lalania1 wrote:

Judith and Quincy started with the same amount of money to invest at the beginning of 2012. Judith's investments increased by P percent in the year 2012 and then increased by Q percent in the year 2013. From the start of 2012 to the end of 2013, Quincy's investment increased by R percent. Which one of them had more money by the end of 2013?

(1) P + Q < R

(2) R - P - Q < (PQ/100)

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.

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