Root of (16*20+8*32)= : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 00:10

### 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

# Root of (16*20+8*32)=

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 36619
Followers: 7103

Kudos [?]: 93599 [0], given: 10579

### Show Tags

03 Sep 2012, 05:00
Expert's post
9
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

78% (02:05) correct 22% (01:48) wrong based on 1041 sessions

### HideShow timer Statistics

$$\sqrt{16*20+8*32}=$$

(A) $$4\sqrt{20}$$
(B) 24
(C) 25
(D) $$4\sqrt{20}+8\sqrt{2}$$
(E) 32

Practice Questions
Question: 35
Page: 156
Difficulty: 600
[Reveal] Spoiler: OA

_________________
Manager
Joined: 16 Feb 2012
Posts: 237
Concentration: Finance, Economics
Followers: 7

Kudos [?]: 287 [2] , given: 121

### Show Tags

04 Sep 2012, 02:39
2
KUDOS
\sqrt{576} = 24
_________________

Kudos if you like the post!

Failing to plan is planning to fail.

Intern
Joined: 28 Aug 2012
Posts: 46
Location: Austria
GMAT 1: 770 Q51 V42
Followers: 3

Kudos [?]: 43 [1] , given: 3

### Show Tags

03 Sep 2012, 05:14
1
KUDOS
$$\sqrt{16*20+8*32}=\sqrt{16*(1*20+8*2)}=4*\sqrt{36}=4*6=24$$

Manager
Joined: 12 Mar 2012
Posts: 172
Location: India
Concentration: Technology, General Management
GMAT Date: 07-23-2012
WE: Programming (Telecommunications)
Followers: 0

Kudos [?]: 51 [1] , given: 4

### Show Tags

03 Sep 2012, 06:56
1
KUDOS
\sqrt{4*4*4*5 + 4*4*4*4} = 2*2*2\sqrt{5+4} = 8*\sqrt{9} = 8*3 = 24

B
_________________

FOCUS..this is all I need!

Ku-Do!

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8339
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 382

Kudos [?]: 2473 [1] , given: 164

### Show Tags

01 Mar 2015, 13:52
1
KUDOS
Expert's post
Hi soniasawhney,

As you've come to realize, you have to be careful when factoring out numbers from large calculations.

There are actually several different ways to 'factor down' and simplify this question, but your second approach is correct (and is just as valid as any other).

Here's another way to do it (based on the same ideas that you were using):

You might catch that 16 is a factor of BOTH terms (16x20 and 8x32). By factoring out 16, we can simplify the calculation even further....

Root[(16)(20) + (8)(32)]

Root[16[(20) + (8)(2)]
Root[16[(20) + 16]]
Root[16[36]]

