Test 1 Section 3 - #9 (page 398)

When you have a number line, and you need to figure out what a particular tick mark represents, the first step is to figure out the range (how much ground is being covered), and how many parts it's being divided into.

On this line, we're covering all the ground between 2 and 42, or a distance of 40.  How many parts are we dividing 40 into? I'll use red numbers to count:

So if a distance of 40 is divided evenly 5 times, then each tick mark must be 8, right?  So x has to be 18.  Let's fill in all the ticks (in green numbers) just to make sure our pattern fits:

Yup, looks good!  Answer (D).


Note: Technically you could backsolve here, too.  Start by trying (C), which says x is 16.  If that's true, then the tick mark before it has to be 9 (halfway between 2 and 16).  Then you fill in all the ticks to make sure your patten fits, but it doesn't.  You get 2, 9, 16, 23, 30, and a 37 where the 42 should be.  You're short by a few by the time you get to 42, so you need to try a bigger number to start with.  (D) of course still works.