GMATPrepNow wrote:

Is |1 - 4k| > k?

(1) k > 4x³

(2) k < 2x – x² - 2

Target question: Is |1 - 4k| > k? Statement 1: k > 4x³ This pretty much tells is that k can have ANY value.

For example, notice that, if x = -100, then 4x³ = -4,000,000

So, for this value of x, k can be any number greater than -4,000,000

Let's TEST some values.

There are several values of k that satisfy statement 1. Here are two:

Case a: k = 0. Here, |1 - 4k| = |1 - 4(0)| = |1| = 1. In this case, the answer to the target question is

YES, it IS the case that |1 - 4k| > kCase b: k = 0.25. Here, |1 - 4k| = |1 - 4(0.25)| = |0| = 0. In this case, the answer to the target question is

NO, it is NOT the case that |1 - 4k| > kSince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k < 2x – x² - 2 Rewrite as: k < –x² + 2x - 1 - 1

Rewrite as: k < –(x² - 2x + 1) - 1

Factor to get: k < –(x - 1)² - 1

Notice that (x - 1)² is always greater than or equal to zero

So, -(x - 1)² is always LESS THAN or equal to zero

So -(x - 1)² - 1 must be NEGATIVE

So, statement 2 essentially tells us that k < some NEGATIVE number

This means

k must be NEGATIVESince

|1 - 4k| is always greater than or equal to zero, the answer to the target question is

YES, it IS the case that |1 - 4k| > kSince we can answer the

target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com