Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 19 Jul 2019, 16:00

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.

Close

Request Expert Reply

Confirm Cancel

If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56300
If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value  [#permalink]

Show Tags

New post 06 Nov 2014, 08:56
1
21
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

65% (03:11) correct 35% (03:07) wrong based on 175 sessions

HideShow timer Statistics


Most Helpful Community Reply
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 604
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value  [#permalink]

Show Tags

New post 06 Nov 2014, 11:59
5
3
Bunuel wrote:

Tough and Tricky questions: Algebra.



If 3x – 2y – z = 32 + z and \(\sqrt{3x} - \sqrt{2y + 2z} = 4\), what is the value of x + y + z?

(A) 3
(B) 9
(C) 10
(D) 12
(E) 14

Kudos for a correct solution.


From equation 1, we know that 3x-32 = 2y+2z.

Now, we also know that \(\sqrt{3x} - \sqrt{2y + 2z} = 4\)
or
\(\sqrt{3x} - 4 = \sqrt{2y + 2z}\) -->\(\sqrt{3x} - 4 = \sqrt{3x-32}\)

Square on both sides, to get \(3x+16 -8\sqrt{3x} = 3x-32\), cancel 3x on both sides, and we get

\(8\sqrt{3x} = 48 --> x = 12\)

Thus, 3x-32 = 2y+2z, hence, y+z = 2 and x+y+z = 14.

E.
_________________
General Discussion
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1787
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value  [#permalink]

Show Tags

New post 10 Nov 2014, 01:32
3
\(\sqrt{3x} - \sqrt{2y + 2z} = 4\)

Say \(\sqrt{2y + 2z} = 2\)

then y = 1, z = 1

Say \(\sqrt{3x} = 6\)

then x = 12

These values also satisfy equation 3x – 2y – z = 32 + z

x+y+z = 12+1+1 = 14

Answer = E
_________________
Kindly press "+1 Kudos" to appreciate :)
Intern
Intern
avatar
Joined: 15 Feb 2016
Posts: 8
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value  [#permalink]

Show Tags

New post 22 Feb 2016, 05:30
3x – 2y – z = 32 + z means 3x – 2y – 2z = 32
Or 3x – (2y +2z) = 32

This is of the form \(a^2 - b^2 = 32\), i.e., (a+b)*(a-b) = 32

The second equation is of the form \(a - b = 4\). This means \(a + b = 32/4 = 8\)

Now a+b = 8, a-b=4. So 2a = 12, or a=6. (a is \sqrt{(3x)}). So x is 12.

Now, \sqrt{(3x)} - \sqrt{(2y + 2z)} = 4, or 6-\sqrt{(2y + 2z)} = 4
\sqrt{(2y + 2z)} = 2, or: (2y + 2z) = 4
(2y + 2z) + 2x = 4 + 2*12 = 28, or x+y+z = 14.
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value  [#permalink]

Show Tags

New post 07 Mar 2016, 07:17
PareshGmat wrote:
\(\sqrt{3x} - \sqrt{2y + 2z} = 4\)

Say \(\sqrt{2y + 2z} = 2\)

then y = 1, z = 1

Say \(\sqrt{3x} = 6\)

then x = 12

These values also satisfy equation 3x – 2y – z = 32 + z

x+y+z = 12+1+1 = 14

Answer = E



The values 1,1 would not always work ..
_________________
Manager
Manager
avatar
B
Joined: 23 Jul 2015
Posts: 59
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value  [#permalink]

Show Tags

New post 19 Apr 2019, 19:42
Hey! Great solutions. I got this after 2 tries. Anyone know a shortcut to this sum?
GMAT Club Bot
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value   [#permalink] 19 Apr 2019, 19:42
Display posts from previous: Sort by

If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne