Lena and Marco are hired to paint a fence at a community park. If each

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 · Accepted Answer

GMAT Club 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 = 1/2 and M = 1/2, 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.

AdarshSambare · Answer

Let Lena’s painting rate be L square meters per hour, and Marco’s rate be M square meters per hour.
We need to determine whether Lena takes more time than Marco to paint 120 square meters.
Time = Work / Rate
So:
Lena’s time for 120 sq m = 120/L
Marco’s time for 120 sq m = 120/M
Question becomes:
Is 120/L > 120/M ?
Since 120 is positive, this simplifies to:
Is L < M ?
So we only need to know whether Lena paints slower than Marco.
Statement (1)
“Lena would take 6 more hours to paint 18 sq m than Marco would take to paint 6 sq m.”
Translate:
18/L = 6/M + 6
Multiply by LM:
18M = 6L + 6LM
Divide by 6:
3M = L + LM
This equation alone does not determine whether L < M.
Try values:
If M = 1:
3 = L + L
3 = 2L
L = 1.5
Here L > M.
Another example:
If M = 3:
9 = L + 3L
9 = 4L
L = 2.25
Here L < M.
Both are possible.
Statement (1) is insufficient.

Statement (2)
“Lena would take twice as long to paint 4 sq m as Marco would take to paint 1 sq m.”
Translate:
4/L = 2(1/M)
4/L = 2/M
Cross multiply:
4M = 2L
2M = L
So L > M.
That means Lena paints faster, so Lena takes less time for 120 sq m.
Answer to the question: No, Lena does not take more time.
Statement (2) alone is sufficient.
Correct answer: B

BongBideshini · Answer

Statement (1):

Let Marco’s time to paint 6 sq m = t hours.
Lena’s time to paint 18 sq m = t + 6
Marco’s rate: 6/t
Lena’s rate:18/(t+6)
We need to know whether Lena takes longer than Marco to complete the same work.
That means:
Is Lena’s rate lower?
whether : 18/(t+6) >6/t ?
18t >6(t+6). ?
18t > 6t + 36 ?
12t> 36 ?
t > 3 ?

So, whether Lena takes longer than Marco to complete the same work depends on the value of " t"
 Sufficient 
 
 Statement (2): 
Let Marco’s time for 1 sq m = x
Then Lena’s time for 4 sq m = 2x
Rates:
Marco: 1/x
Lena: 4/(2x) = 2/x
So Lena’s rate is double Marco’s.
Thus, Lena takes less time.
 Sufficient 
Answer: B

AllisonBell · Answer

Let’s see what it looks like to   solve this without equations.

The question is essentially asking if Lena paints at a slower rate than Marco. So we need to be able to compare their rates in order for a statement to be sufficient.

Statement 1:   
This scenario has Lena painting three times as much fence as Marco. So if they worked at the same rate, Lena would take exactly three times as long as Marco.

Is that possible? Sure. Maybe Marco took 3 hours to paint his part of the fence, and Lena took 6 more hours —9 total — meaning her rate is the same as Marco’s. In that case, the answer to the question would be no, Lena is not slower than Marco.

But could she be? To make that happen, we’d have to come up with a duration for Lena that’s more than three times as long as Marco’s, while still being exactly six hours greater. Maybe Marco takes 1 hour and Lena takes 7 hours. That’s seven times as long to paint three times as much fence, meaning Lena is working at a slower rate than Marco. In that case, the answer to the question would be yes, Lena is slower than Marco.

Statement 1 is insufficient .

Statement 2:  
This scenario tells us that Lena takes twice as long to paint four times as much fence. If they worked at the same rates, Lena would take four times as long to paint four times as much fence. So this tells us that Lena works at a faster rate than Marco.

Statement 2 is sufficient, so the correct answer is B.

To learn more common-sense ways to approach Data Sufficiency, check out the in-depth DS fundamentals lesson in ManhattanPrep’s  Free Trial Classes !

Best,
Ally Bell
ManhattanPrep GMAT Instructor

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