Geometry
What if You are Stumped?
There will be an item or two where your knowledge of geometry fails you. Don’t sweat it. It happens to everyone. There are so many rules, one of them is bound to slip through the mental cracks occasionally. When this occurs, take solace in the directions for the Math section, which state:
Figures that accompany problems in this test are intended to provide information useful in solving the problems.
On Treasure Map items, this means you can use your eyes to do some Process of Elimination (shortened to “POE” for those of us on-the-go). If the figure is not drawn to scale (i.e., False Map), or there is no figure (i.e., No Map), this method won’t work.
Eyeballing
4. If ˚, then what is the area of rectangle ACDE?
(A)
(B) 5
(C) 7
(D) 35
(E) 49
Cast your eyes back to this quaint house item again. To find the area of the rectangle, you need length AC. You already have one length, CD=7. Look at AC and ask, “Does AC look shorter, longer, or about the same as CD?” Your eyes should tell you that it looks a bit smaller. So let’s say AC = 6, since 6 is a little smaller than 7.
If AC = 6, then the area of rectangle ACDE is: A = lw = (6)(7) = 42. This isn’t the actual answer, but it’s a good approximation of it. Armed with this guess, you can see that answer choices A, B, and C are all way too small to be the right answer. Recall that numerical answers are always listed in order from smallest to largest or vice versa, so you don’t have to figure out , choice A, to know that it’s smaller than 5 and therefore incorrect.
Using your eyes helps you bypass traps completely. The answer has to be either D or E. If it were E, then the width and length would both be 7. Your eyes tell you that AC is less than CD, so E is not the best guess. Pick D, and you’ll get the right answer. It won’t work this smoothly every time you try eyeballing an item, but you’ll often be able to brush off a few choices and then take a guess.
The house example dealt with lengths, but you can also get some POE distance out of eyeballing angles:
2. If is a line, which of the following is the measurement of ?
(A) 20˚
(B) 80˚
(C) 100˚
(D) 110˚
(E) 160˚
Just eyeball and ask yourself, “Is this angle greater than or less than 90˚?” Everyone has a good idea what a 90˚ angle looks like. is a little more than 90˚. Not much, but a bit more. Scanning the answer choices, you can eliminate choices A and E quickly, since both are way off base. Choice B, 80˚, is closer, but it‘s less than 90˚, so it’s unlikely to be the correct answer. That leaves us with C and D. There’s no way to use your eyes to make a 10˚ call one way or the other, but for a fifty-fifty chance you can guess, which is well ahead of the wrong-answer penalty. The answer, by the way, is C:
You visually estimate any geometry item that’s drawn to scale. Even if you understand the “math” needed, using both approaches to attack an item greatly increases your chance of getting it right. If you don’t understand the math, then using your eyes can often give you a good shot at a tough item.
Plugging In for x
If you’ve tried the step method or eyeballing and neither approach works for you, try plugging in values for x in an equation to see where that gets you. Look at this item:
4. Which of the following is the equation of the parabola pictured above?
(A)
(B)
(C)
(D)
(E)
Here are the two best methods for attacking this item:
  1. Ask yourself, Am I familiar with the standard form of the equation for a parabola? If you know it, you’re golden.
  2. If you don’t know it, who cares? Plug in values for x and see what you get.
There’s a good chance you won’t remember the equation for a parabola, and unfortunately the Math section reference area does not provide this bit of information. So your best bet is to choose a value for x and plug it into the five answer choices. Look at where the parabola dips to its lowest. It’s in the part of the graph where x is negative. Now look at your answer choices. What would happen if x = –5? If that occurs for choice A, you get a big messy number for y. If you plug in x = –5 for choice B, that whole mess of numbers cancels out since the portion inside the parentheses (x + 5) becomes zero. You’re left with y = 2, and if you look at the parabola, you could guess that (–5, 2) is the lowest point on the parabola.
So only answer choices with (x + 5) should be considered, meaning you can get rid of A and C. Now plug in x = 0. You should get two answers (choices D and E) that say y has a negative value when x equals zero, and one choice, B, with a positive value. Look at that parabola. It’s heading toward the sky, baby! And so y is positive, which means the answer must be B.
Note that this method will only work on items where the answer choices are equations or functions. If there is no x in the item, you will not be able to plug in values for it.
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