Don't be fooled! The geometry questions are generally straight forward, and if you think you need to use a complicated formula to get the answer, then think harder, because most likely there is a shortcut. As a rule of thumb, write down what you know and what is given, and from that information, you should be able to arrive at the answer in at most 3 or 4 steps.
For example:
If a triangle with a base
of 10ft has the same area as a circle with radius 3ft, then what is the height of the triangle?
A triangle, a circle? Areas? Huh? Is there a formula? How do they
relate? They don't, but what you'll need to figure out is that you are merely
dealing with the area formula for a triangle and a circle, both of which are
easy formulas.
A circle with radius of 3ft has an area of pi*r2,
and if r=3, then the area of the circle is 9pi. So 9pi is equal to the
area of a triangle, and we know that the area formula for a triangle is base
times height, divided by 2 (and we know that the base is 10). So we set up the
following equation, and follow through with the calculations:
9pi
|
=
|
(10 *
height) / 2
|
18pi
|
=
|
10 *
height
|
18pi/10
|
=
|
height
|
There are
certain key facts that you should remember when dealing with products, sums,
etc. The product of 0 and any other number is always 0. If the product of 2
numbers is 0, then at least one of the numbers must be 0.
The sum of any number and its opposite is
always 0.
For example, the sum of 4 and its opposite, -4, is 0, because 4 + (-4) = 0.
For example, the sum of 4 and its opposite, -4, is 0, because 4 + (-4) = 0.
A sample GRE arithmetic question that requires you to have knowledge of
opposite numbers is the following:
How many pairs of opposite numbers are there which are greater than -9 and smaller than 11? |
The integers that are greater than -9 and smaller than 11 include -8,
-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. And there are
8 pairs of opposite numbers.
If you have an
even amount of negative numbers, then the product of those numbers is positive.
If you have an odd amount of negative numbers, then the product of those
numbers is negative. This is an often-tested concept on the GRE, so be ready!
For example, (-1)(-2)(-5) = -10 and
(-1)(-2)(-5)(-2) = 20
For example, the
first 15 positive prime numbers, starting with 2, are 2, 3, 5, 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43 and 47. Should you memorize these? NO! But you
should be able to look at a number and determine if it is not a prime number.
If the number can be divided by 2, 3, 4, 5, ..., etc, or by any number other
than itself and 1, then it is NOT prime.
What are the
prime factors of 54?
First, you must determine the factors of 54,
which are 1, 2, 3, 6, 9, 18, 27 and 54, and which of those are prime? Only 2
and 3 are prime numbers -- remember that 1, by definition, is NOT a prime number.
Lesson 3 is available in simplified format as a download
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