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
The OA is D.
I'm confused with this PS question. Experts, any suggestion about the solution? Thanks in advance.
A satellite is composed of 30 modular units, each of...
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Call the total # of upgraded sensors 'u.'LUANDATO wrote: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
The OA is D.
I'm confused with this PS question. Experts, any suggestion about the solution? Thanks in advance.
The # of non-upgraded sensors on one unit = (1/5)u
# of non-upgraded inits on 30 units = (1/5)u * 30 = 6u
If there are 'u' upgraded sensors and 6u non-upgraded sensors, then there would be 7u sensors in total. Upgraded/Total = u/7u =1/7. The answer is D
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Or pick an easy number.LUANDATO wrote: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
The OA is D.
I'm confused with this PS question. Experts, any suggestion about the solution? Thanks in advance.
Total # of upgraded sensors on 30 units. = 5.
# of non-upgraded sensors on one unit = (1/5)*5 = 1
# of total non-upgraded sensors on 30 units = 1*30 = 30
Total # of sensors = 5 + 30 = 35.
Upgraded/Total = 5/35 = 1/7- The answer is D
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Since we're asked to find a certain FRACTION, we can plug in some nice values that meet the given conditions.LUANDATO wrote: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
Let's say that there's a TOTAL of 5 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)(5) = 1.
Since there are 30 modular units altogether, the TOTAL number of non-upgraded sensors = (30)(1) = 30.
So, the TOTAL number of sensors = (number of non-upgrades) + (number of upgraded)
= 30 + 5
= 35
What fraction of the sensors on the satellite have been upgraded?
= 5/35
= 1/7
Answer: D
Cheers,
Brent
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A student asked me to add some graphics to my solution, so......BTGmoderatorLU wrote: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
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