Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 May 2015, 18:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 1/(2 - \sqrt3) = ?

Author Message
TAGS:
Intern
Joined: 29 Mar 2006
Posts: 27
Followers: 0

Kudos [?]: 3 [0], given: 0

1/(2 - \sqrt3) = ? [#permalink]  23 May 2008, 10:00
00:00

Difficulty:

35% (medium)

Question Stats:

75% (01:36) correct 25% (01:22) wrong based on 14 sessions
$$\frac{1}{2 - \sqrt{3}} = ?$$

A. $$\sqrt{3} - 2$$
B. $$2 + \sqrt{3}$$
C. $$\sqrt{2} + \sqrt{3}$$
D. $$2 - \sqrt{3}$$
E. $$\sqrt{3} + 4$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 May 2015, 09:02, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Current Student
Joined: 28 Dec 2004
Posts: 3390
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 182 [0], given: 2

Re: 1/(2 - \sqrt3) = ? [#permalink]  23 May 2008, 10:04
i get B

just multiply the equation by [2+sqrt(3)] / [2+sqrt(3)]
Intern
Joined: 26 May 2015
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: 1/(2 - \sqrt3) = ? [#permalink]  26 May 2015, 06:14
OMG IT"S VERY HARD!!!!
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 2203
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 95

Kudos [?]: 596 [1] , given: 43

Re: 1/(2 - \sqrt3) = ? [#permalink]  26 May 2015, 08:51
1
KUDOS
Expert's post
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

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
_________________

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

EMPOWERgmat GMAT Club Page, Study Plans, & Discounts

Math Expert
Joined: 02 Sep 2009
Posts: 27512
Followers: 4319

Kudos [?]: 42453 [0], given: 6029

Re: 1/(2 - \sqrt3) = ? [#permalink]  26 May 2015, 09:02
Expert's post
chengliu wrote:
$$\frac{1}{2 - \sqrt{3}} = ?$$

A. $$\sqrt{3} - 2$$
B. $$2 + \sqrt{3}$$
C. $$\sqrt{2} + \sqrt{3}$$
D. $$2 - \sqrt{3}$$
E. $$\sqrt{3} + 4$$

Multiply both numerator and denominator by $$(2 + \sqrt{3})$$. That yields $$\frac{2 + \sqrt{3}}{(2 + \sqrt{3})(2 - \sqrt{3})} = \frac{2 + \sqrt{3}}{4 - 3} = 2 + \sqrt{3}$$.

This algebraic manipulation is called rationalisation and is performed to eliminate irrational expression in the denominator. For this particular case we are doing rationalisation by applying the following rule: $$(a-b)(a+b)=a^2-b^2$$. The concept of rationalisation of a fraction used to solve this problem is often tested on the GMAT.

Questions relied on this technique:
if-x-0-then-106291.html
if-n-is-positive-which-of-the-following-is-equal-to-31236.html
in-the-diagram-not-drawn-to-scale-sector-pq-is-a-quarter-139282.html
in-the-diagram-what-is-the-value-of-x-129962.html
the-perimeter-of-a-right-isoscles-triangle-is-127049.html
which-of-the-following-is-equal-to-98531.html
if-x-is-positive-then-1-root-x-1-root-x-163491.html

Hope it helps.
_________________
Re: 1/(2 - \sqrt3) = ?   [#permalink] 26 May 2015, 09:02
Similar topics Replies Last post
Similar
Topics:
4 If a^{2/3} - b^{2/3} = 12, then \sqrt[3]{a} + \sqrt[3]{b} = ? 5 06 Nov 2014, 08:02
sqrt3 + 1/3+sqrt3 - 1/3-sqrt3 1 29 Nov 2013, 04:25
1/(2 - sqrt(3)) = ? (m25#36) 2 15 Feb 2012, 06:04
frac{1}{2 - \sqrt{3}} = ? * \sqrt{3} - 2 * 2 + \sqrt{3} * 3 18 Oct 2008, 23:46
1/(2+ sqrt(3)) = sqrt(3) - 2 2 - sqrt(3) sqrt(2) + 4 08 Jul 2007, 12:53
Display posts from previous: Sort by