Bunuel wrote:

If (x−2.5)(x+0.5) = 4, what is the value of x?

(1) (x+1.5)(x−1.5) = 0

(2) (x − 3.5)(x+1.5) = 0

Target question: What is the value of x? Given: (x−2.5)(x+0.5) = 4 This information is HUGE, since

it tells us the only 2 possible values of xGiven: (x−2.5)(x+0.5) = 4

Expand and simplify to get: x² - 2x - 1.25 = 4

Subtract 4 from both sides: x² - 2x - 5.25 = 0

Multiply both sides by 4 to get: 4x² - 8x - 21 = 0

Factor to get: (2x + 3)(2x - 7) = 0

If 2x + 3 = 0, then x = -3/2 = -1.5

If 2x - 7 = 0, then x = 7/2 = 3.5

So,

EITHER x = -1.5 OR x = 3.5So, which value is it? Statement 1: (x+1.5)(x−1.5) = 0 This tells us that EITHER x = -1.5 OR x = 1.5

Since we already know that

EITHER x = -1.5 OR x = 3.5, we can be certain that

x = -1.5Since we can answer the

target question with certainty, statement 1 is SUFFICIENT

Statement 2: (x − 3.5)(x+1.5) = 0 This tells us that EITHER x = -1.5 OR x = 3.5

Since we already knew that

EITHER x = -1.5 OR x = 3.5,

this statement provides no new information.

So, all we can conclude from this is that

EITHER x = -1.5 OR x = 3.5Since we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com