Brent@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
NO, it is NOT the case that |1 - 4k| < k
Case b: k = 0.25. Here, |1 - 4k| = |1 - 4(0.25)| = |0| = 0. In this case, the answer to the target question is
YES, it IS the case that |1 - 4k| < k
Since 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 NEGATIVE
Since
|1 - 4k| is always greater than or equal to zero, the answer to the target question is
NO, it is NOT the case that |1 - 4k| < k
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