4(6) = 24

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Math Expert Joined: 02 Sep 2009 Posts: 36619 Followers: 7103 Kudos [?]: 93599 [0], given: 10579 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 03 Sep 2012, 05:01 Expert's post 4 This post was BOOKMARKED SOLUTION $$\sqrt{16*20+8*32}=$$ (A) $$4\sqrt{20}$$ (B) 24 (C) 25 (D) $$4\sqrt{20}+8\sqrt{2}$$ (E) 32 Factor out 16: $$\sqrt{16*20+8*32}=\sqrt{16(20+8*2)}=\sqrt{16*36}=4*6=24$$. Answer: B. _________________ Math Expert Joined: 02 Sep 2009 Posts: 36619 Followers: 7103 Kudos [?]: 93599 [0], given: 10579 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 07 Sep 2012, 04:23 SOLUTION $$\sqrt{16*20+8*32}=$$ (A) $$4\sqrt{20}$$ (B) 24 (C) 25 (D) $$4\sqrt{20}+8\sqrt{2}$$ (E) 32 Factor out 16: $$\sqrt{16*20+8*32}=\sqrt{16(20+8*2)}=\sqrt{16*36}=4*6=24$$. Answer: B. Kudos points given to everyone with correct solution. Let me know if I missed someone. _________________ Intern Joined: 11 Sep 2012 Posts: 6 Location: Norway Concentration: Healthcare, International Business Schools: Insead '14 (A) GMAT Date: 11-19-2013 WE: Brand Management (Pharmaceuticals and Biotech) Followers: 0 Kudos [?]: 71 [0], given: 1 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 14 Oct 2012, 07:05 Obviously I don't get this..... I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help! Rt (16*20)+(8*32)= Rt(2^4*2^2*5)+(2^3*2^5)= 2^3 Rt(5)+2^4= 8Rt5+16 ?? Senior Manager Joined: 03 Sep 2012 Posts: 338 Location: United States Concentration: Healthcare, Strategy GMAT 1: 730 Q48 V42 GPA: 3.88 WE: Medicine and Health (Health Care) Followers: 16 Kudos [?]: 179 [0], given: 31 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 14 Oct 2012, 22:47 Quote: Obviously I don't get this..... I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help! Rt (16*20)+(8*32)= Rt(2^4*2^2*5)+(2^3*2^5)= 2^3 Rt(5)+2^4= 8Rt5+16 ?? If you find the shortcuts difficult then take the longer method, by which you can still solve it under the recommended time ... We are to find the Root of 16x20 + 8x32.. 16x20 = 320 , and 32 x 8 = 256 .. Adding them we get , 576 So we are to find the root of 576... 4 root 20 cannot be equal to 576 ( in order to get 576 from this root of 20 would have to be 144 which is obviously not possible) SO A IS OUT .. 24 . Multiplying 24 by 24 we get 576 therefore b is the correct answer.. _________________ "When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas Math Expert Joined: 02 Sep 2009 Posts: 36619 Followers: 7103 Kudos [?]: 93599 [0], given: 10579 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 15 Oct 2012, 02:02 asveaass wrote: Obviously I don't get this..... I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help! Rt (16*20)+(8*32)= Rt(2^4*2^2*5)+(2^3*2^5)= 2^3 Rt(5)+2^4= 8Rt5+16 ?? It should be: $$\sqrt{16*20+8*32}=\sqrt{2^4*2^2*5+2^3*2^5}=\sqrt{2^6*5+2^8}=\sqrt{2^6(5+2^2)}=\sqrt{2^6*9}=2^3*3=24$$. Hope it's clear. _________________ Director Status: Done with formalities.. and back.. Joined: 15 Sep 2012 Posts: 647 Location: India Concentration: Strategy, General Management Schools: Olin - Wash U - Class of 2015 WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 549 [0], given: 23 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 15 Oct 2012, 10:12 asveaass wrote: Obviously I don't get this..... I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help! Rt (16*20)+(8*32)= Rt(2^4*2^2*5)+(2^3*2^5)= 2^3 Rt(5)+2^4= 8Rt5+16 ?? Check highlighted portion, when u took out 2^3 , outside the root, basically you left inside only 2^2. However in highlighted portion, you marked it as 2^4 and hence the wrong answer. _________________ Lets Kudos!!! Black Friday Debrief SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 1937 [0], given: 193 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 25 Mar 2014, 01:19 Factor out 64 which is a perfect square $$\sqrt{64 * (5 + 4)}$$ $$\sqrt{64 * 9}$$ 8 * 3 = 24 = Answer = B _________________ Kindly press "+1 Kudos" to appreciate Current Student Joined: 14 Oct 2013 Posts: 48 GMAT 1: Q V Followers: 0 Kudos [?]: 6 [0], given: 120 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 28 Feb 2015, 17:15 why can't you factor out a 4? it doesnt work when I do it. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8339 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 382 Kudos [?]: 2473 [0], given: 164 Root of (16*20+8*32)= [#permalink] ### Show Tags 28 Feb 2015, 17:52 Hi soniasawhney, You CAN factor out a 4, but I'd like to see your work so that we can assess whether you're factoring out that 4 correctly or not. So, can you post your work/"steps"? As an aside, after factoring out a 4, you'd then have more work to do to get to the solution. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Current Student
Joined: 14 Oct 2013
Posts: 48
GMAT 1: Q V
Followers: 0

