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what percent of solution S was ammonia?

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by jbsocal » Thu Dec 27, 2012 9:54 pm
If P and R were solutions of water and ammonia and if solution S consisted of 2 parts of P and 3 parts of R, what percent of solution S was ammonia?

(1)Solution P contained 10 percent ammonia and solution R contained 3 percent ammonia.

(2) There was a total of 10 liters of solution S. A
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by GMATGuruNY » Thu Dec 27, 2012 10:43 pm
jbsocal wrote:If P and R were solutions of water and ammonia and if solution S consisted of 2 parts of P and 3 parts of R, what percent of solution S was ammonia?

(1)Solution P contained 10 percent ammonia and solution R contained 3 percent ammonia.

(2) There was a total of 10 liters of solution S. A
Statement 1: Solution P contained 10 percent ammonia and solution R contained 3 percent ammonia.
Since Solution S consists of 2 parts of P and 3 parts of R, Solution S is composed of 2 parts 10% ammonia and 3 parts 3% ammonia.
Thus, in every 5 parts, the average percentage of ammonia = (2*10 + 3*3)/5 = 29/5 %.
SUFFICIENT.

Statement 2: There was a total of 10 liters of Solution S.
No information about the percentage of ammonia.
INSUFFICIENT.

The correct answer is A.
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by jbsocal » Fri Dec 28, 2012 9:47 am
thanks gmatguru.

can this be solved using allegation?
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by GMATGuruNY » Fri Dec 28, 2012 10:27 am
jbsocal wrote:thanks gmatguru.

can this be solved using allegation?
Here's how we could use alligation to evaluate statement 1.

Step 1: Plot the 3 percentages on a number line, with the percentage of ammonia in P and R (10% and 3%) on the ends and the unknown percentage of ammonia in mixture S in the middle.
P 10%-------------------S------------3% R

Step 2: Plot the distances between the percentages.
(distance between P and S) : (distance between S and R) is equal to the RECIPROCAL of the ratio of P to R in the mixture.
Since P:R = 2:3, we get:
P 10%--------3x---------S-----2x-----3% R

Step 3: Determine the percentage of ammonia in the mixture.
The number line indicates that the distance between 10% and 3% is equal to 3x+2x:
10-3 = 3x + 2x
7 = 5x
x = 7/5.

Since the distance between P and S is equal to 3x, we get:
10 - S = 3(7/5)
S = 10 - 3(7/5) = 29/5.

For another problem that I solved with alligation, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html
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