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

 It is currently 21 Feb 2019, 16:55

### 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

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# (5 + 5√5)/(10 + √500)

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53063
(5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

23 Sep 2015, 01:38
1
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:15) correct 6% (01:46) wrong based on 100 sessions

### HideShow timer Statistics

$$\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}=$$

A) 1/2
B) 2
C) 1 + √5
D) 1 + 5√5
E) 5 + √5

Kudos for a correct solution.

_________________
Intern
Joined: 02 Jan 2014
Posts: 38
Re: (5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

23 Sep 2015, 01:50
1

5(1+root5)/10(1+root5) which equals 1/2
Intern
Joined: 27 Jun 2015
Posts: 6
Concentration: Marketing, Entrepreneurship
Schools: Haas '18
Re: (5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

23 Sep 2015, 02:42
1
Bunuel wrote:
$$\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}=$$

A) 1/2
B) 2
C) 1 + √5
D) 1 + 5√5
E) 5 + √5

Kudos for a correct solution.

numerator: [5 + 5(5)^1/2] X [5 - 5(5)^1/2]
denominator: [10 + (500)^1/2] x [5 - 5(5)^1/2]

numerator = 25 -5x5x5 = -100
denominator = 50 - 5x5x10 = -200

numerator/denominator = -100/-200 = 1/2
Intern
Joined: 22 Sep 2015
Posts: 5
(5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

23 Sep 2015, 02:57
1

(5+5√5)/(10+√500)

=(5+5√5)/(10+√5³*2²)

=(5+5√5)/(10+5*2√5)

=(5+5√5)/(10+10√5)

=(5(1+√5))/(10(1+√5))

=5/10 = 1/2
Manager
Joined: 29 Jul 2015
Posts: 158
(5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

23 Sep 2015, 04:24
2
Bunuel wrote:
$$\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}=$$

A) 1/2
B) 2
C) 1 + √5
D) 1 + 5√5
E) 5 + √5

Kudos for a correct solution.

$$\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}$$

=$$\frac{5 + 5\sqrt{5}}{10+10\sqrt{5}}$$

=$$\frac{5(1 + \sqrt{5})}{10(1+\sqrt{5})}$$

=$$\frac{5}{10}$$

=$$\frac{1}{2}$$

Intern
Joined: 08 Sep 2015
Posts: 1
Re: (5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

23 Sep 2015, 05:26
1
I struggled on solving so I used trick :

1st - convert the square root of 500 in decent form : (5 + 5√5)/(10 + 10√5)
2nd - Factorise 5 in numerator and denominator : 5*(1+√5) / 5*(2+2√5)

You end up with the following expression : 1+√5 / 2+2√5

Now if you look at the answer choices, there's only one that holds value between 0 and 1 (1/2-answer A).

Looking again at the expression, you can see that it cannot be above 1, so answer A it is.
Intern
Joined: 02 Feb 2014
Posts: 37
Concentration: Finance, General Management
GPA: 3.5
Re: (5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

23 Sep 2015, 06:05
1
Toutatis wrote:
I struggled on solving so I used trick :

1st - convert the square root of 500 in decent form : (5 + 5√5)/(10 + 10√5)
2nd - Factorise 5 in numerator and denominator : 5*(1+√5) / 5*(2+2√5)

You end up with the following expression : 1+√5 / 2+2√5

Now if you look at the answer choices, there's only one that holds value between 0 and 1 (1/2-answer A).

Looking again at the expression, you can see that it cannot be above 1, so answer A it is.

If you have: $$\frac{5 + 5√5}{10 + 10√5}$$, you can factorise:
Numerator: $$1*(5 + 5√5)$$
Denominator: $$2*(5 + 5√5)$$.

So you have $$\frac{1*(5 + 5√5)}{2*(5 + 5√5)}$$ $$=\frac{1}{2}$$

Hope it helps.
_________________

"The stock market is filled with individuals who know the price of everything, but the value of nothing." - Philip Fisher

Intern
Joined: 03 May 2015
Posts: 2
Re: (5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

24 Sep 2015, 07:15
1

5 (1+ root5) / 10 (1+ root5) = 5/10 = 1/2 (A)
Manager
Joined: 22 Aug 2012
Posts: 73
Concentration: Technology
GMAT 1: 710 Q47 V40
Re: (5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

24 Sep 2015, 08:31
1
I believe the answer is A. See below for explanation.

(5 + 5√5) / (10 + √500)
5(1+√5) / 10(1+√5)
5/10*(1+√5)/(1+√5)
1/2*1
1/2
Non-Human User
Joined: 09 Sep 2013
Posts: 9879
Re: (5 + 5√5)/(10 + √500)  [#permalink]

### Show Tags

27 Oct 2017, 21:47
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: (5 + 5√5)/(10 + √500)   [#permalink] 27 Oct 2017, 21:47
Display posts from previous: Sort by