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

Sorry to revisit an old post but this was a toughy! Its not a necessary condition that d be an integer.

So working together they can do the job is d days.
Let \(r_1\) be the rate of A
Let \(r_2\) be the rate of B

Working together their rates to do the job is
Equation1:
\((r_1+r_2)d=1 (job)\)

A working alone can do the job by
Equation2:
\((r_1)(d+5)=1 (job)\)

B working alone can do the job by
Equation3:
\((r_2)(d+45)=1 (job)\)

Now set the first equation to the second equation

\((r_1+r_2)d=1 = (r_1)(d+5)\) solve for d to get \(d=5(r_1/r_2)\)

Now set equation1 to equation2

\((r_1)(d+5)=1 =(r_2)(d+45)\) solve to get \(r_1/r_2=(d+45)/(d+5)\)

Now substitute \(d=5(r_1/r_2)=5((d+45)/(d+5))\)

to get \(d(d+5)=5(d+45)\)

which leads you to \(d^2=5*45\). Which is equal to \(d=15\) when you square root both sides (of couse d must be positive, were talking about days here!).

Again, tough problem. If anyone has an easier method let us know.

1/(d+5) +1/(d+45)= 1/d
=> (2d+50)d = (d+5)*(d+45)
=> d^2 = 9*5*5
=> d= 15

hence option C.

take the total work as X

so both A & B can do it in d days, A alone in d+5 and B alone in d+45

rate calculation is total rate = sum of individual rates

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

we can remove X, then the equation becomes as below

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

simplification leads to

d^2 = 225

d= + or - 15

u cannot have days in negative right as it should take some time to do a task...hence 15 is the answer...

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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

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

When you do the math you end up with d^2 = 225. Therefore, d=15

Could you please show the expanded form as to how to solve for d please? Thank you.

1 thing I would mention here as Bunuel has mentioned as well, you need to be intelligent to pick your battles in GMAT. It is not about finding the correct answer but you also need to make sure that you do not spend more time than what you should be spending.

Putting in the values in the options after you get 1/(d+5) + 1/(d+45) = 1/d , is the fastest way to solve this equation.

But for the sake of your question, look below for the solution:

1/(d+5) + 1/(d+45) = 1/d ---> \(\frac{(2d+50)}{(d+5)(d+45)} = \frac{1}{d}\) ---> \(2d^2+50d=d^2+50d+225\) ---> \(d^2=225\) --->\(d = \pm 15\), you can not have d < 0 as the number of days can only be >0.

Thus d= 15 is the only acceptable solution.

Hope this helps.

Rate of \(A=\frac{1}{(d+5)}\)

Rate of \(B=\frac{1}{(d+45)}\)

Rate of \(A+B= \frac{1}{d}\)

Rate of \(A+B= \frac{1}{(d+45)} + \frac{1}{(d+5)}\)

\(\frac{2d+50}{(d+5)(d+45)}=\frac{1}{d}\)

\((2d+50)d= (d+5)(d+45)\)

\(2d^2+50d=d^2+5d+45+225\)

\(2d^2+50d=d^2+50d+225\)

\(2d^2-d^2=225\)

\(d^2=225\)

\(d=\sqrt{225}\)

\(d=15\)

Answer is C

Hi All,

Since we have two entities working on a job together, we're dealing with a Work Formula question.

Work = (A)(B)/(A+B) where A and B are the two individual times it takes to complete the job.

We're told that it takes two people D days to complete a task - and the individual times are (D+5) days and (D+45) days. From the answer choices, we know that D is an INTEGER... so we're going to end up reducing a fraction to an integer. This question is perfect for TESTing THE ANSWERS.

Notice how we're adding A and B in the denominator; that sum will almost certainly be a nice 'round' number - again, since the fraction reduces to "D" - so the correct answer is likely A, B or C. Let's TEST Answer C first...

IF....
D=15 days...
then the two individual rates are 20 days and 60 days.
When we plug those two values into the Work Formula, what do we end up with....?
(20)(60)/(20+60) =
1200/80 =
15
That is an exact match for the value of D, so this MUST be the answer.

Final Answer:

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

Seems like I didn't have the intuition to start with testing C. I started testing B and D as that what I usually do, and ended up wasting too much time.

Rate of A & B together = Rate of A + rate of B

i.e. 1/d = 1/(d+5) + 1/(d+45)

d must be a multiple of 5 for this equation to be true so check with a few values d = 5, 10, 15, 20 etc.

1/15 = 1/20 + 1/60
hence d = 15 fits

Answer: option C

Hi memyselfi,

TESTing Answer B or D first is often the best first move in these types of situations; these answers were arranged 'out of order' though (which is not something that you will likely see on Test Day). If these answers were in order - and you had started with Answer D (re: D = 25), then you would have had proof that that answer was incorrect (you'd end up with a value of 21 days, wheres D = 25 days was what you started with). Since those two values are relatively close to one another, the next logical step would have been to TEST Answer C (re: D = 15) and then you would have been done.

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

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