On January 1, 2010, Dolly invests 30% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 20% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dolly has the same total amount of retirement savings as he did two years before, then x is between  Choices:
A) 10 and 20  B) 20 and 30  C) 30 and 40  D) 40 and 50  E) 50 and 60
Pick a smart number for the total retirement savings Dolly starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.)   Here are the starting values:   L = $3000   M = $3000   S = $4000   Apply the first year’s changes, so that you have these numbers on 1/1/2012:   Newer L = $3000 + 10% = $3300   Newer M = $3000 + 20% = $3600   Newer S = $4000 + 15% = $4600   Now apply the second year’s changes to L and M:   Newest L = $3300– 20% = $3300– $660 = $2640   Newest M = $3600– 10% = $3600– $360 = $3240   Add these to get $5880. So the newest S must be $10,000 (the target final total of Dolly’s retirement savings) minus $5880, $4120   The dollar change in S from 1/1/12 to 1/1/13 is $4600 – $480 = $4120. So the question is this: what percent change does $480 represent, from a starting point of $4600? Since $4600 is a nasty divisor, switch to benchmarks:   10% of $4600 = $460.   So 20% is just double that, or $920.   And so on.   From this $480 lies between $460 and $920   The correct answer is 10 and 20.
<result>A</result>
On January 1, 2010, Dolly invests 30% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 20% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dolly has the same total amount of retirement savings as he did two years before, then x is between