<p>I'm stumped =/</p>
<p>----A----|----(x)----B----(x+y)----C----(x+y)/2----|----D----|----E----></p>
<p>On the number line above, the tick marks are equally spaced. Which of the lettered points represents y?</p>
<p>(A) A
(B) B
(C) C
(D) D
(E) E</p>
<p>I figured out how to solve this but I find it perhaps more helpful in general math studying to have a method that can be applied anywhere. </p>
<p>We don't know where zero is but we do know relative distances. Let's say zero is on the left, then as long as we are consistent we know:</p>
<p>(X+Y)-X=2 tickmarks
(X+Y)/2-(X+Y)=2 tickmarks</p>
<p>The first gives us Y=2 (1)
Multiply second by 2 on both sides:
(X+Y)-2(X+Y)=4
-X-Y=4
X+Y=-4....but we have (1) so....X=-4-Y=-4-2=-6</p>
<p>So X corresponds to a value of -6. But we also know Y=2. So where is Y? Well, just count 8 tickmarks to the right of X (we assumed zero was on the left). That takes us to E</p>
<p>a quicker way:</p>
<p>x is on the left, and (x+y)/2 is simply the average of x and y. so y must be just as far to the right as x is to the left.</p>
<p>that makes Y all the way at E just like X is just as far away on the other side.</p>
<p>Nice way of looking at the problem Thorps.</p>