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

 It is currently 14 Oct 2019, 09:02 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.  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  Joined: 02 Aug 2015
Posts: 41
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

8
111 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:59) correct 24% (02:22) wrong based on 2269 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
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

28
1
33
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.

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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  Joined: 02 Jul 2015
Posts: 16
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

36
2
10
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  Joined: 07 Apr 2015
Posts: 154
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

6
1
2
$$0,02*x + 0,12 * (60-x) = 0,05 * 60$$
$$0,02*x + 7,2 - 0,12*x = 3$$
$$4,2 = 0,1*x$$
$$x = 0,42$$

= 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  Joined: 24 Aug 2015
Posts: 7
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

3
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  Joined: 15 Sep 2011
Posts: 310
Location: United States
WE: Corporate Finance (Manufacturing)
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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 V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

2
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager  S
Joined: 30 Dec 2015
Posts: 82
GPA: 3.92
WE: Engineering (Aerospace and Defense)
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

5
3
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  B
Joined: 08 Sep 2015
Posts: 62
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

4
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 V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
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

4
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....

GMAT assassins aren't born, they're made,
Rich
_________________
VP  P
Joined: 07 Dec 2014
Posts: 1223
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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  S
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

9
2 CEO  V
Joined: 12 Sep 2015
Posts: 3995
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

4
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

RELATED VIDEO

_________________
CEO  V
Joined: 12 Sep 2015
Posts: 3995
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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

RELATED VIDEO

_________________
VP  P
Joined: 07 Dec 2014
Posts: 1223
Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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  S
Joined: 06 Jul 2014
Posts: 88
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 660 Q48 V32 Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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  B
Joined: 18 May 2017
Posts: 13
WE: Corporate Finance (Health Care)
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

.02A +.12B=.05(A+B)
2A+12B=5A+5B
7B=3A
7/3 = A/B
7*6=42
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1366
Location: India
WE: Engineering (Other)
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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

Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: Jackie has two solutions that are 2 percent sulfuric acid  [#permalink]

Show Tags

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

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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: Jackie has two solutions that are 2 percent sulfuric acid   [#permalink] 27 Sep 2017, 03:10

Go to page    1   2    Next  [ 28 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

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