M47-152

Question

Lena and Marco are hired to paint a fence at a community park. If each of them paints at a constant rate, does Lena, working alone, take more time than Marco, working alone, to paint 120 square meters of the fence?

(1) Lena, working alone, would take 6 more hours to paint 18 square meters of the fence than Marco, working alone, would take to paint 6 square meters of the fence.
 
(2) Lena, working alone, would take twice as long to paint 4 square meters of the fence as Marco, working alone, would take to paint 1 square meter of the fence.

Bunuel · Answer

Official Solution:

Lena and Marco are hired to paint a fence at a community park. If each of them paints at a constant rate, does Lena, working alone, take more time than Marco, working alone, to paint 120 square meters of the fence?

Let \(L\) and \(M\) be Lena’s and Marco’s times, respectively, in hours, to paint 1 square meter.

The question asks whether Lena takes more time than Marco to paint 120 square meters. Since both paint at constant rates, this is the same as asking whether \(L > M\).

(1) Lena, working alone, would take 6 more hours to paint 18 square meters of the fence than Marco, working alone, would take to paint 6 square meters of the fence.

This gives:

\(18L = 6M + 6\)

\(3L - M = 1\)

This does not determine whether \(L > M\).

For example, if \(L = 1\) and \(M = 2\), then \(L < M\).

But if \(L = \frac{2}{5}\) and \(M = \frac{1}{5}\), then \(L > M\).

Not sufficient.

(2) Lena, working alone, would take twice as long to paint 4 square meters of the fence as Marco, working alone, would take to paint 1 square meter of the fence.

This gives:

\(4L = 2M\)

\(2L = M\)

So, \(L < M\), and the answer to the question is no.

Sufficient.

Answer: B

M47-152

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards