Jordan and Michael begin filling a number of sandbags at the

Question

Jordan and Michael begin filling together a number of sandbags at their respective constant rates. If he worked alone, Jordan would take 12 minutes less than Michael to fill all of the sandbags. Jordan stops working when he has filled one-fourth of the sandbags, and it takes Michael 21 minutes to fill the rest on his own.

How many minutes would it have taken Michael to fill all of the sandbags by himself?

A. 28
B. 36
C. 42
D. 48
E. 63

Show Answer

Official Answer

B

How many minutes would it have taken Michael to fill all of the sandbags by himself?

A. 28
B. 36
C. 42
D. 48
E. 63

ankushsambare · Answer

Let Michael take  M minutes  to fill all the sandbags.
Then Jordan would take  M − 12 minutes .
Since Jordan fills  1/4  of the sandbags, the time Jordan spends is  1/4 of his total time :
Jordan's working time = (M − 12)/4.
After that,  3/4 of the sandbags remain .
Michael fills these remaining sandbags in  21 minutes .
Since 21 minutes is the time Michael needs to fill  3/4  of all the sandbags, Michael's full time is:
21 × (4/3) = 28 minutes.
Therefore, Michael would need  28 minutes  to fill all the sandbags by himself.
 Answer: A. 28 .

kevincan · Answer

Jordan doesn’t work by himself

GMATinsight · Answer

I think this question needs to have clarity in language.

kevincan · Answer

Jordan stops working when he has filled one-fourth of the sandbags. This does not mean that he stops working when 1/4 of the bags are filled.

kevincan · Answer

I have added the word simultaneously for clarity

kevincan · Answer

If Michael would need x minutes, Jordan would need x − 12 minutes.

Their rates are:  \frac{1}{x}  and  \frac{1}{x-12}  of the job per minute, respectively.

Jordan stops after completing  \frac14  of the work, so they work together for  \frac14(x-12)  minutes.

During that time, Michael completes fraction   \frac{\frac14(x-12)}{x} = \frac{x-12}{4x}  of the job.

Thus, when Jordan stops, the fraction of the work completed is   \frac14+\frac{x-12}{4x}

The remaining work is completed by Michael in 21 minutes, so   \frac14+\frac{x-12}{4x}+\frac{21}{x}=1

Simplifying the first two terms on the left :   \frac14+\frac{x-12}{4x} = \frac{x+(x-12)}{4x} = \frac{2x-12}{4x}=\frac{x-6}{2x}

Therefore,   \frac{x-6}{2x}+\frac{21}{x}=1

Multiply both sides by  2x :

x-6+42=2x  
  x=36

Therefore, Michael would need  36  minutes to fill all the sandbags by himself

keshubhturakhia · Answer

J takes 12 minutes less than M to fill all the sandbags is what they have said. Thus we can say that it takes J 3 mins less than M if they both were filling 1/4 of the sandbags each.

In the above case, say J finishes filling 1/4 of the bags at time x. So at x+3 M has finished filling his own 1/4 bags. Now that they both have finished filling 1/4 each, 1/2 the work is done, which M now has to complete by himself.

After J stops working it takes M 21 minutes to finish the rest of the work. This includes 3 minutes to first finish 1/4 bags which he was already working on while J was working, and then the remaining 18 minutes it takes him to finish the final 1/2 of the bags. Thus if 1/2 of the bags takes M 18 minutes, all the bags will take him 36 minutes.

Please let me know if my explanation was clear and if not i will explain better. Thanks

kevincan · Answer

That’s simply wonderful !

Adit_ · Answer

The key thing to notice is that both work together.

When Jordan completes 1/4th of HIS work. Some amount was being done by Michael as well.
The remaining after this portion is what is completed by Michael.

On taking J = 1/(x-12), M = 1/x:

x-12/4 ( 1/x-12 + 1/x) = x-6/2x.

Now the remaining work left:
1-(x-6/2x)
= x+6/2x

Michael takes 21 mins to complete x+6/2x of work:

21(1/x) = x+6/2x.

On solving x =  36 .

keshubhturakhia · Answer

Hello sir
Just solved a few of your other questions as well which i believe you have just recently posted. Are these questions meant for speed solving and if yes could you help with the smarter solutions. I am asking since a lot of the questions i found the solutions to be lengthy. If you think we should discuss this on PM instead please let me know and i will message you there

kevincan · Answer

I get the impression that some people try to be helpful by posting AI explanations. You do everyone a great service by asking for a faster solution to a question .

It’s also true that even if you are on your way to a top quant score , challenging lengthy questions are interspersed with more routine ones, so don’t worry if the odd question takes you more than 3 minutes.

Keep in mind that these are not official questions : they are meant to be for practice and improvement. Questions with a success rate below 15% and/or an average time greater than 3:30 minutes would probably never appear in the exam , or only for the top 5%.

kevincan · Answer

Let’s see whether this wording works better

Jordan and Michael begin filling a number of sandbags at the

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