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Time and Work - Understanding the Method

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Time and Work - Understanding the Method

by s91arvindh » Mon Apr 21, 2014 8:35 pm
If 2000 pints of glucose can last 50 patients for 30 days, then for how many weeks will 1680 pints of glucose last 60 patients?
a) 3.5 weeks b) 2 weeks c) 2.5 weeks d) 3 weeks

Answer : 3 Weeks

I was introduced to use the below Method to solve these type of questions easily

Patients Pints Days

50 2000 30
60 1680 X

To find X

x=30*50/60*1680/2000

X= 21 days / 3 Weeks .

I am confused with the values assigned in the above Method. Requesting to help me with a detailed concept of the above method ..

Thanks for your support !
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by [email protected] » Mon Apr 21, 2014 11:15 pm
Hi s91arvindh,

This is essentially just a rate question, although it has more "pieces" to it than a typical GMAT rate question. The fact that this example includes just 4 answer choices is further proof that this is NOT a GMAT question.

Here's the basic run-down of how to solve it:

The first piece of info is that 2000 pints can last 50 patients (for 30 days).

2000/50 = 40 pints/person (for 30 days)

40/30 = 4/3 (pints/person) / DAY

So, each day, each person needs 4/3 pints of glucose. Now that we have the rate, we can apply it to any situation and solve.

We're asked for how many WEEKS 1680 pints will last 60 patients....

60 patients x 4/3 = 80 pints/day needed

(1680 pints available)/(80 pints/day needed for those 60 patients) = 21 days long

Final Answer: [spoiler]D; 21 days = 3 weeks[/spoiler]

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Rich
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by s91arvindh » Mon Apr 21, 2014 11:37 pm
Hi Rick,

Thanks for clarifying the question!

You have any idea about the method used to solve this question

Patients Pints Days

50 2000 30
60 1680 X

To find X

x=30*50/60*1680/2000 .

I tired to solve as per your approach But I found this was much quicker than the basic Since we need to just apply the values and multiply them .

Thanks for your support !

Regards
Arvindh
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by sukriti2hats » Mon Jun 02, 2014 10:40 pm
Hi s91arvindh,

The shortcut that you have mentioned in this problem is based on a simple fact - when we multiply a number with an improper fraction its value incrases and when we multiply a number with proper fraction its value decreases.

In this case the number of days is found out in three steps, but the reason behind these steps is the normal method by which we find out time required to get the work done.

Firstly as you constructed the table,
Patients Pints Days
Case 1: 50 2000 30
Case 2: 60 1680 X

Step 1: firstly we consider the ratio of the number of days now and the number of days earlier that is X/30

Step 2: now, in case 2 the number of patients have increased, so it will take less days to finish the amount of glucose and the ratio X/30 will decrease. Since the ratio is decreasing we make a proper fraction out of the the number of patients in case 1 and 2 that is 50/60. The ratio x/30 will decrease and will be equal to 50/60 (given the amount of glucose remains same) X/30=50/60 [ had the ratio been increasing, we would have meade an improper fraction out of the two figures].

Step 3: now we consider a decrease in the amount of glucose available. Pints of glucose decrease so it will take less number of days for glucose to finish, thus ratio X/30 will decrease. Again, we make a proper fraction out of the pints in both cases, that will be 1680/2000. But since the number of patients have alreafy increased, the ratio X/30 will be
X/30 = 50/60 x 1680/2000
X= 30 x 50/60 x 1680/2000

When encountered with such a problem you can create this table quicky and depending on the effect the change in other values have on X you can create proper or improper fractions and multiply them.

For example you can consider another problem,
Men Days Work
20 10 2
10 12 X
X= 2 x 10/12 x 20/10
(Amount of work earlier) x (days increased so work decreased - proper fration) x men decreased so work increased - improper fraction)

Cheers
Sukriti
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