quantQ
 Forget a formula? Just derive it!

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Despite your best efforts, you will probably not be able to remember every single fact about every single possible algebra or geometry property in the universe for the GRE. The good news – it doesn’t matter!

Beyond the simplest properties, most relevant information can be derived from what you know. When solving the following problem, see if you can do it without knowing the formula for a trapezoid.

Question of the Day


The figure shows two squares ABCD and PQRS having a common center O and having sides of 6 units and 4 units respectively. A semicircle passes through the center O. What is the area of the shaded region?

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Even if you don’t have the formula for the area of a trapezoid memorized, you can still solve this problem, because a trapezoid is made up of a rectangle and two triangles (the formulae of which you DO definitely need to know). So if you come across a fact or figure on a test that you can’t calculate, don’t freak out – see if you can use what you already know to solve the problem!

quantQ
 Geometry Shortcuts

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For each and every question on the GRE, there is a way to calculate the answer. However, as we know, there are often better (meaning faster and/or simpler) methods of solving that are possible. Can you figure out a way to solve the following problem in only two steps?

Question of the Day

The following figure shows square ABCD such that each of its sides is 2 units long. If a triangle EGF is drawn inside square ABCD such that EF is parallel to side BC and EG=GF, what is the area of triangle EGF?

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To avoid performing any ugly calculations, try the following approach: Each small triangle is 1/8 of the large square, so two of those triangles must be 1/4 the area of the large square. Since the large square is 2 by 2 = 4 units, then the area of the triangle EGF (composed of two small triangles) must be 1/4th of that, or 1.