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224) Time to work

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224) Time to work

by ern5231 » Fri May 14, 2010 3:25 am
X does first half of work and then Y does second half of the work. Together, they take 6 hours. In how much time can X complete work alone?

1)X&Y together complete the task in 3 hours.
2)X worked faster than Y
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Source: — Data Sufficiency |
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by ilikaroy » Fri May 14, 2010 3:58 am
Let X do 1 work in "a" hours and let Y do 1 work in "b" hours.
X does 1/2 work in a/2 hours and Y does 1/2 work in b/2 hours.
So a/2 + b/2 = 6.
Or a+b = 12. b= 12 - a
(1) means 1/a + 1/b = 1/3. Or 3(12-a) +3a = 12a - a^2
Or a^2 - 12a +36 = 0.
Or a = 6.
So (1) is suff.
(2) is not sufficient.

Correct answer is (A).
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