Wrong GMATPrep Problem

Question

Is this possible? I took a GMATPrep a few days ago and found 2 questions I'm pretty confident are wrong. I'll post the PS one here. Unfortunately, it's a picture so I'm just going to describe it.

It was on a coordinate plane with a semi circle resting ontop of the x-axis. It had a right angle drawn that looked to be bisected by the y axis. The angle intersected the circle twice, one in the left quadrant, once in the right.

The coordinates for the left intersection were "(-root3, 1) and the right intersection was (r,s). The question was, what is r?

Looking at this, the only answer I can understand is positive root3, since, if it's a right angle bisected by the y axis, the y's would be the same and the x would be the same absolute value.

However the answer given is 1. I understand that the picture could be misleading and the angle is not perfectly bisected, but if that were the case, the problem would be impossible to solve, not 1.

Any thoughts? If this is wrong, how can old GMAT questions (which is what the gmatprep software uses right?) be wrong??? Especially 2 of them?

Thanks!

ykaiim · Answer

Attach the screenshot. That will be easy.

shammokando · Answer

I resketched my copy of it (I copied it down, didn't think to screenshot, and now I can't access it again...)

Also, is there anyone I can look at my old test again? I thought I clicked for it to keep the test unfinished. It's making me take the test again if I click practice test 1... is this a new test?

chix475ntu · Answer

the bolded assumption is not corrct. You are assuming that the angle between x axis and the line passing through (-root3, 1) is 45 but its not given in the question.

based on the information given
we know that the length of (-root3, 1) to origin and length of (r,s) to the origin are the same
so r^2 + s^2 = 4 ... I

and also as lines passing through (-root3, 1) and (r,s) are perpendicular, the product of slopes is -1

s/r * 1/-root3 = -1 
s = r * -root3 ... II
substitutiona II in 1 
r = 1

fivezero7 · Answer

hi,
you have mentioned that the angle between the two lines is a right angle.
however it is nowhere mentioned that the y-axis bisects the right angle.
so we will have to solve it using the slopes of the lines.
the slope of the line which passes through  (-\sqrt{3},1)  and (0,0) when multiplied with the slope of the line which passes through (r,s) and (0,0) will give -1 as the product.

hence on finding the slopes of both equations, we can find out that r will be 1.

shammokando · Answer

Thanks! Very helpful

Posted from my mobile device

shahideh · Answer

we have:

r^2+s^2=4 
and
 \frac{1}{\sqrt{3}}=\frac{r}{s}

So, r=1

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