It is currently 24 Feb 2018, 07:59

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 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

Math Expert
Joined: 02 Sep 2009
Posts: 43896
If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value [#permalink]

### Show Tags

06 Nov 2014, 07:56
Expert's post
17
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

71% (02:56) correct 29% (03:08) wrong based on 200 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.
[Reveal] Spoiler: OA

_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value [#permalink]

### Show Tags

06 Nov 2014, 10:59
3
This post received
KUDOS
3
This post was
BOOKMARKED
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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
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

10 Nov 2014, 00:32
3
This post received
KUDOS
$$\sqrt{3x} - \sqrt{2y + 2z} = 4$$

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
Joined: 15 Feb 2016
Posts: 10
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value [#permalink]

### Show Tags

22 Feb 2016, 04:30
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.
Retired Moderator
Joined: 12 Aug 2015
Posts: 2428
GRE 1: 323 Q169 V154
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value [#permalink]

### Show Tags

07 Mar 2016, 06:17
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 ..
_________________

Getting into HOLLYWOOD with an MBA

Stone Cold's Mock Tests for GMAT-Quant(700+)

Non-Human User
Joined: 09 Sep 2013
Posts: 13763
Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value [#permalink]

### Show Tags

08 Mar 2017, 12:17
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: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value   [#permalink] 08 Mar 2017, 12:17
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 Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.