On January 1, 2011, John invests 60% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 20% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 10% in the Antarctic stock market; however, in 2012, largecaps fall 10% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013, John 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 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 John starts with—say, $1,000. (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 = $600   M = $200   S = $200   Apply the first year’s changes, so that you have these numbers on 1/1/2012:   Newer L = $600 + 10% = $660   Newer M = $200 + 20% = $240   Newer S = $200 + 10% = $220   Now apply the second year’s changes to L and M:   Newest L = $660 – 10% = $660 – $66 = $594   Newest M = $240 – 10% = $240 – $24 = $216   Add these to get $810. So the newest S must be $1,000 (the target final total of John’s retirement savings) minus $810, $190   The dollar change in S from 1/1/12 to 1/1/13 is $220 – $30 = $190. So the question is this: what percent change does $190 represent, from a starting point of $220? Since $220 is a nasty divisor, switch to benchmarks:   10% of $220 = $22.   So 20% is just double that, or $44.   And so on.   From this $30 lies between $22 and $44   The correct answer is 10 and 20.
<result>A</result>
On January 1, 2011, John invests 60% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 20% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 10% in the Antarctic stock market; however, in 2012, largecaps fall 10% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013, John has the same total amount of retirement savings as he did two years before, then x is between