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	Choose the correct choice from the following options
A) 10 and 20	B) 20 and 30	C) 30 and 40	D) 40 and 50	E) 50 and 60
Here are the starting values:   L = $7,000   M = $2,000   S = $1,000   Apply the first year’s changes, so that you have these numbers on 1/1/2011:   Newer L = $7,000 + 5% = $7,350   Newer M = $2,000 + 10% = $2,200   Newer S = $1,000 + 15% = $1,150   Now apply the second year’s changes to L and M:   Newest L = $7,350 – 10% = $7,350 – $735 = $6,615   Newest M = $2,200 – 20% = $2,200 – $440 = $1,760   Add these to get $8,375. So the newest S must be $10,000 (the target final total of Dave’s retirement savings) minus $8,375, or $1,625.   The dollar change in S from 1/1/11 to 1/1/12 is $1,625 – $1,150 = $475. So the question is this: what percent change does $475 represent, from a starting point of $1,150? Since $1,150 is a nasty divisor, switch to benchmarks:   10% of $1,150 = $115.   So 20% is just double that, or $230.   And 40% is double that, or $460.   Since $475 is just slightly larger than $460 (but not enough to get you to 50%, which would be $460 + $115), x must be between 40 and 50.   Intuitively, it should make sense that you’d need a much bigger positive percent change in the smallest investment (S) to make up for even a moderate downturn in the larger investments (L and M), so if you were completely stuck for time and needed to guess in a hurry, you should favor C/D/E over A or B.   The correct answer is 40 and 50.
<result>D</result>
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