Square inscribe in a Square

[nareshchowdary28]

hi,

The Perimeter of the square S is 40 and square T is inscribed in a Square S then what is least possible area for the square T..?

As I can see the scope the square and the geometric calculations are simple I thought like it is an easy one, but looks like I'm missing some fundamentals here, so please help me how to solve this.

Naresh

[tommywallach]

Hey Naresh,

Turns out questions like this really stress people out, because you can't actually know whether the interior square touches on the midpoints of the bigger square. But you must know that it COULD touch the midpoints of the bigger square. So basically, picture a diamond inside a square, touching at all the midpoints of the square.

From here, you can see that you've created four right triangles in the corners of the bigger square. These triangles are 45/45/90 triangles, and their two perpendicular sides are both equal to half the length of one side of the big square. So if big square has sides of 10, then the triangle has perpendicular sides of 5. This means that the hypotenuse is 5 rt. 2, which equals one side of the smaller square. So the least possible area is (5 rt. 2)^2, or 50.

Let me know if I missed something, but I don't see that I did. Also, where is this question sourced from?

-t

[nareshchowdary28]

Yeah that is cleared,

Actually I thought like square area means it is a perfect square so it should be something like 36, 49, 81 like that.

But I need to find the square which has maximum area so for that I need to find the points where exactly I need to draw my square. and it is midpoint of all sides.

Great understand the funda that I should go by the logic in the question some times but not always using concept.

by the way it surprised me that you didn't know the source of this question...?

and it is from Powerprep 2.

sometimes I feel no body can trick the questions in Gre like ETS folks does.

Though Manhattan is testing the people at it's best but still it lacking the twists in the questions.

I have taken my Gre exam and planning to reappear.

so what I understand was Gre doesn't want people to understand high level concepts and work out 2 to 3 mins for each bit, but they they really want the people to the decipher the logic behind the question.

Please Tom, Just twist the material in Manhattan as much as possible.

Thanks,
Naresh

[tommywallach]

Hey Naresh,

Sorry you don't feel that our questions mimic the real test. It sounds like you may be talking about our books, rather than our practice tests (I don't see that you've actually taken any of our practice tests). It's worth keeping in mind that the books are not built to simulate the GRE on every question, but to help you build up the skills in order to do GRE questions. The books teach you the skills from the ground up, then you would apply those skills on our practice tests. Try taking our free practice test and see how you feel.

Thanks!

-t

[nareshchowdary28]

HiTom,

If I buy a Manhattan Gre books obviously I'll get six codes to write exams, So I have used three codes for multiple times practive and my Math scores went like this.

Maths - 152 (Start of the preparation)
159 (after one month)
162 (another one month)
166,
166
166 (continuosly)

but finally I got 162 on actual.

SO I'm so dissppointed about my scores.

Yaa I agree that Manhattan test are really good and I suggested to so many but felt like something is missing.

by the way for my exam in this month again I'm going to use Manhattan tests as a practice.

Thanks,
Naresh

[tommywallach]

Hey Naresh,

You may need to find other tests, as you will know these tests too well by now if you took them recently. I wish I could very easily recommend other tests, but there aren't a ton of good ones. Have you taken the ones from ETS themselves? If not, those might be a good bet. Remember to practice concepts as well, not just tests. Also, I still couldn't find you in our system. What name did you use to take those tests?

Thanks!

-t

[nareshchowdary28]

Yaa, I have taken ETS Tests, and that has disappointed me in Verbal section because have got very good scores in Practcie but not in final.

Yaa I'm concentrating on all the concepts that are required for the exam.

and by the way it's nareshchowdary28@gmail.com (the mail id which I was used for registering my tests)

Waht do you say about Barrons tests..?
and please let me know if there are any good test resources as my exam is in another 20 days I need to practice all the tests.

Please suggest.

Thanks,
Naresh

[tommywallach]

Hey Naresh,

I can't help but notice you've only taken the math sections of all the tests, and never the verbal sections. Is there a reason for that? It won't simulate your test day experience if you don't do the sections together, as that increases the amount of stamina required, and also the tension (pacing yourself for a long test).

As for more tests, I doubt Barron's are any good. Kaplan's might be okay (their GMATs aren't great, but GRE may be better?). TPR's are awful.

-t

[dddannie6]

Hey T,

So about the question on the Square inscribe in a a square. How is one suppose to make the connection that when you inscribe the square as a diamond shape into the other bigger square the smaller right triangles are exactly half of the lengths of the bigger square?

Is there a rule that I am missing here?

Best,
Dannialles D

[tommywallach]

Hey DDD,

If you just draw it, you'll see it. I'm not quite sure how else to explain it. There's no way to draw a diamond where the points don't meet right at the center of the sides. So the resultant triangles will have two sides that are exactly half the length of the sides of the square.

-t

[kpkanupriyakhmi]

Why touch at mid point only? why not anywhere else?

[tommywallach]

Because it's physically impossible. Try drawing it and you'll see what I mean. If you really think you've drawn an exception, scan it and put it in a post and we can chat about it!

-t

[lilyshay]

Hi Tom,

I just wanted to check a vocab term re: this question.

Does "inscribe" have to mean that it touches each side of the square? Why couldn't I draw a square that was 2x2 inside of the 10x10 square? That was the part that threw me while I did this problem.

I did the diamond thing and got 50, but thought that it was a 'trick' because the square could be smaller.

Thanks!
Lily

[tommywallach]

Hey Lily,

A 2x2 square would not be inscribed, as it would only touch one side. The official definition (from Wikipedia!) of inscribed is: "an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid."

It's the "fits snugly" part that matters here. The 2x2 would not fit snugly!

-t