Let's say that there's a TOTAL of x upgraded sensors on the entire satellite

the number of non-upgraded sensors on one modular unit is 1/5 the TOTAL number of upgraded sensors on the entire satellite
So, the number of non-upgraded sensors on EACH modular unit = (1/5)(x) = x/5.

Since there are 30 modular units altogether, the TOTAL number of non-upgraded sensors = (30)(x/5) = 30x/5 = 6x.

So, the TOTAL number of sensors = (number of non-upgrades) + (number of upgraded)
= 6x + x
= 7x

What fraction of the sensors on the satellite have been upgraded?
= x/7x
= 1/7

Answer: D

Cheers,
Brent

Let no. of non-upgraded sensors per module be x
Total non-upgraded sensors = 30x (since each module has same no. of non-upgraded sensors)

Let total upgraded sensors be T
From given condition: x=1/5*T
or, T= 5x

Now,
Total no. of sensors = upgraded + non-upgraded

Total no. of sensors = 5x+30x = 35x

so fraction of upgraded = 5x/35x = 1/7

So, answer is D

Wow, this is the topic! How much I know, but this is the first time I've ever met! Wow!

A student asked me to add some graphics to my solution, so......

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.
So, here's a sketch of 30 modular units.

The circles inside each unit represent sensors. The circles with black centers represent NON-upgraded sensors, and the empty red circles represent upgraded sensors.
For my sketch, I placed ONE NON-upgraded sensor in each of the 30 modular units (since we're told that each unit contains the same number of non-upgraded sensors)

The number of non-upgraded sensors on ONE UNIT is 1/5 the total number of upgraded sensors on the ENTIRE satellite
This tells us that there aren't many upgraded sensors among the satellite's 30 modular units
So, let's REDRAW the diagram to start with 1 NON-upgraded sensor in each of the 30 modular units



Okay, so if there's 1 NON-upgraded sensor in EACH of the 30 modular units, then there is a TOTAL of 5 UPgraded sensors on the ENTIRE satellite.
So, let's add 5 UPgraded sensors to our diagram to get:


At this point, our diagram meets all of the conditions in the question.

What fraction of the sensors on the satellite have been upgraded?
We can see that we have a total of 35 sensors, and 5 of them are upgraded.
So, the fraction = 5/35 = 1/7

Answer: D

Cheers,
Brent

Let the non-upgraded sensors be \(N\) and upgraded sensors be \(U\)

\(N = \frac{1}{5}(30U)\)
\(N = 6U\)

Total sensors \(= U + N = U + 6U = 7U\)

Required fraction = \(\frac{U}{7U} = \frac{1}{7}\)

Hence, option D

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Mandatory

Regards

I assumed concrete numbers.
Let's assume there are 30 upgraded sensors on the whole satellite (this value will be easy, because that means there is 1 on each module).
So then we know there are 1/5*30 = 6 non-upgraded sensors on 1 module.
Therefore, on one module, we have 7 total sensors = 6 non-upgraded and 1 upgraded.
Upgraded = 1/7 = D

Let total number of upgraded sensors on satellite be b

and number of non upgraded sensor in one modular unit be x



x = b/5

So total number of nonupgraded sensors on satellite

b/5 x 30 = 6b


Fraction required

b/b + 6b

b/7b

1/7

Answer D
Adewale Fasipe, GRE/GMAT quant instructor from Nigeria

https://www.teacheron.com/tutor-profile/8tG7?r=8tG7

Thank you sir for contributing to the forum with neat and clear explanations

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