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
A real estate investment firm began the year with 80% of its
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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.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 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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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.
$$Answer\ is\ Option\ C$$
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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Let the total investment = $1000, implying that commercial holdings = 80% of 1000 = $800 and that residential holdings = 1000-800 = $200.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%
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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