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

It is currently 11 Dec 2019, 11:49
Register
GMAT Club Tests
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
CLICK HERE TO HIDE/SHOW EVENTS

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
Print view
First unread post
 
  Sort by Date Sort by Kudos  
Search for:
 
PREVIOUS TOPIC
NEXT TOPIC
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
CAT Tests
Top Member of the Month
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
23
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

65% (03:12) correct 35% (03:07) wrong based on 178 sessions

HideShow timer Statistics

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.
Spoiler: OA

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Most Helpful Community Reply
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 583
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.
_________________
All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions
Signature Read More
General Discussion
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
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
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: 2551
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 ..
_________________
Give me a hell yeah ...!!!!!

MBA Recruiting:- EMPLOYMENT AND SALARY STATISTICS AT TOP B-SCHOOLS IN THE US! (2018)
MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!
The MOST AFFORDABLE MBA programs!
STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)
AVERAGE GRE Scores At The Top Business Schools!
Signature Read More
Manager
Manager
avatar
B
Joined: 23 Jul 2015
Posts: 79
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
Print view
First unread post
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  

Moderators: chetan2u, Bunuel, VeritasKarishma, Gladiator59, generis

Search for:
PREVIOUS TOPIC
NEXT TOPIC





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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions