Two machines, A and B, each working at a constant rate, can

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Sun May 14, 2017 8:28 am

Two machines, A and B, each working at a constant rate, can complete a certain task working together in 6 days. In how many days, working alone, can machine A complete the task?

(1) The average time A and B can complete the task working alone is 12.5 days.

(2) It would take machine A 5 more days to complete the task alone than it would take machine B to complete the task.

OA is B

My doubt:- In both the statements, there is a quadratic equation, and i have to solve them to get the answer. Is there any alternative approach without solving the quadratic equations for both the statements.

Thanks

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Source: Beat The GMAT — Data Sufficiency | Sun May 14, 2017 8:28 am

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun May 14, 2017 11:26 am

Hi vinni.k,

This is actually a great 'concept' question - you can get the correct answer without doing any math at all, IF you recognize the concepts involved. This question is ultimately based on "system math" (in this case, 2 variables and 2 equations). However, unless we're told which machine is the FASTER machine, we'll end up with 2 rates without knowing which rate belongs to which machine.

To start, we know that, working together, Machine A and Machine B can complete a task in 6 days. We can use the Work Formula to create the following equation:

(A)(B) / (A+B) = 6
(A)(B) = 6A + 6B

We're asked for the value of A.

1) The average time A and B can complete the task working alone is 12.5 days.

With this Fact, we can create a second equation:

(A+B)/2 = 12.5
A+B = 25

Notice how we still don't know which machine is faster/slower... We could combine this equation with the initial equation (above) and solve algebraically... and we'd end up with the values 10 and 15... BUT we won't know which one represents A.
Fact 1 is INSUFFICIENT

2) It would take machine A 5 more days to complete the task alone than it would take machine B to complete the task.

With this Fact, we can create a second equation:

A = B + 5

Here, we know that B is the smaller (re: faster) number, so while we would again end up with 10 and 15, we know that B=10 and A=15.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Thu May 18, 2017 12:26 am

Thanks

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