It is currently 24 Feb 2018, 00:03

### 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

# The concentration of a certain chemical in a full water tank

Author Message
TAGS:

### Hide Tags

Director
Joined: 17 Oct 2005
Posts: 922
The concentration of a certain chemical in a full water tank [#permalink]

### Show Tags

16 Nov 2005, 17:58
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:45) correct 24% (02:26) wrong based on 306 sessions

### HideShow timer Statistics

The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is $$3 + \frac{4}{\sqrt{5-x}}$$ parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Mar 2014, 03:36, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director
Joined: 21 Aug 2005
Posts: 785

### Show Tags

16 Nov 2005, 18:39
3 + 4/sqrt(5-x) = 6

4/sqrt(5-x) = 3

16/(5-x) = 9

9x = 29 -> x = 3.2
Current Student
Joined: 28 Dec 2004
Posts: 3342
Location: New York City
Schools: Wharton'11 HBS'12

### Show Tags

16 Nov 2005, 18:48
I was going to go with 3.0...but then the question says witin 0.1 feet...and with 3.0..we get within 0.2 feet...so I would have just picked 3.2 at that point....

anyway

4/sqrt(5-x)=3

16/(5-x)=9

16=45-9x

solve for X...
VP
Joined: 06 Jun 2004
Posts: 1049
Location: CA

### Show Tags

16 Nov 2005, 18:49
joemama142000 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is 3 + 4/sqrt(5-x) parts per million, where 0< x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

A) 2.4 ft
B) 2.5 ft
C) 2.8 ft
D) 3.0 ft
E) 3.2 ft

3 + 4/sqrt(5-x) = 6

solve for x, x = 29/9 = 3.2 ft

E
Director
Joined: 21 Aug 2005
Posts: 785

### Show Tags

16 Nov 2005, 18:49
fresinha12 wrote:
I was going to go with 3.0...but then the question says witin 0.1 feet...and with 3.0..we get within 0.2 feet...so I would have just picked 3.2 at that point....
anyway
4/sqrt(5-x)=3
16/(5-x)=9
16=45-9x
solve for X...

You are tired. Go to bed
Current Student
Joined: 28 Dec 2004
Posts: 3342
Location: New York City
Schools: Wharton'11 HBS'12

### Show Tags

16 Nov 2005, 18:51
not yet...its raining here...and I want to go to the gym

to go or not to go to gym is the question...what would GSR do?hmm

gsr wrote:
fresinha12 wrote:
I was going to go with 3.0...but then the question says witin 0.1 feet...and with 3.0..we get within 0.2 feet...so I would have just picked 3.2 at that point....
anyway
4/sqrt(5-x)=3
16/(5-x)=9
16=45-9x
solve for X...

You are tired. Go to bed
Director
Joined: 21 Aug 2005
Posts: 785

### Show Tags

16 Nov 2005, 18:57
Thumbs up! for a 'go' to gym!
Current Student
Joined: 28 Dec 2004
Posts: 3342
Location: New York City
Schools: Wharton'11 HBS'12

### Show Tags

16 Nov 2005, 19:00
gym it is...see you in an hr...

gsr wrote:
Thumbs up! for a 'go' to gym!
Current Student
Joined: 08 Nov 2013
Posts: 166
GMAT 1: 710 Q43 V44
GMAT 2: 770 Q49 V46
GPA: 3
Re: The concentration of a certain chemical in a full water tank [#permalink]

### Show Tags

01 Mar 2014, 12:11
My brain is cloudy, going to gym to clear it up....but how did you guys know to set the equation equal to 6? Once we get to the equation the math is easy but I did not know where to begin. Can someone explain?
_________________

"Never, Never, Never give in."

From 510 to 770:
http://gmatclub.com/forum/510-to-770-49q-46v-7ir-what-worked-for-me-2-years-176580.html#p1394349

From 2 dings to multiple admits (use Paul Bodine):

Math Expert
Joined: 02 Sep 2009
Posts: 43894
Re: The concentration of a certain chemical in a full water tank [#permalink]

### Show Tags

02 Mar 2014, 03:40
1
KUDOS
Expert's post
PeterHAllen wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is $$3 + \frac{4}{\sqrt{5-x}}$$ parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

My brain is cloudy, going to gym to clear it up....but how did you guys know to set the equation equal to 6? Once we get to the equation the math is easy but I did not know where to begin. Can someone explain?

