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

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Math Expert
Joined: 02 Sep 2009
Posts: 52108
A real estate investment firm began the year with 80% of its investmen  [#permalink]

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13 Feb 2017, 02:23
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2
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:26) correct 29% (02:26) wrong based on 78 sessions

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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%

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Joined: 21 Mar 2016
Posts: 523
Re: A real estate investment firm began the year with 80% of its investmen  [#permalink]

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13 Feb 2017, 05:12
1
consider the overall investment to be 100..
since the investment increased by so after increase its 103.5

also the commercial investment increased by 7%,, hence 7% of 80 = 5.6

overall increase 3.5 has to account for the increase of 5.6,, difference = 5.6 - 3.5 = 2.1

2.1/20 = 10.5%
hence ans C
Target Test Prep Representative
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Re: A real estate investment firm began the year with 80% of its investmen  [#permalink]

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14 Feb 2017, 15:51
1
Bunuel 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%

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.

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Re: A real estate investment firm began the year with 80% of its investmen  [#permalink]

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11 Mar 2017, 13:34
80+20=100
in a year
80*1,07+?=100*3,5
cca. 86 + ? = 103,5
?=17,5
(17,5-20)/20= -2,5/20 =>cca 12% < 14% =>C
Re: A real estate investment firm began the year with 80% of its investmen &nbs [#permalink] 11 Mar 2017, 13:34
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