# [SOLVED] SAT-type problem... should be easy - mind blocked?

• Jun 6th 2008, 07:57 PM
vxcv
[SOLVED] SAT-type problem... should be easy - mind blocked?
On the number line shown, the tick marks are equally spaced. Which of the lettered points represents $y$?

http://i28.tinypic.com/ih7gjr.gif

The answer key says that the correct answer is E, but what I am looking for is an explanation.

Any help as to how to explain the solution to this problem would be much appreciated. I'm trying to help my sister prepare for her SAT.

What I tried was setting $\begin{cases} 2x = x+y \\ 3x = \frac{x+y}{2}\end{cases}$... but that didn't work. In the end, that method resulted in $3x=\frac{1}{2}(2x) \rightarrow 3x = x \rightarrow x = 1, y = 2$, which is impossible given the graph. I've also tried a number of other things to no avail.

• Jun 6th 2008, 08:25 PM
o_O
$\frac{x+y}{2}$ represents the average/midpoint between two numbers.

For example, if I asked you to find the average/middle number between 14 and 100, you would perform the same operation: $\frac{14+100}{2} = 57$

So you know where x is, you know where the mid-point of them is, so you can certainly find where y is.
.
• Jun 6th 2008, 08:41 PM
Soroban
Hello, vxcv!

There's something wrong with the diagram.
That $x+y$ doesn't belong there . . .

Quote:

On the number line shown, the tick marks are equally spaced.
Which of the lettered points represents $y$?
Code:

        A          B      C          D      E       - + - + - * - + - + - + - * - + - + - + - + -                 ↑              ↑                 x            ½(x+y)

$\frac{x+y}{2}$ is the average of $x$ and $y.$
. . . It must lie halfway between $x$ and $y.$

Since $\frac{x+y}{2}$ is 4 units above $x$, it must be 4 units below $y.$

And that is why $y$ is at E.

• Jun 6th 2008, 09:11 PM
math sucks
Why is everybody saying that the diagram is wrong? For example, set $x=-3$. Then $y=1$ and $-2=x+y<\frac{x+y}{2}=-1$ matches the diagram perfectly.
• Jun 6th 2008, 09:40 PM
Isomorphism
Ya I know. if x+y < (x+y)/2, then x+y is negative. This clearly means x is negative and y is positive. But the answer is still E because x+y/2 is the midpoint. x is 5 units away from x+y/2 and x+y/2 is the midpoint of x and y. This means y is also 5 units away from x+y/2 on the other side. Thus E is the answer
• Jun 6th 2008, 09:59 PM
vxcv
Thanks so much! Would you believe I got an 800 on my Math SATs when I took 'em?

Didn't think about midpoints though. Thanks again!