BTGmoderatorDC wrote:A real estate investment firm began the year with 80% of its investments in commercial real estate and 20% in residential real estate. Over the course of the year, the total value of its investments increased by 3.5%, with the value of its commercial real estate holdings growing by 7%. This means that the value of its residential real estate holdings:
A. Did not change
B. Decreased by 14%
C. Decreased by 10.5%
D. Decreased by 3.5%
E. Increased by 1.5%
Let the total investment = $1000, implying that commercial holdings = 80% of 1000 = $800 and that residential holdings = 1000-800 = $200.
Since the total $1000 investment grows by 3.5%, the total growth = 3.5% of 1000 = $35.
Since the $800 in commercial holdings grows by 7%, the growth in commercial holdings = 7% of 800 = $56.
Change for residential holdings = (total growth) - (commercial growth) = 35-56 = -$21.
Since the $200 in residential holdings suffers a $21 loss, we get:
Percent decrease = decrease/original * 100 = 21/200 * 100 = 10.5%.
The correct answer is
C.
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