# GRE and Grad School Admissions Blog

### Number Lines and Number Properties

Check out the Question of the Week:

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 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 ∙ can be anywhere between -2 and 4.
• However, do the possible products include -2 and 4? No they do not! is less than (not less than or equal to) 2. That means could be anything right up to 2, but not 2 exactly. For instance, could be 1.9999999. This means that the product r ∙ could almost get to 4 but never exactly reach it.
• By the same rules, r ∙ could almost get to -2 but will never actually be -2.
• Therefore, the range of values for r ∙ are everything between -2 and 4.
• -2 <  r ∙ s < 4
• C and D are the correct answers.

### Register for Tonight's Webinar!

Whenever we do a Question of the Week, we make a corresponding topic on our GRE Forum. Register for free to discuss the problem there, try out other problems, and find answers to your GRE questions.

Also, don't forget that tonight at 8 pm Eastern we are excited to bring you our totally updated, free Math Essentials WebinarThere's still time to register, and everyone who attends will receive a recording of the webinar and a discount code good for our GRE courses. We hope to see you there tonight!