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

It is currently 15 Aug 2018, 04:08

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

Jackie has two solutions that are 2 percent sulfuric acid

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

Hide Tags

Intern
Intern
avatar
Joined: 02 Aug 2015
Posts: 43
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 20 Aug 2015, 19:27
8
50
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:29) correct 23% (01:56) wrong based on 1576 sessions

HideShow timer Statistics

Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

A) 18
B) 20
C) 24
D) 36
E) 42
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 20 Aug 2015, 21:48
17
18
Akgmat85 wrote:
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

A) 18
B) 20
C) 24
D) 36
E) 42


Use weighted average:

2% and 12% solutions mix to give 5% solution.

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (12 - 5)/(5 - 2) = 7/3

You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution.
If total 5% solution is actually 60 litres, you need 7*6 = 42 litres of 2% solution and 3*6 = 18 litres of 12% solution.

Answer (E)

The formula and its application in mixtures are discussed in the following two posts:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Most Helpful Community Reply
Intern
Intern
avatar
Joined: 02 Jul 2015
Posts: 17
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 24 Aug 2015, 06:18
13
3
let a=amount of 2% acid and b= amount of 12% acid.

Now, The equation translates to,
0.02a + .12b = .05(a+b)
but a+b= 60

therefore .02a + .12b = .05(60)
=> 2a + 12b = 300

but b=60-a

therefore
2a+ 12(60-a) = 300
=> 10a = 420
hence a = 42.
General Discussion
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 176
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post Updated on: 25 Aug 2015, 07:34
5
\(0,02*x + 0,12 * (60-x) = 0,05 * 60\)
\(0,02*x + 7,2 - 0,12*x = 3\)
\(4,2 = 0,1*x\)
\(x = 0,42\)

= 42%

Originally posted by noTh1ng on 24 Aug 2015, 08:17.
Last edited by noTh1ng on 25 Aug 2015, 07:34, edited 1 time in total.
Intern
Intern
User avatar
Joined: 24 Aug 2015
Posts: 8
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 24 Aug 2015, 11:19
2
Alright I'm so frustrated but after reading the article she posted. I try my best to answer using my way of thinking:

7 cups + 3 cups = 10 cups..so you need 10 cups of 5% solution to produce 60 liters. There is 10 cups and there is 60 liters. We have 60, we have 10 so the other number is missing is 6 therefore 6*7 cups = 42 liters of solution
Senior Manager
Senior Manager
avatar
Joined: 15 Sep 2011
Posts: 343
Location: United States
WE: Corporate Finance (Manufacturing)
GMAT ToolKit User
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post Updated on: 25 Aug 2015, 03:33
blendercroix wrote:
Alright I'm so frustrated but after reading the article she posted. I try my best to answer using my way of thinking:

7 cups + 3 cups = 10 cups..so you need 10 cups of 5% solution to produce 60 liters. There is 10 cups and there is 60 liters. We have 60, we have 10 so the other number is missing is 6 therefore 6*7 cups = 42 liters of solution


Hi blendercroix,

She got the 6 because it's the unknown multiplier of the ratio of 3x:7x. That is, \(3x + 7x = 10x\), and 10x into \(60\) is \(6\). Six isn't a value but what helps calculate the ratio. Anyhow, it seems your logic is similar to what she posted, but instead of \(x\) you made the unknown multiplier a "cup."

Kr,
Mejia

Originally posted by mejia401 on 24 Aug 2015, 17:49.
Last edited by mejia401 on 25 Aug 2015, 03:33, edited 1 time in total.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 24 Aug 2015, 21:01
1
blendercroix wrote:
Alright I'm so frustrated but after reading the article she posted. I try my best to answer using my way of thinking:

7 cups + 3 cups = 10 cups..so you need 10 cups of 5% solution to produce 60 liters. There is 10 cups and there is 60 liters. We have 60, we have 10 so the other number is missing is 6 therefore 6*7 cups = 42 liters of solution



Yes, you are right. Look, for every 10 cups/liters/ml/gallons/units etc of 5% solution, you need 7 cups/liters/ml/gallons/units etc of 2% solution and 3 cups/liters/ml/gallons/units etc of 12% solution.

