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A real estate investment firm began the year with 80% of its

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A real estate investment firm began the year with 80% of its

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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%

OA C

Source: Veritas Prep

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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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Let overall investment = 100 %
Investment increase by 3.5%
Investment = 100 + 3.5 = 103.5%
Commercial Investment = 80 %
Commercial Investment increase by 7%
7% of 80 = 5.6
Residential real estate = 20%
Changes in Residential real Estate = 3.5 - 5.6 = -2.1
$$-\frac{2.1}{20\%}=-0.105\%$$
Since the % change is negative, then the value of investment in residential real estate decreased by 10.5.

$$Answer\ is\ Option\ C$$

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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%

OA C

Source: Veritas Prep
We are given that a real estate investment firm began the year with 80% of its investments in commercial real estate and 20% in residential real estate. If we let the total investments = 1000, then 0.8 x 1000 = 800 = commercial real estate and 0.2 x 1000 = 200 = residential real estate.

We are also given that the total investments increased by 3.5% and that commercial real estate investments increased by 7%. We need to determine the change in percentage for residential real estate investments.

We can let n be the change in percentage and create the following equation:

1.07(800) + (1+n/100)(200) = 1.035(1000)

856 + 200 + 2n = 1035

1056 + 2n = 1035

2n = -21

n = -10.5

Since n is negative, the value of investments in residential real estate decreased by 10.5 percent.

Answer: C

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\(80+20=100\)
In a year
\(80\cdot 1,07 + ? =100\cdot 3,5\)
cca. \(86 + ? = 103,5\)
\(?=17,5\)

\(\frac{17,5-20}{20}= -\frac{2,5}{20} \Rightarrow\) cca \(12\% < 14\% \Rightarrow \) __C__

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