A and B working together can finish a job in d days...

[BTGmoderatorLU]

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

A. 25
B. 60
C. 15
D. 14
E. 13

The OA is C.

I'm confused by this PS question. Experts, any suggestion? Thanks in advance.

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Hi LUANDATO,

We're told that A and B working together can finish a job in D days, if A works alone and completes the job, he will take (D + 5) days and if B works alone and completes the same job, he will take (D + 45) days. We're asked for the value of D. This is an example of a Work Formula question. Any time you have two entities (people, machines, water pumps, etc.) working on a job together, you can use the following formula:

(AB)/(A+B) = Total time to do the job together, where A and B are the individual times it takes the two entities to complete the job done.

Here's how you can TEST THE ANSWERS to answer this question. The answer choices to this question are all INTEGERS - which means that D, (D+5) and (D+45) will ALL be integers. That does not happen very often in Work Formula questions (usually one or more of the values ends up being a non-integer). Thus, since we're dealing with "+5" and "+45", it's likely that D will probably be a multiple of 5 (meaning that all of the numbers we end up plugging in will be 'nice, round numbers').

Let's TEST Answer C: 15

IF.... D=15, then (D+5) = 20 and (D+45) = 60....
If we plug 20 and 60 into the Work Formula, we get... (20)(60)/(20+60) = 1200/80 = 120/8 = 15
In this calculation, we end up with the value of D (re: 15), so this MUST be the answer.

Final Answer: C

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

[Scott@TargetTestPrep]

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

A. 25
B. 60
C. 15
D. 14
E. 13

We can create the equation:

1/(d + 5) + 1/(d + 45) = 1/d

Multiplying by (d + 5)(d + 45)d we have:

d(d + 45) + d(d + 5) = (d + 45)(d + 5)

d^2 + 45d + d^2 + 5d = d^2 + 50d + 225

d^2 = 225

d = 15

Answer: C