Number Lines and Number Properties

Attempt the question; then read the explanation below.

Good Scratch Work is Essential

Start by Recording What You Know™, drawing a picture, and getting your answer choices set up.
- This step is absolutely essential with many GRE problems, especially the more difficult ones.
- You need a chance to get your bearings. You may look at writing out the information as redundant or a waste of time, but it’s not. Getting the information down gives you an opportunity to take note of what you have at your disposal to work with.
- As you Record What You Know™ you will prepare yourself to solve the puzzle.
Make note of what A, B, C, D, and E roughly correspond to.
Next, check out the range of values for r and s.
Start playing around with different values. Let’s look at the extremes. There are four possible products we can get from the extreme values:
- -½ ∙ -1 = ½
- -½ ∙ 2 = -1
- -1 ∙ 2 = -2
- 2 ∙ 2 = 4
So what’s the span in the range of values? The product r ∙ s can be anywhere between -2 and 4.
However, do the possible products include -2 and 4? No they do not! r is less than (not less than or equal to) 2. That means r could be anything right up to 2, but not 2 exactly. For instance, r could be 1.9999999. This means that the product r ∙ s could almost get to 4 but never exactly reach it.
By the same rules, r ∙ s could almost get to -2 but will never actually be -2.
Therefore, the range of values for r ∙ s are everything between -2 and 4.
-2 < r ∙ s < 4
C and D are the correct answers.