GMAT Prep Test 1 Q10

sandeep_chhabra · Posted: Sat May 10, 2008 7:13 am Post subject: GMAT Prep Test 1 Q10

No Idea how to think over this...

ptgbeauregard · Posted: Mon May 12, 2008 7:02 am Post subject:

this one gave me fits too.

i had the answer the same as you did, but GMAT says the answer is 1. i was assuming that since O was the center and the right angle appears to be bisected by the y-axis, then the x coordinate should be the exact same distance away on the other side, or the square root of 3. it seems so simple, evidently it is not.

jscoligan · Posted: Mon May 12, 2008 9:18 am Post subject: You would think....

My first answer was D also, but since it's wrong, we must be assuming that point O lies at (0,0), which it obviously does not.

Find the radius OP using pyth and you get 2.

Thus, radius OQ also equals 2.

Using pyth to find PQ you get 2root2.

Subtracting root3 from 2root2 gives you something very close to 1, or answer B.

AleksandrM · Posted: Mon May 12, 2008 9:20 am Post subject:

That's funny. I had this same question yesterday when I took my first GMATPrep. I chose the same answer.

I'm curious, if I take the same test again, will I get the same questions? I thought that these tests have qustion bins out of which questions are chosen. This means that each test can be take at least twice. Is that the case?

jscoligan · Posted: Mon May 12, 2008 9:22 am Post subject: Answer Edit

I would edit my response, omitting the part about O not being (0,0).

8)

AleksandrM · Posted: Mon May 12, 2008 9:32 am Post subject:

jscoligan,

Nice job! I really fell for the trick in this question. Good for you, though.

II · Posted: Mon May 12, 2008 1:28 pm Post subject:

When looking at this question's answers ... answer D comes across as too easy. This clearly looks like a trap setup by GMAC ! They certainly dont like to make things easy for us ... and this choice would be just too easy.

Certainly on this type of question, which appears to be a 600+ question ... this would certainly make me think twice and be careful about my approach. Like all Geometry questions ... the key is to use the information provided and get started.
Here we have the coordinates of P. We can use this information to find OP=2. And as jscoligan explained ... we now know the radius of the circle. And also know one side of the of the big OPQ triangle. Also we can deduce that OQ=2, and hence PQ = 2(sqrt2), using pythagorus.

So we can subtract sqrt3 from 2(sqrt2) ... coming to our answer of 1.

I suppose the lesson here is to watch out for the "obvious" or "trap" answer choices.

Stuart Kovinsky · Posted: Mon May 12, 2008 2:52 pm Post subject:

There are a few different approaches we can take to this question.

First, we can know a very esoteric rule about circles with centre O:

If you draw a right angle triangle with the right angle at the origin and with the other two vertices on the circuference of the triangle, the x/y co-ordinates of the two points will be reversed (with signs appropriate for the respective quadrant).

For example:

If one point were at (1,0), the other point would be at either (0,1) or (0,-1).

If one point were at (1/2, 1/3), the other point would be at (-1/3, 1/2) or (1/3, -1/2).

In this question, since we have one point at (-root3, 1), and the point we want is in quadrant I, the other point is at (1, root3) (and so the value of s is 1).

If you're really bored one day, you can use either the pythagorean formula or trig to prove this rule.

Second, we can recognize that we can make a special right triangle as half of the right triangle linking the two points.

Going from (-root3, 1) to the origin (0,0) and then to (0,1), we have a 1/root3/2 triangle. If we know that this is a 30/60/90 triangle, we realize that the angle formed near the origin is 60 degrees (since it's opposite the root3 side of the triangle).

Now we know that the portion of the right triangle on the other side of the y-axis is 30 degrees (90- the 60 we used on the left side). We can draw another right triangle from the origin (0,0) to (s,t) to (0,t), which is also a 30/60/90. In this triangle, the side connecting points (0,t) and (s,t) is opposite the 30 degree angle, so that side has a length of 1.

Therefore, the value of s is 1.

This long-winded explanation is a great lesson in why it's vital to redraw diagrams on your scratch paper - this question is MUCH easier to explain (and solve) while referring directly to a picture.

II · Posted: Mon May 12, 2008 3:17 pm Post subject:

Thanks Stuart ... some great points to note there !