Source: Official Guide Revised GRE 1st Ed. Part 8; Section 5; #25

6

A desert outpost has a water supply

A desert outpost has a water supply that is sufficient to last 21 days for 15 people. At the same average rate of water consumption per person, how many days would the water supply last for 9 people? 28.0, 32.5, 35.0, 37.5, 42.0

3 Explanations

2

Sofia Ababou

Cydney Seigerman, Magoosh Tutor:

I tried to use the equation offered in your explanation : 15 people / 21 days = (x days / 9 people)

But the numbers just don't add up and don't give the correct answer, 35 days. Rather, with the equation stated in your explanation, it gives approximately 6 days (which doesn't make sense)

Nov 13, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Sofia,

Sorry for the delayed response! After reviewing the work in my original explanation, yes, you're completely correct that the math doesn't quite work out. While the idea of inverse proportions is a valid way to approach the problem, the proportion is not correct. Here are two correct ways to express the situation using proportions:

15 people / 9 people = x days / 21 days

or

15 people / x days = 9 people / 21 days

In the first proportion, we have people/people = days/days so that the ratios of the two groups should be equal, which is what we see when we write the proportion in this way. In the second proportion, the unit "people" is in the numerator and "days" in the denominator. This makes sense, since this set up allows us to compare people with people and days with days. On the other hand, in my original explanation, I incorrectly compared people with days.

I hope this clears up again doubts! Thanks again for pointing out this out :)

Dec 5, 2016 • Reply

4

Jacob Elder

I know up there the question was asked "Is this not a ratio problem?" but I'm still uncertain why doesn't solving it as "15/21 = 9/x" and solving for x isn't adequate? I feel like I've done this sort of problem plenty of times before, and that manner of doing it has been effective, so I'm confused what the difference is with this problem.

Jan 24, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

The key to this problem is to recognize that when we have more people drinking the water, the water supply will be used up more quickly, given the fact that the rate at which an individual consumes water remains constant. With this in mind, we can say that the number of days the water lasts is inversely proportional to the number of people:

15 people / 21 days = (9 people / x days)^(-1) -->
15 people / 21 days = (x days / 9 people)

Conversely, the equation you've written

15 people /21 days = 9 people /x days

is an example of a direct proportion and would be correct if as the number of people increased, the number of days the water supply lasts increased. That's not what happens, though, as the number of days the water supply lasts is inversely proportional to the number of people.

I hope this helps! :)

Feb 15, 2016 • Reply

Jitesh Dange

Same problem here Jacob, Thanks for the explanation.

Apr 26, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

You're welcome, Jitesh :) Happy studying!

Apr 28, 2016 • Reply

3

Gravatar Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

Y L

Is this not a ratio problem?

Nov 26, 2013 • Reply

Lucas Fink, Magoosh Tutor

It looks similar to a ratio, but it's actually a work-rate question. Ratios require direct correlations--when you increase one side of the ratio, the other side goes up appropriately. When you decrease on side, the other side goes down, too.

Meanwhile, the relationship between people and days is quite different: as the number of people goes up, the number of days goes down. The relationship is inverse.

We can think of this water volume as being enough for 315 people-days. What I mean by that is 315 times what one person drinks in one day, because we were given 21 people over 15 days and 21*15 = 315. So one person could drink for 315 days or 315 people could drink for 1 day.

As a work-rate question, then, we get 315 / 9 = 35, our answer.

Dec 3, 2013 • Reply

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