Can anyone explain this? From GMAT Prep

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acon: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Wed Jan 20, 2010 10:46 pm

by acon » Wed Jan 20, 2010 10:49 pm

Can anyone explain this? I don't understand why they say the answer is 1.

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Source: Beat The GMAT — Problem Solving | Wed Jan 20, 2010 10:49 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jan 20, 2010 10:51 pm

Brent Hanneson - Creator of GMATPrepNow.com

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acon: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Wed Jan 20, 2010 10:46 pm

by acon » Wed Jan 20, 2010 10:54 pm

Wow, thank you for that very fast and detailed response! Did you have to create that, or was this asked before?

Thanks again!

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Jan 20, 2010 11:12 pm

acon wrote:Can anyone explain this? I don't understand why they say the answer is 1.

We actually have an isosceles right triangle OPQ with O containing the right-angled vertex of it. Things are given on a real rectangular coordinate plane in such a way that we can easily understand that O is (0, 0) and s is positive. One can apply basics of coordinate geometry to come down to the following equations:

s^2 + t^2 = 4 and

(s + âˆš3)^2 + (t - 1)^2 = 8, which reduces to t = s âˆš3

And therefore s^2 = 1 or s = Â±1, NO...

Just 1

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jan 20, 2010 11:17 pm

acon wrote:Wow, thank you for that very fast and detailed response! Did you have to create that, or was this asked before?

Thanks again!

That was asked before - I already had the slide prepared

Brent Hanneson - Creator of GMATPrepNow.com

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acon: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Wed Jan 20, 2010 10:46 pm

by acon » Thu Jan 21, 2010 12:20 am

Well cheers to a fellow British Colombian. Sunshine coast is a beautiful spot! I'm down in Victoria, but grew up in Vancouver also. I checked out your site, it seems you offer a great service!

I am writing the GMAT tomorrow, and today is my first and last real day of preparations. Would have liked to have been more prepared, but time constraints don't permit much.

The following are the only other two questions that I haven't been able to figure out on my own from the GMAT Prep.

Their answer in this first one is 16, which I would have thought to be correct had the question been 32 + ...,

This one I am entirely lost in..

If anyone is able to help it would be greatly appreciated!

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chaitanya.sonavale: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Jan 13, 2010 2:10 am; Thanked: 1 times

by chaitanya.sonavale » Thu Jan 21, 2010 2:08 am

Hi acon,

All the best for tomorrow!!!

1. let equal sides of iso. tri. be x. Then perimeter = 2x + âˆš2x

So 2x + âˆš2x = 16 + 16âˆš2. Now the equation does not hold when âˆš2x = 16âˆš2. So âˆš2x = 16.
Now multiplying both sides by âˆš2 => 2x = 16âˆš2 => x = 8âˆš2
Hypo = âˆš2x = 8âˆš2 * 2 = 16.

2. for iso. tri. QRS, let equal angles be a. for iso. tri. QRS, let equal angles be b.

a+b+x = 180 & x + P = 180. but P = 90 => a+b=90

Hence x = 90

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Jan 21, 2010 2:31 am

acon wrote:Well cheers to a fellow British Colombian. Sunshine coast is a beautiful spot! I'm down in Victoria, but grew up in Vancouver also. I checked out your site, it seems you offer a great service!

I am writing the GMAT tomorrow, and today is my first and last real day of preparations. Would have liked to have been more prepared, but time constraints don't permit much.

The following are the only other two questions that I haven't been able to figure out on my own from the GMAT Prep.

Their answer in this first one is 16, which I would have thought to be correct had the question been 32 + ...,

This one I am entirely lost in..

If anyone is able to help it would be greatly appreciated!

We must keep in wits some special triangles that the GMAT tests very recurrently, more than ever 45-45-90 and 30-60-90 ones. Your first problem is the case of a 45-45-90 triangle whose sides opposite those angles in order bear the ratio 1:1:âˆš2. Hence, if a be each leg of the isosceles right triangle, then a âˆš2 will be its hypotenuse and 2 a + a âˆš2 its perimeter, which is given as 16 + 16 âˆš2 in your problem.

Take 2 a + a âˆš2 = 16 + 16 âˆš2

Or a (2 + âˆš2) = 16 + 16 âˆš2

Or a = (16 + 16 âˆš2)/( 2 + âˆš2)

But we want its hypotenuse, which is a âˆš2

Hence a âˆš2 = (âˆš2) (16 + 16 âˆš2)/ (2 + âˆš2) = (16 âˆš2 + 32)/ (2 + âˆš2) = 16 (2 + âˆš2)/ (2 + âˆš2) = 16.

Take B.

For your second problem, let's make few assumptions first, like as if âˆ PRT = Î± so that âˆ PTR = 90 - Î± .

Now (1) allows us to let âˆ RQS = âˆ RSQ = 1/2 (180 - Î±) = 90 - (Î±/2).

Whereas âˆ TSU = 180 - {x+90 - (Î±/2)} = 90 - x + (Î±/2)

And of course âˆ TUS = 180 - {90 - x + (Î±/2) + 90 - Î±} = 2 x - (Î±/2)

We can now come inside the quadrilateral PQSU that will contain the four interior angles as 90, 90 + (Î±/2), x, and 180 - 2 x + (Î±/2) such that

90 + 90 + (Î±/2) + x + 180 - 2 x + (Î±/2) = 360

Or simply, x = Î±. So x can be known only if Î± is known. Insufficient.

Now switch to statement (2). Even this information alone plus our valid assumptions take us to the same situation as it was with statement (1) alone. Hence it is too insufficient.

Now take the two statements together, I mean take âˆ TSU = âˆ TUS or 90 - x + (Î±/2) = 2 x - (Î±/2) with x = Î±, or we can now have 90 - x + (x/2) = 2 x - (x/2) or x = 45. SUFFICIENT

C.

All the best acon!

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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