BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:46 pm

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

Answer: D
Source: Manhattan prep

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

BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:46 pm

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

Answer: D

Solution:

If each unit has 1 non-upgraded sensor, then in 30 units, there are a total of 30 non-upgraded sensors and only 5 upgraded sensors (notice that 1 is 1/5 of 5). Therefore, the total number of (upgraded and non-upgraded) sensors is 35 and the fraction of the sensors on the satellite have been upgraded is 5/35 = 1/7.

If each unit has 2 non-upgraded sensors, then in 30 units, there are a total of 60 non-upgraded sensors and only 10 upgraded sensors (notice that 2 is 1/5 of 10). Therefore, the total number of (upgraded and non-upgraded) sensors is 70 and the fraction of the sensors on the satellite have been upgraded is 10/70 = 1/7.

As we can see, no matter how many non-upgraded sensors each unit has, the fraction of the sensors on the satellite have been upgraded is always 1/7.

Answer: D