Last year Luis invested x dollars for one year, half at 8 percent simp

Year 1:
Rate of return for x/2 and x/2 amount are 8% and 12%. This gives us an average rate of return of 10% (since the two amounts are the same, average will just be the simple average)

Year 2:
We need a 10% rate of return. One investment is available at 12%. The other rate of return can be anything from 0% to 8%. The amount invested in the two investments will be adjusted to get 10%.

For example, say the second rate of return is 6%,

w1/w2 = (12 - 10)/(10 - 6) = 1/2
So 1/3 part of x should be invested at 6% and 2/3 part at 12%

Say second rate of return is 4%
w1/w2 = (12 - 10)/(10 - 4) = 1/3
So 1/4 part of x should be invested at 4% and 3/4 part at 12%

Say second rate of return is 0%
w1/w2 = (12 - 10)/(10 - 0) = 1/5
So 1/6 part of x should be invested at 0% and 5/6 part at 12%.

and so on...
We need the fraction that must be invested at 12%. For this, we need to know the second rate of return.

(1) The lower rate is now 6 percent.

Sufficient.

(2) The total amount of interest earned from the two investments last year was $3,000.

Not sufficient. We get the amount x using this information. But the question is still the same - we need total 10% return. What is the second rate of return? Not known.

Not sufficient.

Answer (A)

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