January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52231

A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
03 Mar 2015, 06:03
Question Stats:
82% (01:36) correct 18% (02:11) wrong based on 258 sessions
HideShow timer Statistics




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India

Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
03 Mar 2015, 21:35
Bunuel wrote: A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?
A. 200 B. 400 C. 500 D. 600 E. 800
Kudos for a correct solution. Using the weighted average formula, w1/w2 = (12  10)/(10  6) = 1/2 So every unit of 6% solution, he should add 2 units of 12% solution. Since he has 400 units of 6% solution, he should add 800 units of 12% solution. Answer (E)
_________________
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: 26 Mar 2010
Posts: 10

Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
03 Mar 2015, 12:21
With mixture problems I usually take following approach
10%=Total mix of acid/Total amount of mixture.
With X= amount of 12% acidic solution we have:
10%=(400*0.06+.12*X)/400+X)
40+0.1X=24+0.12X 16=0.002X X=800
Answer E



Intern
Joined: 22 Aug 2014
Posts: 40

Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
03 Mar 2015, 22:46
Bunuel wrote: A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?
A. 200 B. 400 C. 500 D. 600 E. 800
Kudos for a correct solution. The acid solution level in the first is half of the second one. So the ratio of the acid solution in S1:S2 = 1:2 Now the simple way to go about this apart from weighted average would be assuming that you have 1 unit of 6% acid solution. A General rule when the mixtures are in the ratio 1:2 When you add 1 part of second solution, the mixed solution will contain 50% more than the first solution. i.e, 1.5*6 = 9 When you add 2 parts of second solution, the mixed solution will contain 66% more than the first solution. i.e, 1.6*6 = 10 Thus the required solution = 400*2 = 800 Option E



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13331
Location: United States (CA)

Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
03 Mar 2015, 22:46
Hi All, While an Algebra approach (using the "weighted average" formula) would work nicely on this prompt, you can also answer it rather quickly by TESTing THE ANSWERS and using a bit of logic. Here, we're going to mix 400 ounces of a 6% acid solution with X ounces of a 12% acid solution to form a 10% acid solution. We're asked for the value of X. The answers are all nice, round numbers, so we can take advantage of them.... Let's start with Answer B.... IF..... X = 400 ounces Then we'd have the same amount of each solution: 400 ounces of 6% and 400 ounces of 12% > this would produce a (6%+12%)/2 = 9% mixture, which is TOO SMALL. X must be BIGGER. Eliminate Answers A and B. Now, let's TEST Answer D... IF.... X = 600 ounces Then with 400 ounces of 6% and 600 ounces of 12%, we'd have... [(400)(.06) + (600)(.12)]/(400 + 600) = (24 + 72)/1000 = 96/1000 = 9.6%, which is TOO SMALL. X must be BIGGER. Eliminate C and D. 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
CoFounder & 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!*****



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 416
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
04 Mar 2015, 03:13
Or using the scaling method:
6%.........10%...........12% __________________ .......4................2
We draw the number line, from lowest to greatest as this is the expected, and find the difference between the first solution and the wanted and the second solution and the wanted.
\(\frac{6%}{12%}\) \(=\)\(\frac{2}{4}\) \(=\)\(\frac{1}{2}\)
When we write the ratios we make sure to flip, as seen above. So, it is 1 unit for the 6% solution and 2 units for the 12% solution, instead of the opposite. This is derived from the weighted averages formula.
Then we have:
\(\frac{6%}{12%}\) =\(\frac{1}{2}\) = \(\frac{400}{x}\) \(=\)\(2*400\) \(=\) \(800\)



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1823
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
04 Mar 2015, 21:04
Answer = E = 800 Say "x" units of 12% solution is added. Equation setup would be as follows: \(\frac{6}{100} * 400 + \frac{12}{100}* x = \frac{10}{100}(400+x)\) x = 800
_________________
Kindly press "+1 Kudos" to appreciate



Math Expert
Joined: 02 Sep 2009
Posts: 52231

Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
08 Mar 2015, 13:33
Bunuel wrote: A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?
A. 200 B. 400 C. 500 D. 600 E. 800
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:We could backsolve from the numerical answer choices, but let’s use a straight algebra approach. Let X equal the units of 12% phosphoric acid solution we use, and let Y be the units of 10% sulfuric acid solution that result. The volume equation is: 400 + X = Y In the first solution, we have 6% of 400, or 24 units of phosphoric acid. In the second solution, we have 12% of X = 0.12*X of phosphoric acid. In the resultant solution, we have 10% of Y = 0.10*Y of phosphoric acid. The concentration equation is: 24 + 0.12*X = 0.10*Y Multiply this by 100, to clear the decimals: 2400 + 12X = 10Y Everything is even, so divide by 2 to simplify: 1200 + 6X = 5Y We want X, so let’s multiply the volume equation by 5 and add that to this equation we just got: 1200 + 6x = 5y 2000  5x = 5y _____________ 800  x = 0 x = 800. Answer = E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 9416

Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
Show Tags
24 May 2018, 08:35
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl &nbs
[#permalink]
24 May 2018, 08:35






