Two workers, Ava and Ben, are hired to mow a field at a community park

Question

Two workers, Ava and Ben, are hired to mow a field at a community park. If Ava and Ben work at their respective constant rates, by what percent is the time Ben would take to mow the field alone less than the time Ava would take to mow the field alone?

(1) Ben, working alone at his constant rate, would take 2 hours less to mow the field than Ava, working alone at her constant rate, would take.

(2) Ava and Ben, working simultaneously and independently at their respective constant rates, can mow the field in 3/5 of the time that Ben, working alone at his constant rate, would take to mow the field.

M47-228

Bunuel · Accepted Answer

GMAT Club Official Solution:

Two workers, Ava and Ben, are hired to mow a field at a community park. If Ava and Ben work at their respective constant rates, by what percent is the time Ben would take to mow the field alone less than the time Ava would take to mow the field alone?

Let A be Ava’s rate and B be Ben’s rate, measured in fields per hour.

Ava’s time to mow the field alone is 1/A.

Ben’s time to mow the field alone is 1/B.

The question asks by what percent 1/B is less than 1/A.

(1) Ben, working alone at his constant rate, would take 2 hours less to mow the field than Ava, working alone at her constant rate, would take.

This gives only the difference between their times, not the percent difference.

For example, if Ava takes 6 hours and Ben takes 4 hours, then Ben’s time is 2 hours less, and the percent decrease is:

2/6 * 100 = 33 1/3%

But if Ava takes 10 hours and Ben takes 8 hours, then Ben’s time is also 2 hours less, and the percent decrease is:

2/10 * 100 = 20%

So the percent can be different.

Not sufficient.

(2) Ava and Ben, working simultaneously and independently at their respective constant rates, can mow the field in 3/5 of the time that Ben, working alone at his constant rate, would take to mow the field.

Since Ava’s rate is A and Ben’s rate is B, their combined rate is A + B fields per hour. Since time = work/rate, the time they take together to mow 1 field is:

1/(A + B)

Ben’s time to mow the field alone is:

1/B

So statement (2) gives:

1/(A + B) = 3/5 * 1/B

5B = 3A + 3B

2B = 3A

B/A = 3/2

This gives the ratio of Ben’s rate to Ava’s rate. Since time is the reciprocal of rate, it also gives the ratio of Ben’s time to Ava’s time. Therefore, we can answer the question.

For reference:

Ben’s rate : Ava’s rate = 3 : 2

So Ben’s time : Ava’s time = 2 : 3

Thus, Ben’s time is 1/3 less than Ava’s time, or 33 1/3% less.

Sufficient.

Answer: B.

Edskore · Answer

This is a work-rate Data Sufficiency question, and the whole point is noticing the difference between a statement giving you an absolute difference versus a ratio.

1. Say Ava takes a hours alone, Ben takes b hours alone. The question wants (a-b)/a as a percent, basically how much smaller Ben's time is relative to Ava's.

2. Statement 1 tells you b = a - 2, a flat two-hour gap. Problem is, 2 hours off a 4-hour job is a 50% difference, but 2 hours off a 20-hour job is only 10%. Without knowing the actual size of a, this statement can't nail down the percent. Not sufficient.

3. Statement 2 gives you the combined time: working together, Ava and Ben finish in 3/5 of Ben's solo time. Set up the combined rate formula, ab/(a+b) = (3/5)b, and simplify: a/(a+b) = 3/5, so 5a = 3a + 3b, meaning 2a = 3b, or b = (2/3)a. Now plug into (a-b)/a: that's (a - (2/3)a)/a = 1/3. A clean 33.3%, no matter what the actual hours are. Sufficient.

4. Answer is B.

The trap is that both statements look like they're giving you "enough" info, one gives a time gap, one gives a combined-time relationship, and it's tempting to assume you need both or that they're interchangeable. They're not. A flat difference only tells you something once you know the base number, but a ratio relationship locks in the percent regardless of the actual values. I used to instinctively reach for combining statements before checking whether one of them was already a self-contained ratio. Once I started asking "does this statement give me a ratio or just a raw number," sufficiency calls got a lot faster.

If a statement gives you a fixed ratio between two unknowns, you usually don't need the other one.

Two workers, Ava and Ben, are hired to mow a field at a community park

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Two workers, Ava and Ben, are hired to mow a field at a community park

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