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GMAT Diagnostic Test Question 29 Field: word problems (work problems) Difficulty: 700

Mac can finish a job in M days and Jack can finish the same job in J days. After working together for T days, Mac left and Jack alone worked to complete the remaining work in R days. If Mac and Jack completed an equal amount of work, how many days would have it taken Jack to complete the entire job working alone?

(1) M = 20 days (2) R = 10 days

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient
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It's clear that neither Statement 1 nor Statement 2 is sufficient by itself. Let's see if both statements together give us enough info to answer the question.

Mac and Jack together would have the rate of \(\frac{1}{J}+\frac{1}{20}=\frac{J+20}{20J}\). They worked together for \(T\) days, so \(\frac{T(J+20)}{20J}\) of work was finished and \(1-\frac{T(J+20)}{20J}\) of work was left for Jack to finish by himself. Now, using all information we have at the moment, we can construct a system of two equations:

The first equation is based on the S2 and question stem's statement that the work was finished by Jack alone (after working together with Mac for \(T\) days). The second one is based on S1+S2 and statement that amount of work finished by Jack and Mac was equal.

The answer should be found upon solving this system of equations. S1+S2 is sufficient.
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After 4 hours of reading work-rate stuff, trying to understand %#$@# topic, here's my explanation.

we need to know if we can calculate for the number of days if jack do the entire work. So, in order to know calculate for the number of days, we need to know jack's work rate and total amount of work. work=rate*time Work = 1, given in the question, only rate is missing !

From the given information, Jack+Max working together during T days, and Jack works alone for R days. => Max works for T days, Jack works for T+R days !

choice 1) It tells us that Max can finish the entire job on his own in 20 days.. From this information, we know that his rate is 1/20 Also, from the question, "if Max and Jack completed an equal amount of work, ....". It tells us the amount of work for both Max and Jack. At this point, we know the time that Max spent in this half work and we know "T"

Though, it's still not enough to find jack's work rate ! So, choice 1) is insufficient

Before moving on, let's try 1) and 2) from 1) we know T (hint, T=10) from 2) we know R So T+R is the total time that Jack finish his half work. From this, we can find his rate !!

I think that this question is in 750 range! Intuitively, I could guess that the answer is C, but to be sure, very tough calculations are needed. Very time consuming question and thus I would give it the hardest rate.

it was said that mac left after t days and jack alone completed the rest of the work

If Mac and Jack completed an equal amount of work after working T days together than it doesn't mean that the mac and jack work at the same rate .

so if mac takes 20 days to complete the job than isn't it the same for jack ( 20 days to complete the work )

can someone please explain why the answer is not A going by the above analogy....

The ans cannot be A for the following reasons:

The stem says Mac took M days to complete the job alone; while Jack took J days to complete the same amount of job.

We are not told that M = J; the amount of job equaled one another only after (T + 20) days: After T days, Mac left - having done 1/2 of the work - and Jack continued for R (20) more days. Clearly, Mac has a much faster rate than Jack. R = W/T: The amount of work - RxT - increases (for one) faster than the other.
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Now we know that Mac and Jack completed an equal amount of work

We get 2 equations : (1) \(\frac{(T+R)}{J} = \frac{1}{2}\)

(2) \(\frac{T}{M} = \frac{1}{2}\)

Using (1) and (2) J = M + 2R

Since we need M and R

Answer is C

I dont understand how you got J = M + 2R from the 2 equations.. when setting the 2 equations equal to each other and cross multiplying I get JT = MT + MR, so I'm not sure how we get rid of the T. Could someone who understands explain this step?

I'm very confused to why this is considered a difficult question and why the need for different equations. Someone please correct me if I'm wrong.

The question stem tells us:

1) Mack can finish in: M days 2) Jack can finish in: J Days 3) After working together for T days (T is irrelevant), Mack leaves Jack and Jack completes the remaining work in R days. 4) They completed the same amount of total work.

The formula here seems very easy to me.

Since they finish the same amount of total work then we can already see that Mack is more productive than Jack by R days thus M = J+R

Statement 1: M = 20 Days We can derive 20 = J+R (NSF because we have two variables)

Statement 2: R = 10 We can derive M = J+10 (NSF because we still have two variables)

Put the statements together we have 20 = J + 10 (Sufficient and J = 10)

We know that it took a total time of M+J+R to finish the work and we know that M = J+R then the total work for Jack to do it alone would be J+R+J+R thus 10+10+10+10 = 40.

GMAT Diagnostic Test Question 29 Field: word problems (work problems) Difficulty: 700

Rating:

Mac can finish a job in M days and Jack can finish the same job in J days. After working together for T days, Mac left and Jack alone worked to complete the remaining work in R days. If Mac and Jack completed an equal amount of work, how many days would have it taken Jack to complete the entire job working alone?

(1) M = 20 days (2) R = 10 days

Mac can finish the job in M days --> the rate of Mac is \(\frac{1}{M}\) job/day; Jack can finish the job in J days --> the rate of Jack is \(\frac{1}{J}\) job/day;

After working together for T days, Mac left and Jack alone worked to complete the remaining work in R days --> Mac worked for T days only and did \(\frac{T}{M}\) part of the job while Jack worked for T+R days and did \(\frac{T+R}{J}\) part of the job;

Since Mac and Jack completed an equal amount of work (so half of the job each) then \(\frac{T}{M}=\frac{1}{2}\) and \(\frac{T+R}{J}=\frac{1}{2}\) --> \(T=\frac{M}{2}\) and \(T=\frac{J}{2}-R\) --> \(\frac{M}{2}=\frac{J}{2}-R\) --> \(J=M+2R\).

(1) M = 20 days. Not sufficient, we still need the value of R. (2) R = 10 days. Not sufficient, we still need the value of M.

i interpreted the question as: T(1/M+1/J) +R*1/J=1 and T*1/M=T*1/J+R*1/J

now:

S1- can solve T but not R or J

S2- can solve R but not T or M

both: knowing T R and M can solve J.

Found this really easy to understand as compared to some other replies posted.. Thanks.
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GmatPrep1 [10/09/2012] : 650 (Q42;V38) - need to make lesser silly mistakes. MGMAT 1 [11/09/2012] : 640 (Q44;V34) - need to improve quant pacing and overcome verbal fatigue.