(0.3*56000+0.4*72000)/(72000+56000)=0.35625
D
thank you

John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes $72000, what is their combined tax rate?

a. 32%
b. 34.4%
c. 35%
d. 35.6%
e. 36.4%

Great solution everyone! Yes, the answer is (D) 35.6.

Now let me explain why I like this question. The big numbers - 56000 and 72000 have limited utility. I could have as well given 86380 and 111060 as their salaries; I would have still obtained the same answer!
We need to find the weighted average of their tax rate. The important thing is their individual tax rates and the ratio of their salaries 7:9 (56000:72000), not the actual salaries



The length between 30% and 40% i.e. 10% is split in the ratio 9:7.
So the average will be at (9/16)*10 + 30 = 35.6%.

So you don't have to do any long calculations. If there is a doubt in this method, check out this link:
http://gmatclub.com/forum/tough-ds-105651.html#p828579

When we want to find the average of lets say age of 2 groups - one group has average age of 30 yrs and there are 10 people in it and the other group has average age of 40 yrs and there are 40 people in it, all we need is the relative weights (relative number of people) in the two groups i.e. 1:4. It doesn't matter whether there are 10 and 40 people or 100 and 400 people... It's exactly the same concept here.

Let me know if there is a doubt in this concept.

and when we say, "A makes $100,000," we mean gross by default. Taxes are a part of your salary just like your other expenses.
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Hi Karishma,

I really love the weighted averages shortcut method you use every time,but I get confused in using it.

In the problem above,please advise,why you have used 9:7 instead of 7:9?


Thanks!

regards,

Nice shortcut method!!...Great!

I am lost at (9/16)*10 + 30 = 35.6%. where YOU add 30. I want to learn how to use this method completely so I can have it in my back pocket ready to use. I feel that we already found the ratio and then flipped it so it would be the distance and could put it in the chart. We divided 9/16 to find the middle number that was missing and multiplied by 10 because that was the weight? Is the only reason because 10+30 = the original 40?

Using weighted averages...

(1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 72000/128000 = 72/128 = 9/16. 9/16 is a little above 8/16 = 1/2. Thus, our answer is just a little above 35.

Answer: D

For details on Weighted Averages: Weighted Averages