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by finance » Wed Aug 10, 2011 8:12 am
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

4
6
8
10
12
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by sumgb » Wed Aug 10, 2011 8:29 am
the answer is 12. here's why -
area of square has to be 100 so side must be of length 10.
if one point is on origin say point A(0,0) other point could be (10,0)
you can also get a side of length 10, if the other point is at (8,6) or (6,8) so possible squares here are 3.

you can have any sign for x and y co-ordinates of this other point with length of side of square = 10. so making it 4 * 3 = 12 squares.

this is not the best explanation, but if you imagine a little bit you can get a picture of what's going on here.

hope this helps...
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by mikebarmy » Wed Aug 10, 2011 9:16 am
this is confusing because it says it has to be a square and by definition, a square has to be the same measurement on all sides, so wouldn't there be only ONE square (with sides 10) to make one wiht an area of 100?
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by gmatboost » Wed Aug 10, 2011 11:04 am
I agree that the question is phrased poorly. Abstractly, there is only one square that can drawn, but it can be placed in different places on the coordinate plane. The question wants to know how many different ways you can place it in the plane with one of the coordinates at (0,0) and the others at coordinates that have integer values.
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by finance » Wed Aug 10, 2011 11:12 am
How can we be sure that the other 2 coordinates will be integers??
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by GmatKiss » Wed Aug 10, 2011 11:18 am
Is it not 8 then?
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by finance » Wed Aug 10, 2011 11:31 am
OA is 12
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by force5 » Wed Aug 10, 2011 11:43 am
as everyone has mentioned square has side 10 and all we need to do is find combinations for which a^2+b^2=10^2 where a and b are integers too. Here are all the combinations

(-10,0)
(0,-10)
(-8,6)
(6, -8)
(10,0)
(0, 10)
(8, -6)
(-6,8)
(-6, -8)
(-8, -6)
(6,8)
(8,6)
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by GMATGuruNY » Wed Aug 10, 2011 12:47 pm
Here is a drawing of the 12 squares that can be formed:

Image

In the top two figures:
There are two sets of 4 squares -- for a total of 8 -- all centered about the origin.
Each side is the hypotenuse of a 6-8-10 triangle.

In the bottom figure:
There are 4 squares centered about the origin.
Each side is a horizontal or vertical line segment of length 10.
Last edited by GMATGuruNY on Wed Feb 22, 2012 7:57 am, edited 1 time in total.
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by finance » Wed Aug 10, 2011 1:39 pm
GMATGuruNY wrote:Here is a drawing of the 12 squares that can be formed:

Image

The squares comprise:

-- horizontal and vertical line segments, each with a length of 10
-- the hypotenuses of 6-8-10 triangles, each hypotenuse with a length of 10
Hi!

It is given that one of the vertices has to be the origin, not the center of the square.
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by GMATGuruNY » Wed Aug 10, 2011 1:43 pm
finance wrote:
GMATGuruNY wrote:Here is a drawing of the 12 squares that can be formed:

Image

The squares comprise:

-- horizontal and vertical line segments, each with a length of 10
-- the hypotenuses of 6-8-10 triangles, each hypotenuse with a length of 10
Hi!

It is given that one of the vertices has to be the origin, not the center of the square.
Yes, indeed.
The drawing shows 3 sets of squares.
Within each set, each of the 4 squares has both a side of length 10 and a common vertex at the origin.
Total possible squares = 3*4 = 12.
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by finance » Wed Aug 10, 2011 1:58 pm
Thank you GmatGuruNY!!!

Sorry for the previous post, I have been studying gmat the whole day and I can not concentrate any more:)

You are absolutely right, thank you! I just saw the minimized version of the pic.

While solving I lost time because I was not sure whether all vertices would be integers.
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by finance » Thu Aug 11, 2011 2:58 am
Can someone please tell me how Manhattan scores correlate approx. with real GMAT scores. I get around 680 in Manhattan Cats:((do I have any hopes for 700? My exam is after three weeks.
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by sss2534 » Thu Aug 11, 2011 6:39 am
Manhattan's quant is definitely harder than GMAC's. But Manhattan's verbal is very similar to that of GMAC. MGMAT's scoring is pretty good actually -- especially compared to that of Kaplan or PR.

If you wrote the AWA section and followed the exact format of the GMAT(10 minute breaks and no pausing between questions to take a sip of Gatorade or a bite off an energy bar) -- then I think you can reasonably expect a few points more on the real GMAT.

But all that said -- GMAT Prep CATs provide the best estimate.
finance wrote:Can someone please tell me how Manhattan scores correlate approx. with real GMAT scores. I get around 680 in Manhattan Cats:((do I have any hopes for 700? My exam is after three weeks.
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by finance » Thu Aug 11, 2011 6:48 am
Thank you sss2534. My GMat Prep is 710,,Princeton 730...but when I am distracted I get even 630..I think it depends a lot on my mood:(...
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