A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

a) 5/6
b) 1/5
c) 1/6
d) 1/7
e) 1/24

I think I understand the question because I got the right answer of 1/7, but I solved it differently than how MGMAT solved it. Would someone check to make sure my logic works?

Each unit had some upgraded and non-upgraded sensors. I used X to denote the number of non-upgraded sensors per unit.
Given that there is 30 units, total non-upgraded sensors is 30X.

So, the statement "If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite" is translated to

X=1/5(Total Sensors - 30X)

and "what fraction of the sensors on the satellite have been upgraded?" is translated to

(Total Sensors - 30X)/Total Sensors.

I solve for the first equation for Total Sensors or T

X=1/5(T - 30X)
X=1/5T-6X
35X=T

With T, I plug into second equation

(35X-30X)/35X = 1/7.

Is this an appropriate logic? I used a table to help me organize this on my paper, but I don't know how to make a table here.

shaw, well done! I think you did a terrific job and thank you for providing a wonderful resource for this problem in your detailed explanation. Other students will be grateful. :-)

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Jamie Nelson
ManhattanGMAT Instructor

thanks! much more helpful than the description on the test. Got this one wrong, but guessed pretty quickly since I knew I was short on time at the point I got to it... key part was to understand that you're going for
X=1/5(total-30X)

so that you can define

(Total-X)/Total

:-)

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Jamie Nelson
ManhattanGMAT Instructor

One more way. Please let me know if there's a mistake with this.

Let number of non-upgraded sensors in a unit = N
Let number of upgraded sensors in a unit = U

Total number of non-upgraded sensors = 30N and total number of upgraded sensors = 30U and therefore total number of sensors = 30(N+U)

Since number of non-upgraded sensors in a unit is 1/5th of total number of upgraded sensors, we get

5N = 30U or N = 6U.

Fraction of upgraded sensors = 30U/ 30(N+U)

= U/(N+U) = U/7U = 1/7

You can not assume that the number of upgraded sensors (U in your discussion) is the same for each unit. You need to replace the 30 U with the actual number of upgraded sensors, call that S [the sum of the upgraded sensors over all units]. Things will work out the same from there though:
Total = T = 30 N + S
N = (1/5) S or S = 5 N

Fraction = S / T = 5 N / (30 N + 5 N) = 1 / 7

Note that shaw.s.li used Total Sensors rather than assuming something about the number of upgraded sensors (and thus Total Sensors) in each unit.

It can be done in fewer steps.

Once you assume that the number of upgradable sensors in 1 unit is x, we know that the total number of upgradable sensors is 30x.

Now the number of non upgraded sensors in 1 unit = 30x * 1/5 = 6x. Therefore, there are 7x sensors in 1 unit (x + 6x).

Now, fraction of up-gradable sensors in 1 unit = x/(7x)=1/7

Wow! Good stuff on this thread--thanks all!

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Jamie Nelson
ManhattanGMAT Instructor

You do not need to assume, the question stem states that each unit contains same number of non-upgraded units. Thereby, for each unit, (1 minus non-upgraded units = upgraded units per unit).

Otherwise, I agree with the rest of the post, where you are looking for the basic formation pattern of
( Y / X + Y) = > X = (1/5)(30)(Y) or X = 6Y
(Y/ 7y) or 1/7.

thanks for sharing..

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Tim Sanders
Manhattan GMAT Instructor

Video explanation? I am totally lost with this problem.

if you want more help than what has been provided already, you're going to have to be more specific with your question..

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Tim Sanders
Manhattan GMAT Instructor