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

 It is currently 18 Oct 2019, 07:39

### 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

# Which of the following equals (2^2 + 2^2 + 2^3 +2^4)(5^(1/2) + 3^(1/2)

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
Which of the following equals (2^2 + 2^2 + 2^3 +2^4)(5^(1/2) + 3^(1/2)  [#permalink]

### Show Tags

26 Aug 2018, 06:33
00:00

Difficulty:

25% (medium)

Question Stats:

79% (00:56) correct 21% (01:03) wrong based on 32 sessions

### HideShow timer Statistics

Which of the following equals $$\frac{2^{2}+2^{2}+2^{3}+2^{4}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}$$?

(A) 2
(B) 4
(C) 8
(D) 16
(E) 32

_________________
Intern
Joined: 25 Aug 2018
Posts: 4
Re: Which of the following equals (2^2 + 2^2 + 2^3 +2^4)(5^(1/2) + 3^(1/2)  [#permalink]

### Show Tags

26 Aug 2018, 06:36
(4+4+8+16)/(5-3)
=32/2
=16

Posted from my mobile device
Intern
Joined: 20 Aug 2018
Posts: 6
Location: United States (NJ)
Concentration: Finance, Economics
GPA: 3.5
WE: Engineering (Energy and Utilities)
Re: Which of the following equals (2^2 + 2^2 + 2^3 +2^4)(5^(1/2) + 3^(1/2)  [#permalink]

### Show Tags

26 Aug 2018, 09:27
(4+4+8+16)/(5-3)
32/2
=16

D
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: Which of the following equals (2^2 + 2^2 + 2^3 +2^4)(5^(1/2) + 3^(1/2)  [#permalink]

### Show Tags

26 Aug 2018, 10:24
Bunuel wrote:
Which of the following equals $$\frac{2^{2}+2^{2}+2^{3}+2^{4}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}$$?

(A) 2
(B) 4
(C) 8
(D) 16
(E) 32

$$\frac{2^{2}+2^{2}+2^{3}+2^{4}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}$$
=$$\frac{2^2(1+1+2+2^2)}{{\sqrt{5}}^2-{\sqrt{3}}^2}$$ (Rationalizing denominator using axiom:-$$(a+b)(a-b)=a^2-b^2$$)
=$$\frac{4*8}{5-3}$$
=$$\frac{4*8}{2}$$
=16

Ans. (D)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Re: Which of the following equals (2^2 + 2^2 + 2^3 +2^4)(5^(1/2) + 3^(1/2)   [#permalink] 26 Aug 2018, 10:24
Display posts from previous: Sort by