Given: at a depth that is x feet below the top of the tank, the concentration is $$3 + \frac{4}{\sqrt{5-x}}$$ parts per million.

Question: at what depth, for which x, is the concentration equal to 6 parts per million? So, for which x, is $$3 + \frac{4}{\sqrt{5-x}}$$ equal to 6?

$$3 + \frac{4}{\sqrt{5-x}}=6$$ --> $$x\approx{3.2}$$.

Hope it's clear.
_________________
Intern
Joined: 11 Jul 2015
Posts: 2
Re: The concentration of a certain chemical in a full water tank [#permalink]

### Show Tags

29 Sep 2015, 02:32
I've been trying to wrap my head around how to set up that equation, but am not able to. Could someone please help me out with why I should be equating 6ppm with the concentration at x feet?
Intern
Joined: 16 Oct 2017
Posts: 25
Re: The concentration of a certain chemical in a full water tank [#permalink]

### Show Tags

10 Feb 2018, 14:46
Can you show me step-by-step how to solve this one? I'm missing something...
VP
Joined: 22 May 2016
Posts: 1349
The concentration of a certain chemical in a full water tank [#permalink]

### Show Tags

10 Feb 2018, 19:37
1
KUDOS
joemama142000 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is $$3 + \frac{4}{\sqrt{5-x}}$$ parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

OCDianaOC wrote:
Can you show me step-by-step how to solve this one? I'm missing something...

OCDianaOC - This question's wording is not easy. I rephrased it.

Given: a chemical concentration of 6
Given: a formula that will tell how deep the water is at a particular concentration, IF we have the concentration (we do)
Formula: $$3 + \frac{4}{\sqrt{5-x}}$$

Set the formula equal to concentration. The concentration of 6, in tandem with the formula, will yield depth.

$$3 + \frac{4}{\sqrt{5-x}} = 6$$
Subtract 3 from both sides:

$$\frac{4}{\sqrt{5-x}} = 3$$
Square both sides:

$$(\frac{4^2}{(\sqrt{5-x})^2}) = 3^2$$

$$(\frac{16}{(5-x)}) = 9$$
Multiply both sides by denominator and solve:

$$16 = 9(5 - x)$$
$$16 = 45 - 9x$$
$$9x = 29$$

$$x = \frac{29}{9} = 3.2$$ feet

Hope that helps.

**The language "where 0 < x < 4," is mostly irrelevant. It's to keep the denominator in the formula positive. (Can't divide by zero, can't take the square root of a negative number.)
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Intern
Joined: 16 Oct 2017
Posts: 25
Re: The concentration of a certain chemical in a full water tank [#permalink]

### Show Tags

10 Feb 2018, 19:49
1
KUDOS
generis wrote:
joemama142000 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is $$3 + \frac{4}{\sqrt{5-x}}$$ parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

OCDianaOC wrote:
Can you show me step-by-step how to solve this one? I'm missing something...

OCDianaOC - This question's wording is not easy. I rephrased it.

Given: a chemical concentration of 6
Given: a formula that will tell how deep the water is at a particular concentration, IF we have the concentration (we do)
Formula: $$3 + \frac{4}{\sqrt{5-x}}$$

Set the formula equal to concentration. The concentration of 6, in tandem with the formula, will yield depth.

$$3 + \frac{4}{\sqrt{5-x}} = 6$$
Subtract 3 from both sides:

$$\frac{4}{\sqrt{5-x}} = 3$$
Square both sides:

$$(\frac{4^2}{(\sqrt{5-x})^2}) = 3^2$$

$$(\frac{16}{(5-x)}) = 9$$
Multiply both sides by denominator and solve:

$$16 = 9(5 - x)$$
$$16 = 45 - 9x$$
$$9x = 29$$

$$x = \frac{29}{9} = 3.2$$ feet

Hope that helps.

**The language "where 0 < x < 4," is mostly irrelevant. It's to keep the denominator in the formula positive. (Can't divide by zero, can't take the square root of a negative number.)

YAAAAY! Your explanation is perfect. I finally understand how to solve this now!

Thank you!
Re: The concentration of a certain chemical in a full water tank   [#permalink] 10 Feb 2018, 19:49
Display posts from previous: Sort by

# The concentration of a certain chemical in a full water tank

 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®.