Judith and Quincy started with the same amount of money to invest at t

Let the original investment in each case = 100.

JUDITH:
In 2012, Judith's P% increase = \(\frac{P}{100}(100) = P\).
Thus, Judith's amount at the end of 2012 = \(100+P\).
In 2013, Judith's Q% increase = \(\frac{Q}{100}(100+P) = Q+\frac{PQ}{100}\).
Thus, Judith's total increase = \(P+Q+\frac{PQ}{100}\).


QUINCY:
Quincy's R% increase = \(\frac{R}{100}(100) = R\).


Judith's final amount will be greater than Quincy's final amount if her total increase is greater than his increase:
Question stem, rephrased:
Is \(P+Q+\frac{PQ}{100} > R\)?


Statement 1: \(P+Q < R\)
Case 1: P=10, Q=10 and R=21
In this case, \(P+Q+\frac{PQ}{100} = 10+10+\frac{(10*10)}{100} = 21\) and \(R=21\), so the answer to the rephrased question stem is NO.
Case 2: P=40, Q=50 and R=100
In this case, \(P+Q+\frac{PQ}{100} = 40+50+\frac{(40*50)}{100} = 110\) and \(R=100\), so the answer to the rephrased question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.


Statement 2: \(R - P - Q < \frac{PQ}{100}\)
\(R < P+Q+\frac{PQ}{100}\)
\(P+Q+\frac{PQ}{100} > R\)
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.