Flexxice wrote:
Attachment:
line.jpg
On the number line, the shaded interval is the graph of which of the following inequalities?
A) |x| ≤ 4
B) |x| ≤ 8
C) |x - 2| ≤ 4
D) |x - 2| ≤ 6
E) |x + 2| ≤ 6
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 are included in the shaded interval.
Now let's give ourselves up to 20 seconds to identify a faster approach.
Another approach is to solve each answer choice for x until we find one whose solution matches the given shaded interval.
I'm pretty sure testing values is going to be a lot faster and much easierWhen we check the number line, we can see that
x = -8 is included in the shaded interval, which means
x = -8 must also be a solution to the correct answer choice.
Now plug
x = -8 into each answer choice to get:
A) |
-8| ≤ 4. This simplifies to 8 ≤ 4, which is not true. ELIMINATE.
B) |
-8| ≤ 8. This simplifies to 8 ≤ 8, which is true.
KEEP.
C) |
(-8) - 2| ≤ 4. This simplifies to 10 ≤ 4, which is not true. ELIMINATE.
D) |
(-8) - 2| ≤ 6. This simplifies to 10 ≤ 6, which is not true. ELIMINATE.
E) |
(-8) + 2| ≤ 6. This simplifies to 6 ≤ 6, which is true.
KEEP.
We're already down to just two answer choices!Let's test another extreme x-value...
We can see that
x = 4 is also included in the shaded interval, which means
x = 4 must also be a solution to the correct answer choice.
Plug
x = 4 into the two remaining choices to get:
B) |
4| ≤ 8. This simplifies to 4 ≤ 8, which is true.
KEEP.
E) |
4 + 2| ≤ 6. This simplifies to 6 ≤ 6, which is true.
KEEP.
That was no help!When we examine the two remaining answer choices (B and E), we can see that choice B tells us x CAN equal 8 (since x = 8 satisfies the inequality |x| ≤ 8) , whereas choice E tells us x CAN'T equal 8 (since x = 8 does not satisfy the inequality |x + 2| ≤ 6).
When we check the number line, we can see that x = 8 is NOT included in the shaded region of the number line.
In other words x = 8 cannot be a solution, which means we can eliminate choice B, because it tells us that x CAN equal 8.
By the process of elimination, the correct answer is E.