Kudos [?]: 6 [0], given: 120

### Show Tags

01 Mar 2015, 12:27
This is how I was doing it..

4[(4*5)+(2*8)]
4[20+16]
4[36]
take the square root...
(2)(6)=12

However, I now realize that the way I was factoring it, I actually was taking out 'too many' 4's and I should have done it like so...is this right?
4[(16*5)+(8*8)]
4[80+64]
4[144]
take the square root...
2*12=24

Let me know if that makes sense!
Intern
Joined: 30 Mar 2015
Posts: 1
Followers: 0

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

### Show Tags

14 Aug 2015, 19:58
why is 16 only factored from 2 and the 20 and 8 are left alone? sorry if this is a bad question, I'm new to the gmat and need every explanation i could get
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2654
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 117

Kudos [?]: 1342 [0], given: 789

### Show Tags

15 Aug 2015, 03:18
faizanswx wrote:
why is 16 only factored from 2 and the 20 and 8 are left alone? sorry if this is a bad question, I'm new to the gmat and need every explanation i could get

What post are you referring to?

Look at it this way:

$$\sqrt{16*20+8*32}$$ = $$\sqrt{16*20+8*2*16}$$ = $$\sqrt{16*(20+8*2)}$$ = $$\sqrt{16*(20+16)}$$ = $$\sqrt{16*36}$$ = $$\sqrt{4^2*6^2}$$

= $$4*6$$ = 24

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8339
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 382

Kudos [?]: 2473 [0], given: 164

### Show Tags

15 Aug 2015, 09:11
Expert's post
1
This post was
BOOKMARKED
Hi faizanswx,

When dealing with radicals, you should look for 'perfect squares' (re: 4, 9, 16, 25, etc.) that you can factor-out of the radical...

eg. √50 = √(25x2) = 5√2

In the given prompt, 16 can be factored-out (it becomes '4') and then the 36 can factored-out (it becomes '6').

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 07 Aug 2014
Posts: 9
Followers: 0

Kudos [?]: 3 [0], given: 8

### Show Tags

31 Oct 2015, 22:43
Ok, this problem is completely baffling the crap out of me! lol!!

Let me first state an assumption I made when doing this problem:

Step 1: Sqrt [(16*20)+(8*32)]= sqrt(16*20) + sqrt(8*32)

Step 2: Sqrt (16*20) = 4*Sqrt(20) = is atleast 16 & sqrt(8*32) = 16

So how in the world is this answer not atleast 32 (I know 32 is not in the answer choice) ? or did I make a big mistake in step 1?
Math Expert
Joined: 02 Sep 2009
Posts: 36619
Followers: 7103

Kudos [?]: 93599 [0], given: 10579

### Show Tags

01 Nov 2015, 01:08
EricImasogie wrote:
Ok, this problem is completely baffling the crap out of me! lol!!

Let me first state an assumption I made when doing this problem:

Step 1: Sqrt [(16*20)+(8*32)]= sqrt(16*20) + sqrt(8*32)

Step 2: Sqrt (16*20) = 4*Sqrt(20) = is atleast 16 & sqrt(8*32) = 16

So how in the world is this answer not atleast 32 (I know 32 is not in the answer choice) ? or did I make a big mistake in step 1?

You should brush-up fundamentals before attempting the questions.

Generally $$\sqrt{a+b}\neq \sqrt{a} + \sqrt{b}$$. For example, $$(\sqrt{4+4}=\sqrt{8})\neq (\sqrt{4} + \sqrt{4}=4)$$.

Theory on Exponents: math-number-theory-88376.html
Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

_________________
Re: Root of (16*20+8*32)=   [#permalink] 01 Nov 2015, 01:08

Go to page    1   2    Next  [ 27 posts ]

Similar topics Replies Last post
Similar
Topics:
5 (root2*root5)/[(root7-root2-root5)(root7+root2+root5)] 6 09 Dec 2015, 07:48
8 Root(80)+root(125) 15 01 Oct 2012, 04:02
4 root(16*20+8*32)= 5 23 Apr 2012, 08:35
13 (root(9 + root(80)) + root(9 - root(80)))^2 = 6 09 Jun 2010, 12:55
22 (root(9 + root(80)) + root(9 - root(80)))^2 = 15 02 Jan 2009, 17:42
Display posts from previous: Sort by