So for each 10 litres of 5% solution, you need 7 litres of 2% and 3 litres of 12%.
Then how much will you need for 60 litres of 5% solution?

You will need 6 times the original quantity so you will need 7*6 = 42 litres of 2% solution and 3*6 = 18 litres of 12% solution.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 24 Aug 2015, 21:04
blendercroix wrote:
Alright I'm so frustrated but after reading the article she posted. I try my best to answer using my way of thinking:

7 cups + 3 cups = 10 cups..so you need 10 cups of 5% solution to produce 60 liters. There is 10 cups and there is 60 liters. We have 60, we have 10 so the other number is missing is 6 therefore 6*7 cups = 42 liters of solution



Take a look at the ratios post: http://www.veritasprep.com/blog/2011/03 ... of-ratios/
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
User avatar
S
Joined: 30 Dec 2015
Posts: 91
GPA: 3.92
WE: Engineering (Aerospace and Defense)
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 16 Jan 2016, 22:36
5
2
For a question like this always have 2 equations, one for concentration and one for volume:

Let X = vol of 2% sol
Y = vol of 12% sol

Since both solutions are mixed to make 60liters of 5% solution
X + Y = 60 ----1
Also,
equation for concentration
2X + 12Y = 5 (60)
2X + 12Y = 300 ------2

Solve equation 1 & 2 simultaneously
Y = 18
X = 60-18 = 42
_________________

If you analyze enough data, you can predict the future.....its calculating probability, nothing more!

Manager
Manager
avatar
B
Joined: 08 Sep 2015
Posts: 70
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 14 Feb 2017, 23:21
2
2% 12%

5%

7% 3%

=> we need 7 parts of the 2% solution and 3 parts of the 12% solution => total 10 parts => 60/10 = 3 liters
Therefore, 7 * 3 liters = 42 liters of 2% solution is needed.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12175
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 16 Feb 2017, 14:00
3
1
Hi All,

This is essentially a Weighted Average question, but it can be solved in a variety of different ways. Since the answer choices are "spread out" numbers, there's actually a great 'brute force' approach that you can use to logically answer this question without doing that much math.

We're told to mix a 2% acid solution with a 12% acid solution and end up with 60 LITERS of 5% acid solution. We're asked how many liters (of the 60) would be the 2% solution.

IF....
we had 1 liter of each solution, then the acidity of the mixture would be (2% + 12%)/2 = 7%.... this is clearly too high (it's supposed to be 5%), so we need MORE of the 2% mixture.

IF....
we had 2 liters of the 2% solution and 1 liter of the 12% solution, then the acidity of the mixture would be (2% + 2% + 12%)/3 = 16/3% = 5 1/3%.... this is also clearly too high (it's supposed to be 5%), so we need even MORE of the 2% mixture. In this example, it's worth noting that 2/3 of the mixture is the 2% solution.

Since we need even MORE of that solution, we need MORE than 2/3 of the total to be that 2% mixture. There's only one answer that's more than 2/3 of 60....

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1064
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 16 Feb 2017, 17:56
1
blockman wrote:
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

A) 18
B) 20
C) 24
D) 36
E) 42


let x=liters of 2% solution needed
.02x+.12(60-x)=.05*60
x=42 liters
Intern
Intern
User avatar
B
Joined: 19 Jul 2016
Posts: 14
Location: Moldova, Republic of
Concentration: Strategy, Operations
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 22 May 2017, 13:01
7
1
Image
CEO
CEO
User avatar
P
Joined: 12 Sep 2015
Posts: 2699
Location: Canada
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 10 Aug 2017, 12:36
2
Top Contributor
blockman wrote:
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

