I am also getting 2.28 ( approx 2.3). 2.3 is one of the choices but the correct answer is ( as per the author) is 3.
The explanation provided is
Since 15% is closer to 30% than 50% is to 30% hence A should have a larger content in the mixture.
Assume 2.5( one of the choices) as A. B would then be 1.5
15% of 2.5= .375(alcohol in A)
50% of 1.5= .75(alcohol in B)
Total is .375+.75= 1.125.
Alcohol content in the mixture is 30% of 4=1.2
Hence, the A should be more than 2.5. And to add to my woes, 3 is the only higher choice.
I need to know whether this is a correct explanation or not. I am confused.
What the answer explains directly relates to the equations we have been using:
0.15A + 0.5(4-A) = 0.3(4)
Your example of setting A to 2.5 and then B at 1.5 is the same as setting value of A using an algeraic term and then B as 4 minus that amount.
Now, getting to the choice of 3 gallons.
If A is 3 gallons, then B would be 1 gallon.
3 gallons of A provide 0.15*3=0.45 gallons of alcohol
1 gallon of B provides 0.5*1=0.5 gallons of alcohol
Adding them up gives 0.95 gallons, off the mark from the expected 0.3*4=1.2 gallons of alcohol. (Difference is 0.25)
Given a choice based on how far they deviate from the the desired value, I would go for 2.3 since this value gives 1.195 gallons of alcohol (that's off from the 30% by only 0.005 gallons) compared to 2.5 which gives 1.125 (off by 0.075) and the worse is probably 3 gallons.
I feel the way to solve such mixture problems is still the equate the terms. When you say left side = right side, you can't go wrong. So I reckon the answer is not correct this time round.
I'm still preparing for my first GMAT, so maybe someone around here might have experienced such problems on an actual GMAT. Have anyone seen such a question ?