When you are composing your GRE essays, it is crucial that you use correct grammatical constructs. Apostrophes are used often, mostly to indicate ownership. Colons are used less frequently, and you might not use one at all in your essays. But if you do, you'll want to make sure that you use them correctly. You definitely don't want to incorrectly use a colon, which might then prejudice the reader of your essay to grant you a lower score.
Apostrophes most commonly identify ownership. If a noun is singular, to make it possessive you can simply add an apostrophe and an "s". For example:
Student's book (the book belongs to this one student)
Samantha's brain (the brain belongs to Samantha)
If the singular noun ends in "s" you can still add an apostrophe and an "s". Some examples:
Jones's apples or the boss's car
If the noun is plural and ends in "s," add only an apostrophe:
The girls' jump ropes or The Smiths' mail box.
Apostrophes are also used to identify letters that are removed in contractions:
I can't get there by myself.
The most common and easily understood use of a colon is to identify a list. It sets off the sentence from the first item in the list. For example:
Ice cream will be available in the following flavors: chocolate, vanilla, or cherry.
The colon is also used before a direct quote. While this is similar to comma usage, it tends to read a little more formally and more emphatically sets off the quote from the rest of the sentence.
The salesman always tells his clients: "If you can find a better deal, take it!"
A colon can also be used before an explanation:
The rebel forces were poised to take over the camp: they had circled the area, and were preparing their troops for battle.