A Right Triangle Peg In A Round Hole

Multiple figures geometry questions are common on the GMAT. Make sure you recognize how the two shapes relate to each other by noting

Question of the Day

Evaluate the expression $16p - 6q + 2r$if $p, q$ and $r$are positive numbers in a geometric progression and $r=q+6$and $q=p+3$.

When you see a 60 degree angle in a triangle, you should be thinking one of two possibilities: equilateral or 30-60-90 triangle. Once you spot the latter in this problem, the rest of solving just comes down to arithmetic. Be on the lookout for problem types that show up often on the GMAT!

Avoiding Distracting Information

In addition to testing your knowledge of difficult topics and challenging concepts, the GRE may also try to overwhelm you with an excess of information or complexity.

In the following question, what information is useful, and what is presented simply to distract you from the problem at hand?

Question of the Day

A geometrical figure   is defined such that there are concentric semi-circles with a right isosceles triangle inscribed within each semi-circle. The following figure shows with 3 concentric circles and 3 right triangles, one inside each semi-circle. If the radius of the th innermost circle is , pertaining to the figure, where radius  is given to be  units, what will be the perimeter of the 4th triangle?

Much of the information presented at the outset of this problem is unnecessary, and is presented simply as a means to confuse and overwhelm. Focus on the pertinent data in every problem, and don’t let an excess of information throw you off track!

Forget a formula? Just derive it!

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?