1/(2 - \sqrt3) = ?

Hi Sandra2U,

The GMAT will often test you on ideas/concepts that you know, but in ways that you're not used to thinking about.

This question is built on 2 concepts:
1) Re-writing fractions
2) Quadratics (and how to "get rid of" radicals)

When re-writing a fraction, we're allowed to MULTIPLY or DIVIDE both parts of a fraction (as long as we do it to both parts).

For example...

2/4 = 1/2

1/3 = 5/15

With Quadratics, there are 3 that you should have memorized for Test Day. Here, we're dealing with this one....

(X-Y)(X+Y) = X^2 - Y^2

So, if the first parenthesis is (2−√3), the second parenthesis should be (2+√3).

From here, the math is just as chengliu describes.

As you continue to practice, get in the habit of thinking about what the question REMINDS you of - chances are that those exact concepts/rules are what you're supposed to use to answer the question.

GMAT assassins aren't born, they're made,
Rich