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## Arithmetic - Applying Work Rate Concepts

I came across a question at the GMAT Club today from an unknown source. Test takers have put up long, algebra based solutions to the problem. The question can be solved within 15 seconds if you understand the concepts discussed in the work-rate module.

Recall what we discussed:

If A and B work together and take n days to complete a work, and if we know that their rate of work is same, each will individually take 2n days to complete the same work. When both work together, time taken becomes half and hence becomes n

This helps us eliminate options very quickly. Let me show you how.

Here is the question:

Question: A and B together complete a work in 4 days, B and C together in 6 days, C and A together in 5 days. Working independently, who will finish the work in the least time and in how many days?

(A) A, 120/17 days
(B) A, 120/7 days
(C) B, 120/17 days
(D) B, 120/13 days
(E) C, 120/7 days

Solution:

A and B together take least time i.e. 4 days for the same work. So one of them must be the fastest.

Now note that C and A take 5 days (less than what C and B take together). So A must be faster than B.

Hence A is the fastest and will take the least time. Choose between options (A) and (B).

A and B together take 4 days and A is faster than B. Then, definitely, A takes less than 8 days because if their speeds were the same, both would take 8 days working independently.

Only option (A) has less than 8 days so answer must be option (A).

No algebra, no calculations and you get the answer in no time!