Thread: [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 ?




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 ... but that didn't work. In the end, that method resulted in , which is impossible given the graph. I've also tried a number of other things to no avail.


Thanks in advance!

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:

So you know where x is, you know where the mid-point of them is, so you can certainly find where y is.
.

Hello, vxcv!

There's something wrong with the diagram.
That doesn't belong there . . .

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

Code:

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

is the average of and
. . . It must lie halfway between and

Since is 4 units above , it must be 4 units below

And that is why is at E.

Why is everybody saying that the diagram is wrong? For example, set . Then and matches the diagram perfectly.

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

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!