Bunuel wrote:
If (|x| - 2)(x + 5) < 0, then which of the following must be true?
(A) x > 2
(B) x < 2
(C) -2 < x < 2
(D) -5 < x < 2
(E) x < -5
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test x-values that satisfy the given inequality.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also attempt to solve the inequality, but the absolute value part of the inequality looks tricky. So, I'm pretty sure testing values is going to be a lot faster and much easierLet's find an x-value that satisfies the inequality (|x| - 2)(x + 5) < 0.
x = 0 is an obvious solution, which means
x = 0 must also be a solution to the correct answer choice.
Now plug
x = 0 into each answer choice to get:
(A)
0 > 2. Not true. Eliminate.
(B)
0 < 2. True.
KEEP.
(C) -2 <
0 < 2. True.
KEEP.
(D) -5 <
0 < 2. True.
KEEP.
(E)
0 < -5. Not true. Eliminate.
Now let's find another x-value that satisfies the inequality (|x| - 2)(x + 5) < 0.
I can see that
x = -10 is a solution, since we get (|
-10| - 2)(
(-10) + 5) < 0, which simplifies to be (8)(-5) < 0, which is true.
Now plug
x = -10 into the three remaining answer choices:
(B)
-10 < 2. True.
KEEP.
(C) -2 <
-10 < 2. Not true. Eliminate.
(D) -5 <
-10 < 2. Not true. Eliminate.
By the process of elimination, the correct answer is B.