Geometry Problem-2

[Videoorchard]

Hi,

Author's method:
In the question mentioned below the author made use of the smart number i.e 1 for the smaller square to computer it's area.

My method:
I took the smart number i.e 1 and started computing the area for the larger square(ABDE),once i got it's area=1, i am STUCK! How do i compute the area of smaller square?

Question:
1. Is it necessary that i take smart numbers every-time only for the smaller figure out of the two?

2. How about i pick 2 different(or same) smart numbers for square's that is BCFD and ABDE? Since "they have not specified any number"


Source:
Geometry Guide.
Chapter 2
Problem set- 3Q

[tommywallach]

Hey Video,

That could totally work!

You could set the sides of big square as 1, then solve for a diagonal of the big square, which would be root 2. The square then has sides of (root 2)/2 (half the diagonal). This means the area of the smaller square is ((root 2)/2)^2, or 2/4, or 1/2.

The larger square is 1, so the shaded region is 3/4.

A: 3/4 * 2 = 1.5
B: 3 * 1/2 = 1.5

-t

[Videoorchard]

Hi Tommy,

Thank you for helpful info! :) I worked it out successfully! :)

I also wanted to ask on what the term diagrams "drawn to scale" really means? i keep seeing those keywords on the question, but i am not sure what it refers to? Also in this question how can we "Assume" the point F is the midpoint of BE? (The question hasn't explicitly specified it) :)

Thanx!

[tommywallach]

Great question!

Not drawn to scale means "Do not trust the PROPORTIONS of the drawing." In other words, if a side LOOKS bigger than another side, you don't necessarily KNOW that the side is actually bigger. Similarly, if an angle LOOKS less than 90, we can't say it IS unless they've stated it.

If they DO NOT warn you that the figure isn't drawn to scale, you can trust that the image is a faithful representation (of course, that still doesn't mean that an angle that looks 90 degrees is 90 degrees, because it could be off by a degree or two, but in a "figure not drawn to scale" image, an angle that looks 90 degrees could actually be 10 degrees!).

-t

[Videoorchard]

Thank you tommy for the explanation! :)

here is and additional blog post which people reading this post in the future might find extremely helpfull to clear your doubts regarding "Figures not drawn to scale".

link:
http://www.beatthegmat.com/mba/2011/01/ ... everything

[tommywallach]

Thanks Video. Beat the GMAT is a great site!