On January 1, 2011, James invests 80% of his retirement savings in Antarctic largecap stocks, 10% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 5% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013,James has the same total amount of retirement savings as he did two years before, then x is between	Pick one.
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 James 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 = $800   M = $100   S = $100   Apply the first year’s changes, so that you have these numbers on 1/1/2012:   Newer L = $800 + 10% = $880   Newer M = $100 + 10= 
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
$110   Newer S= $100 + 20= 
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
$120   Now apply the second year’s changes to L and M:   Newest L= $880 – 5% = $880 – $44 = $836   Newest M = $110 – 10% = $110 – $11 = $99   Add these to get $935. So the newest S must be $1,000 (the target final total of James’s retirement savings) minus $935, $65   The dollar change in S from 1/1/12 to 1/1/13 is $120 – $55 = $65. So the question is this: what percent change does $65 represent, from a starting point of $120? Since $120 is a nasty divisor, switch to benchmarks:   20% of $120 = $24.   So 40% is just double that, or $48.   And 50% is equal to or $60.   From this $55 lies between $48 and $60   The correct answer is 40 and 50.
<result>D</result>
On January 1, 2011, James invests 80% of his retirement savings in Antarctic largecap stocks, 10% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 5% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013,James has the same total amount of retirement savings as he did two years before, then x is between