reddox wrote:This is from the OG 13, pg. 142. My question is, by the Princeton Review method, we can use "Hidden Plug-ins" if there are %s or Ratios in the problem. However, I'm only able to use Plug-in-the-Answer (PITA) technique here. Why is that?
How many liters of a solution that is 15 percent salt must be added to 5 liters of a solution that is 8 percent salt so that the resulting solution is 10 percent salt?
A) 2
B) 6
C) 7
D) 10
E) 13
We can plug in the answers, which represent the amount of 15% solution that must be added.
The percentage in the resulting solution (10%) is closer to 8% than to 15%.
Thus, the 5 liters of 8% solution must constitute MORE THAN HALF of the resulting solution, implying that LESS THAN 5 LITERS of 15% solution must be added.
The correct answer is
A.
When the answer choices are FRACTIONS or PERCENTS and there are UNKNOWNS in the problem, we can plug in for the unknowns in the problem.
When the answer choices are NUMBERS and the question asks for a SPECIFIC AMOUNT -- here, the amount of 15% solution that must be added -- we can PLUG IN THE ANSWERS for the specific amount being sought.
An alternate approach is ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the two starting percentages (8% and 15%) on the ends and the goal percentage (10%) in the middle.
8%----------10%-------------------15%
Step 2: Calculate the distances between the percentages.
8%-----
2----10%---------
5---------15%
Step 3: Determine the ratio in the mixture.
The ratio in the mixture is the RECIPROCAL of the distances in red.
8% solution : 15% solution = 5:2.
Thus, 2 liters of 15% solution must be added.
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