GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Feb 2019, 22:26

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free GMAT Strategy Webinar

February 16, 2019

February 16, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# (1+√3+√5)^2-(√3+√5)^2=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6949
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

26 Jun 2016, 06:38
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:46) correct 20% (02:02) wrong based on 195 sessions

### HideShow timer Statistics

(1+√3+√5)^2-(√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

*An answer will be posted in 2 days.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Current Student
Joined: 18 Oct 2014
Posts: 841
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98

### Show Tags

26 Jun 2016, 07:27
3
(1+√3+√5)^2-(√3+√5)^2

(1+√3)^2 + 5 +2 (1+√3) (√5) - ( 3 +5 + 2√3√5)

1+ 3+ 2√3 +5 +2 √5 + 2 √15 - 3-5 -2√15

1+2√3+2√5

_________________

I welcome critical analysis of my post!! That will help me reach 700+

CEO
Joined: 11 Sep 2015
Posts: 3431

### Show Tags

Updated on: 16 Oct 2018, 06:54
3
Top Contributor
1
(1+√3+√5)² - (√3+√5)² = ?

A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

Nice question!
First recognize that (1+√3+√5)² - (√3+√5)² is a DIFFERENCE OF SQUARES.
Here are some examples of differences of squares:
x² - 25y²
4x² - 9y²
49m² - 100k²

In general, we can factor differences of squares as follows:
- = (a+b)(a-b)

So, (1+√3+√5)² - (√3+√5)² = [(1+√3+√5) + (√3+√5)][(1+√3+√5) - (√3+√5)]
= [1+2√3+2√5][1]
= 1+2√3+2√5

_________________

Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 26 Jun 2016, 11:42.
Last edited by GMATPrepNow on 16 Oct 2018, 06:54, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6949
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

27 Jun 2016, 17:30
A^2-B^2=(A+B)(A-B). Hence, the correct answer is A.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Joined: 01 Jan 2016
Posts: 53
GPA: 3.75
WE: Engineering (Energy and Utilities)

### Show Tags

20 Aug 2017, 04:09
MathRevolution wrote:
(1+√3+√5)^2-(√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

*An answer will be posted in 2 days.

you can even do it with (A+B)^2 formula:

let √3+√5=x
Then the question becomes:
(1+x)^2-(x)^2=1^2+x^2+2x-x^2=1+2x=1+2(√3+√5)= option B
_________________

If you like it, give kudos. Thanks

The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand.
~Vince Lombardi

CEO
Joined: 11 Sep 2015
Posts: 3431

### Show Tags

20 Aug 2017, 05:27
Top Contributor
MathRevolution wrote:
(1+√3+√5)^2 - (√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

Another approach:

For test day, everyone should know the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, (1+√3+√5)² - (√3+√5)² ≈ (1+ 1.7 + 2.2)² - (1.7 + 2.2)²
≈ (4.9)² - (3.9)²
≈ 25 - 16
9

A. 1+2√3+2√5 ≈ 1 + 2(1.7) + 2(2.2) ≈ 8.8. CLOSE - KEEP
B. 1+2√3+3√5 ≈ 1 + 2(1.7) + 3(2.2) ≈ 11. ELIMINATE
C. 1-√3+√5 ≈ 1 - 1.7 + 2.2 ≈ 1.5. ELIMINATE
D. 1+√3-√5 ≈1 + 1.7 - 2.2 ≈ 0.4. ELIMINATE
E. √3+√5 ≈ 1.7 + 2.2 ≈ 3.9. ELIMINATE

_________________

Test confidently with gmatprepnow.com

Non-Human User
Joined: 09 Sep 2013
Posts: 9838

### Show Tags

23 Oct 2018, 23:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: (1+√3+√5)^2-(√3+√5)^2=?   [#permalink] 23 Oct 2018, 23:25
Display posts from previous: Sort by