A solution that is 40% acid must be strengthened to become a solution

Question

A solution that is 40% acid must be strengthened to become a solution that is 88% acid. If there are 10 ounces of the 40% solution, how much pure acid must be added?

A. 2.5 ounces
B. 18 ounces
C. 28 ounces
D. 40 ounces
E. 48 ounces

quantumliner · Accepted Answer

In the original Solution of 10 ounces, Acid content is 40%, i.e. 4 ounces

To make this this solution 88% acidic, let the amount of acid added is x ounces.

(4+x)/(10+x) = 0.88

Solving for X, gives x as 40.

Answer is D. 40 ounces

KrishnakumarKA1 · Answer

let the pure acid to be added be x

initially, 10 ounce has 40% = 4 ounce acid and 60% = 6 ounce rest of the stuff
finally 10+x ounce has 88% acid and 12% = 0.12(10+x) ounce rest of the stuff

since rest of the stuff will remain equal in both cases, thereofore

0.12(10+x) = 6

or x = 40 ounce

Option D

EugeneFish · Answer

If we add 10 oz of 100% solution, we will have a 60% mixture. Answer A out
If we add 20 oz of 100% solution, we will have an 80% mixture. Answer B out.

Further, we can use weighted average :

40---------------88------100

Distance between 88 and 40 is 48 
Distance between 88 and 100 is 12

Ratio of 40% sol to 100% sol in the mixture is 12:48 or 1:4
So, the mixture will consist of 1 ratio unit of 40% sol and 4 ratio units of 100% sol. One ratio unit is 10, therefore 4 x 10 = 40.
 Answer D

gracie · Answer

let x=ounces of acid to be added
.4*10+x=.88(10+x)
x=40 ounces
D

akshayk · Answer

We need to make 40% acid solution into a 88% acid solution. A1 = 40% Acid Solution A2 = 100% Acid Solution (Pure Acid) Final = 88% Acid Solution A1:A2 = 1:4 If we have 10 ounces of A1, we need to have 40 ounces of A2. Hence D

Thank you Karishma for the weighted average method.

Shtan1 · Answer

Ballparking, 48 is impossible because the acidic will be more than 88%, a little lesser than 48, which is 40 Answer D.

ccooley · Answer

I'd test the answer choices (possibly with a bit of estimation) on this one. The answer choices are easy numbers, while the math will require some algebra, so let's make it easier on ourselves.

Initially, we have 10 ounces of the solution, and .4(10) = 4 ounces of that consists of acid.

Start by testing (B): if we add 18 ounces of acid, we now have a total of 10+18 = 28 ounces of solution, and 4 + 18 = 22 ounces of that is acid.

How does 22/28 compare to 88%? It looks like we need an easy way to compare 88% to a bunch of different fractions, so let's convert 88% to a fraction as well: 88% = 88/100 = 22/25.

22/28 has a bigger denominator than 22/25, and the same numerator. Therefore, 22/28 is  too small  and we need to test a bigger answer choice.

Next, test (D): if we add 40 ounces of acid, we have a total of 10 + 40 = 50 ounces of solution, and 4 + 40 = 44 ounces of that is acid.

44/50 = 88/100 = 88%.  The correct answer is (D) .

warrior1991 · Answer

chetan2u   Bunuel

What do we mean by 10 ounces of 40% solution ??

I was assuming that 40% solution has 10 ounces

So 100% solution will have 25 ounces.

Total Solution has 25 ounces out of which acid is 40% and that again means 10 ounces of acid and remaining 15 ounces of water.

Now this 25 ounces has to be increased by adding acid such that the acid content is 88%.

(10+x)/(25+x)=88/100

On solving X comes out to be 100.

That means we need to add 100 ounces of acid .

Where am I wrong??

chetan2u · Answer

Hi,

10 ml of 40% solution...This means the solution is a mix of 40% of acid etc and 60% of water, and we are taking 10ml of it, so acid will be 4ml

warrior1991 · Answer

Thank you  chetan2u  for a quick response. You mean to say that  40% solution and 10 ml means same thing ???  Because it is already given that solution has 40% acid and 60% of water.

satya2029 · Answer

Initial quantity of acid=40% of 10=4 ounces
Final quantity of acid= 4+x(added acid)
Which is equal to 88% of( 10+added acid)
so (4+x)=0.88(10+x)
X=40 ounces
D:)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A solution that is 40% acid must be strengthened to become a solution

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A solution that is 40% acid must be strengthened to become a solution

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards