Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The key to this problem is the second sentence. When Becky and Caroline help, the time it takes to build the birdhouse is cut in half. That means that Becky and Caroline, when working together, work at a rate equal to the rate Abby works at.
We can represent the rates that Abby, Becky and Caroline work as 1/a, 1/b and 1/c, respectively. Therefore:
All of the answer choices have an expression equal to 0, so combine fractions and move them all to the left side of the equation. The common denominator for all fractions is abc.
The correct answer is C.