A) 18
B) 20
C) 24
D) 36
E) 42


Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x be the number of liters of 2% solution in the mixture
Since there are 60 liters in total, 60 - x will equal number of liters of 12% solution in the mixture

Now apply the formula:
5 = (x/60)(2) + [(60-x)/60](12)
Multiply both sides by 60 to get: 300 = 2x + (60-x)(12)
Expand: 300 = 2x + 720 - 12x
Rearrange: -420 = -10x
Solve: x = 42

Answer: E

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

CEO
CEO
User avatar
P
Joined: 12 Sep 2015
Posts: 2699
Location: Canada
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 10 Aug 2017, 12:49
Top Contributor
blockman wrote:
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

A) 18
B) 20
C) 24
D) 36
E) 42


Another approach is to keep track of the acid
Let x = number of liters of 2% solution needed
So, 60 - x = number of liters of 12% solution needed

2% of x = 0.02x
So, 0.02x = the number of liters of PURE acid in the 2% solution

12% of 60 - x = 0.12(60 - x) = 7.2 - 0.12x
So, 7.2 - 0.12x = the number of liters of PURE acid in the 12% solution

Now let's COMBINE the two solutions.
Total volume of PURE acid = 0.02x + 7.2 - 0.12x
= 7.2 - 0.1x
So, our NEW solution contains 7.2 - 0.1x liters of PURE acid
Also, the NEW solution has a total volume of 60 liters

Since the NEW solution is 5% PURE acid, we can write: (7.2 - 0.1x)/60 = 5/100
Cross multiply to get: 100(7.2 - 0.1x) = 5(60)
Expand: 720 - 10x = 300
Add 10 x to both sides: 720 = 300 + 10x
Subtract 300 from both sides: 420 = 10x
Solve: x = 42

Answer:

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1064
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 11 Aug 2017, 12:14
blockman wrote:
Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

A) 18
B) 20
C) 24
D) 36
E) 42


let x=liters of 2% solution needed
.02x+.12y=.05(x+y)
x/y=7/3
x=7/10*60=42 liters
E
Manager
Manager
avatar
S
Joined: 06 Jul 2014
Posts: 102
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 640 Q48 V30
GMAT ToolKit User Reviews Badge
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 11 Aug 2017, 12:24
Quantity of Cheaper / Quantity of Dearer= CP of Dearer – Mean Price / Mean Price – CP of Cheaper

Quantity of Cheaper +Quantity of Dearer=60

CP of Dearer – Mean Price / Mean Price – CP of Cheaper= 12-5/5-2=7/3=7/10*60=42
Intern
Intern
avatar
B
Joined: 18 May 2017
Posts: 16
WE: Corporate Finance (Health Care)
GMAT ToolKit User
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 20 Sep 2017, 12:02
.02A +.12B=.05(A+B)
2A+12B=5A+5B
7B=3A
7/3 = A/B
7*6=42
Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1164
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 26 Sep 2017, 06:15
VeritasPrepKarishma

Can you please explain solution posted by EugeneFish?
I went through your blog here
but all I am able to proceed beyond assigning two points (weights) on line segment and invert distance from either of them.
say w1/w2 = d2/d1


Thanks in advance.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

New post 27 Sep 2017, 03:10
adkikani wrote:
VeritasPrepKarishma

Can you please explain solution posted by EugeneFish?
I went through your blog here
but all I am able to proceed beyond assigning two points (weights) on line segment and invert distance from either of them.
say w1/w2 = d2/d1


Thanks in advance.


EugeneFish has given the pictorial representation of the scale method.

You should check out this post instead: https://www.veritasprep.com/blog/2011/0 ... -averages/

It discusses the scale method, why it works and its pictorial and formula depiction.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Re: Jackie has two solutions that are 2 percent sulfuric acid &nbs [#permalink] 27 Sep 2017, 03:10

Go to page    1   2    Next  [ 23 posts ] 

Display posts from previous: Sort by

Jackie has two solutions that are 2 percent sulfuric acid

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.