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 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value

Author Message
TAGS:

### Hide Tags

Math Expert 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

1
21 00:00

Difficulty:   75% (hard)

Question Stats: 65% (03:11) correct 35% (03:07) wrong based on 175 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.

_________________
Verbal Forum Moderator 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

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  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

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

_________________
Kindly press "+1 Kudos" to appreciate Intern  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

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 D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If 3x – 2y – z = 32 + z and √(3x) - √(2y + 2z) = 4, what is the value  [#permalink]

### Show Tags

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

The values 1,1 would not always work ..
_________________
Manager  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

Hey! Great solutions. I got this after 2 tries. Anyone know a shortcut to this sum? 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  