On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps,

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Tue Aug 18, 2020 8:29 am

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On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise $x\%$ in Antarctica. If on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then $x$ is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

Answer: D

Source: Manhattan GMAT

Source: Beat The GMAT — Problem Solving | Tue Aug 18, 2020 8:29 am

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Re: On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcap

by Scott@TargetTestPrep » Sat Aug 22, 2020 8:49 am

VJesus12 wrote: ↑
Tue Aug 18, 2020 8:29 am
On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise $x\%$ in Antarctica. If on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then $x$ is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

Answer: D

Solution:

Let’s let the amount Dave invested on January 1, 2010 be $1,000. So he invested $700 in largecaps, $200 in midcaps, and $100. in smallcaps.

After two years, the amount he has 700 * 1.05 * 0.9 = $661.5 in largecaps, 200 * 1.1 * 0.8 = $176 in midcaps and 100 * 1.15 * (1 + x/100) = 115(1 + x/100) dollars in smallcaps.

Since the total amount is the same as two years earlier, we have:

661.5 + 176 + 115(1 + x/100) = 1,000

115(1 + x/100) = 162.5

1 + x/100 = 1.413

x/100 = 0.413

x = 41.3

Answer: D

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