On January 1, 2011, Dimple invests 20% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 50% in Antarctic smallcaps. In 2011, largecaps rise 20%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2013, Dimple has the same total amount of retirement savings as he did two years before, then x is between
Choose the most appropriate option
A) 0 and 5
B) 5 and 10
C) 10 and 15
D) 15 and 20
E) 20 and 30
Pick a smart number for the total retirement savings Dimple 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 = $2000   M = $3000   S = $5000   Apply the first year’s changes, so that you have these numbers on 1/1/2012:   Newer L = $2000+ 20% = $2400   Newer M = $3000+ 10% = $3300   Newer S = $5000+ 20% = $6000   Now apply the second year’s changes to L and M:   Newest L = $2400– 10% = $2400– $240 = $2160   Newest M = $3300– 20% = $3300– $660= $2640   Add these to get $4800. So the newest S must be $10,000 (the target final total of Dimple’s retirement savings) minus $4800, $5200   The dollar change in S from 1/1/12 to 1/1/13 is $6000 – $800 = $5200. So the question is this: what percent change does $800 represent, from a starting point of $6000? Since $6000 is a nasty divisor, switch to benchmarks:   5% of $6000 = $300.   10% of $6000 = $600.   15% of $6000 = $900.   And so on.   From this $800 lies between $600 and $900   The correct answer is 10 and 15.
<result>C</result>
On January 1, 2011, Dimple invests 20% of his retirement savings in Antarctic largecap stocks, 30% in Antarctic midcaps, and 50% in Antarctic smallcaps. In 2011, largecaps rise 20%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2013, Dimple has the same total amount of retirement savings as he did two years before, then x is between