Last visit was: 22 Apr 2026, 17:49 It is currently 22 Apr 2026, 17:49
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
505-555 (Easy)|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,754
Own Kudos:
810,671
 [3]
Given Kudos: 105,823
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,754
Kudos: 810,671
 [3]
Which of the following is equal to 1/(9 - 45) ? 31 Jan 2023, 07:24
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

79% (01:08) correct 21% (01:45) wrong based on 146 sessions

History

Date
Time
Result
Not Attempted Yet
Which of the following is equal to \(\frac{1}{9 - 4√5}\) ?

A. 9 + 4√5
B. 9 - 4√5
C. 9 + 2√5
D. 9 - 2√5
E. 4 + 9√5
ShowHide Answer
Official Answer
A
User avatar
Catman
User avatar
Joined: 03 Aug 2017
Last visit: 12 Feb 2025
Posts: 314
Own Kudos:
333
 [1]
Given Kudos: 219
Products:
My Reviews
Posts: 314
Kudos: 333
 [1]
Which of the following is equal to 1/(9 - 45) ? 31 Jan 2023, 07:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Multiplying the fraction by 9+\(4\sqrt{5}\),
We get 9+\(4\sqrt{5}\) divided by 1= (81-80) ,
Expression = 9+\(4\sqrt{5}\)
Choice A.
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,904
Own Kudos:
5,450
 [2]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,904
Kudos: 5,450
 [2]
Which of the following is equal to 1/(9 - 45) ? 31 Jan 2023, 08:08
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Which of the following is equal to \(\frac{1}{9 - 4√5}\) ?

A. 9 + 4√5
B. 9 - 4√5
C. 9 + 2√5
D. 9 - 2√5
E. 4 + 9√5
Show more
\(\frac{1}{9 - 4√5}\)

Or, \(\frac{(9 + 4√5)}{(9 - 4√5)(9 + 4√5)}\)

Or, \(\frac{(9 + 4√5)}{(81 - 80)}\)

Or, Or, \((9 + 4√5)\), Answer will be (A) \(9 + 4√5\)
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 22 Apr 2026
Posts: 22,278
Own Kudos:
26,528
 [1]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,278
Kudos: 26,528
 [1]
Which of the following is equal to 1/(9 - 45) ? 31 Jan 2023, 18:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Which of the following is equal to \(\frac{1}{9 - 4√5}\) ?

A. 9 + 4√5
B. 9 - 4√5
C. 9 + 2√5
D. 9 - 2√5
E. 4 + 9√5
Show more

We can multiply the numerator and denominator by 9 + 4√5.

When doing so, we can use the difference of two squares formula in the denominator, and we have

(9 + √5)/[9^2) - (4√5)^2]

(9 + √5)/[81 - 80] = 9 + √5

Answer: A
User avatar
mathlaf
User avatar
Joined: 01 Feb 2023
Last visit: 21 Jan 2024
Posts: 1
Given Kudos: 13
Posts: 1
Kudos: 0
Which of the following is equal to 1/(9 - 45) ? 01 Feb 2023, 07:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How do you know that you have to multiply the numerator by:
9 + 4√5? Abhishek009
User avatar
GKLemon
User avatar
Joined: 14 Aug 2022
Last visit: 29 Jun 2025
Posts: 11
Own Kudos:
3
Posts: 11
Kudos: 3
Which of the following is equal to 1/(9 - 45) ? 04 Feb 2023, 14:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mathlaf
How do you know that you have to multiply the numerator by:
9 + 4√5?Abhishek009[/url]
Show more


The denominator can be rationalized by its conjugate pair to remove a radical and make the fraction easier to understand:

This is done by taking the denominator 9 - 4√5 and multiplying it by its conjugate pair 9 + 4√5. This will result in the removal of a radical to "simplify" the denominator.

(9 - 4√5) x (9 + 4√5)

= (9 x 9) + ((9 x 4√5) - (9 x 4√5)) - (4√5 x 4√5)

= 81 - (16 x 5)

= 81 - 80

= 1

And since we multiply the denominator by the conjugate pair of 9 - 4√5 (i.e. multiplied by 9 + 4√5), we must multiply the numerator by 9 + 4√5

This results in the answer being 9 + 4√5 since 1 x (9 + 4√5) = 9 + 4√5.

This way of simplification is true for all "two-term" denominators with radicals

Conjugate pairs:

1/ (3 + √3) conjugate (3 - √3)

1/ (5√2 + 7) conjugate (5√2 - 7)

1/ (12 - 3√7) conjugate (12 + 3√7)

in essence, when multiplying a two-term radical by its conjugate pair, the radical cancels out. A conjugate pair to two-term radical is always the first term and the "opposite sign" of the second term.

Hope this helps.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
Which of the following is equal to 1/(9 - 45) ? 20 Nov 2025, 01:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109754 posts
Krunaal
Tuck School Moderator
853 posts