This is part of our
GRE Math Essentials project & GRE Math Essentials - A most comprehensive handout!!! that are the best complement to our
GRE Math Book. It provides a cutting-edge, in-depth overview of all the math concepts from basic to mid-upper levels. The book still remains our hallmark: from basic to the most advanced GRE math concepts tested during the exam. Moreover, the following chapters will give you many tips, tricks, and shortcuts to make your quant preparation more robust and solid.
Geometry is one of the areas of math in which you need to sort out and remember all sorts of formulas for area, volume, perimeter, and a variety of other measurements.For most of the students who are studying for the GRE, the statement above is all about the fourth macro-area in which we could categorize the questions in the quant section of the test. As such, the GRE Quantitative section tests four areas: Arithmetic, Algebra, Geometry, and Data Analysis.
A reliable estimation of the number of geometry questions during the quant section is roughly
15 percent of the total centers on geometry. i.e., more or less 3 questions of the entire bill. Thus, geometry problems follow a pretty even distribution of difficulty. The tougher problems tended to feature quadrilaterals or circles. However, the shape tested the most is probably the symbol itself of Geometry:
the triangle.
In this post, what will be relevant are not the formulas, the rules, the angles, and the measurements that I assume you have already learned. The goal here is to teach you how to have the reasoning of the questions. We could approach this by asking ourselves:
- How does a geometry question look like ??
- What steps have I need to follow to figure out the easiest way to solve it efficiently and faster?
- What is the most important tool I have in my arsenal ??
Answering the above pivotal questions, we do have :
- A puzzle
- Start from what you do know and break the question in easy steps
- VISUALIZATION
1) Memorize Key ConceptsThis is the first step you must walkthrough. A necessary evil. Hands down. If you do not have it in mind, if you do not know any possible variation of the key concepts as a second skin, you will never solve a question in the middle-upper range. Keep in mind that the GRE geometry questions are notorious nasty!
For all the possible concepts, there is nothing better than our
GRE - Math Book; specifically the Geometry Theory Chapter, the Practice Questions, and the Video Lessons.
Moreover, use the following Geometry PDF for a summary of all you do need for
Attachment:
Geometry.pdf [5.16 MiB]
Downloaded 479 times
2) Test Yourself With Realistic Practice QuestionsRealistic practice questions familiarize you with the types of geometry questions you’re likely to tackle on the GRE. And the more GRE geometry practice you do with GRE-like questions, the more quickly and accurately you should be able to answer such questions.
3) Know What You Can and Cannot AssumeGeometry diagrams on the GRE are not drawn to scale,
unless is clearly stated. This is an essential part when you approach a question. Assuming or inference based on information that we can not figure out aprioristically will bring you in the wrong direction.
4) Draw a PictureThe best way to tackle the problems is to draw the shapes yourself in the scenario; for instance, the question itself be in the word problem form. Or Re-shape the figure or drawn lines to find a way to the solution.
5) Plug In NumbersCertain questions, often Quantitative Comparisons, may give you geometry problems without offering any actual numbers or enough info to be able to plug in anything to a formula and solve it. Plugin numbers to see what is going on.
6) Approach Inscribed Shapes as Two Separate ShapesNow, finally, we can test a tough question, using all the previous information described, to reach what is the most powerful tool you might have to solve a geometry question:
VISUALIZATIONhttps://gre.myprepclub.com/forum/a-cef- ... tml#p39258Quote:
ACEF is a square region, and B, D, and G are midpoints of AC, CE, and BD.
Quantity A |
Quantity B |
The fraction of ACEF that is shaded |
\(\frac{7}{16}\) |
We will apply to solve the above question: the key geometry concepts, breaking down step by step the question, reshape the figure, visualize what is the question is asking us to solve, reach the solution straightforwardly.
Imagine that the red portion fills the small triangle \(BCD\), and we do have a straight line from C to G.
This represents the diagonal of our square. Actually, the square is equally divided into two parts: black and white.
Now pick a number and suppose that one side of the square is 4. So the area on the entire square is \(s^2=4^2 = 16\)
We do know that the square is equally divided into two areas: the black and the white.
So, the total black area is 8 (
black zone + red zone) and the white is also 8.
We also know that B and D are midpoints from the stem, so they are cut into two equal parts on the side of the square.
Pick the small triangle as follow.
The base is half the entire side CE which was 4, so the base CD is 2
Similarly, the height: the side CA was 4, so BC is 2
Area of the small triangle is \(\frac{b \times h}{2} = \frac{2 \times 2}{2} = 2\)
Now, half of the small triangle area is 1: the red part which is CGD = 1; the white part CGB is also 1.
At this point, we have all the information we do need to answer the question correctly:
1) The black area of the square was 8 over the entire square area, which was 16 :
\(\frac{8}{16}\)
MINUS the red part
CGD (
which is 1) \(=\frac{7}{16}\)
Therefore, the shaded region is \(\frac{7}{16}\) and quantity B is \(\frac{7}{16}\).
A = BThe answer is CAttachment:
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