > 0

Target question: What is the value of x?

Given: x is an integer

Statement 1: x² - 4x + 3 < 0
First solve the EQUATION x² - 4x + 3 = 0
(x - 1)(x - 3) = 0
So, x = 1 and x = 3 satisfy the EQUATION x² - 4x + 3 = 0

Now check the RANGES OF VALUES when x equals neither 1 nor 3
case a: x < 1
Try x = 0
If x = 0, then (x - 1)(x - 3) is POSITIVE. This means that for ANY value of x where x < 1, (x - 1)(x - 3) will always be POSITIVE

case b: 1 < x < 3
Try x = 2
If x = 2, then (x - 1)(x - 3) is NEGATIVE. This means that for ANY value of x where 1 < x < 3, (x - 1)(x - 3) will always be NEGATIVE

case c: 3 < x
Try x = 4
If x = 4, then (x - 1)(x - 3) is POSITIVE. This means that for ANY value of x where 3 < x, (x - 1)(x - 3) will always be POSITIVE

Statement 1 tells us that x² - 4x + 3 [aka (x - 1)(x - 3)] is NEGATIVE (case b).
This means that 1 < x < 3
Since we're told that x is an integer, it must be the case that x = 2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x² + 4x +3 > 0
First solve the EQUATION x² + 4x + 3 = 0
(x + 1)(x + 3) = 0
So, x = -1 and x = -3 satisfy the EQUATION x² + 4x + 3 = 0

Now check the RANGES OF VALUES when x equals neither -1 nor -3
case a: x < -3
Try x = -4
If x = -4, then (x + 1)(x + 3) is POSITIVE. This means that for ANY value of x where x < -3, (x + 1)(x + 3) will always be POSITIVE

case b: -3 < x < -1
Try x = -2
If x = -2, then (x + 1)(x + 3) is NEGATIVE. This means that for ANY value of x where -3 < x < -1, (x + 1)(x + 3) will always be NEGATIVE

case c: -1 < x
Try x = 0
If x = 0, then (x + 1)(x + 3) is POSITIVE. This means that for ANY value of x where -1 < x, (x + 1)(x + 3) will always be POSITIVE

Statement 2 tells us that x² + 4x + 3 [aka (x + 1)(x + 3)] is POSITIVE (cases a & c).
This means that EITHER x < -3 OR x > -1
This means that there are several different possible values of x.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent