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

[VJesus12]

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

[Scott@TargetTestPrep]

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