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Re: A satellite is composed of 30 modular units, each of which [#permalink]
jagdeepsingh1983 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?

No of Units-30
Let there T-Total no of sensor
U-no of upgraded sensors in one unit
Nu-No of Not upgraded senor in one unit

T= 30U+30Nu

Now we know that Nu=1/5 (30U)= 6U

So Total= 30U+30*6U = 30U+180U= 210U

Fraction= 30U/210U = 1/7 Answer is D

Regards
Jagdeep
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Hello jagdeep,
Thank you very much for your explanation, you turn a difficult exercise in a easy one.
But I have one question:

If you say T= 30U+30Nu, don't you assume each U is equal to all Us such as Nu is equal to all Nus? - N1=N2=N3=...=N30
I mean, every N is equal (and Nu) and the question didn't say it. Because I didn't get it, I couldn't solve the exercise.

Thank you!
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A satellite is composed of 30 modular units, each of which [#permalink]
How I somehow managed to solve this fun one:

I started off by initially defining some variables:
(1) New = upgraded sensors on one unit
(2) Old = non-upgraded sensors on one unit
(2) Not a variable, but important to note that the number of units on the satellite is equal to 30.

Let's take this quote and translate that into an equation:
"number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite"

Old/30(New) = 1/5.

It's important to realize that the New variable must be multiplied by 30 because it states the "total number ... on on the entire satellite"

We can solve for New, which is equal to Old = 6(New). In other words this means that on a given UNIT of the satellite there is 6 new units for everyone one old unit.

Now let's get to our answer, since we're asked to find "what fraction of the sensors on the satellite have been upgraded?" we need the following formula:

30(New)/30(New) + 30(Old), and with our ratio that we determine above we can say that 30(New)/30(New)+30(6(New), which leaves us with 30(New) / 210(New), and 1/7 is our answer.
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Re: A satellite is composed of 30 modular units, each of which [#permalink]
Just confused by the language....!!
When we upgrade a sensors why do we add them?....shouldn't we replace the available sensors.
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A satellite is composed of 30 modular units, each of which [#permalink]
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

My Approach:
Let, total number of upgraded sensors in 30 units be= 5
so, number of non-upgraded sensor in 1 unit= (1/5)*5= 1
Total number of non-upgraded sensors in 30 units= 30*1= 30
Total Sensors= Upgraded+Non-upgraded= 5+30= 35

So, fraction of the sensors on the satellite have been upgraded= 5/35= 1/7

Answer: D. 1/7
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A satellite is composed of 30 modular units, each of which [#permalink]
Dear BrentGMATPrepNow, @Care

In my view, the difficult degree is not the math, but it is the English. For not native people such as me, I did not understand the meaning of the first sentence: "A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded".

Now, when my English grammar was upgraded a bit, I understood it as follows:

A satellite is composed of 30 modular units,
each of which is equipped with a set of sensors = each of modular unit is equipped with a set of sensors.
some of which have been upgraded = in each of modular unit, some of sensors have been upgrade (saying U), and the rest, of course, are non-upgraded sensors (saying Un).

Now, the total of sensors of 30 units is: 30*(U+Un).
the number of non-upgraded sensors on one unit is Un.
the total number of upgraded sensors on the entire satellite: 30*U.

Un = 1/5 (30*U) = 6*U

The fraction of the sensors on the satellite have been upgraded: 30U / 30 *( U + 6U) = 1/7

In fact, in official math books in my country, authors avoid this wording style as it confuses readers.
Anyway, it is English, we have to accept.

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


BrentGMATPrepNow wrote:
varunmaheshwari 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 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



Cares wrote:
Does anyone else find this problem hard to understand and translate into an equation? I understand it clearly after the explanation but I think it is poorly worded.
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Re: A satellite is composed of 30 modular units, each of which [#permalink]
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I totally agree, TrungTiger
There are many official quantitative questions that test Reading Comprehension more than they test mathematical properties.
Great job interpreting the question as you did!
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Re: A satellite is composed of 30 modular units, each of which [#permalink]
Thank you BrentGMATPrepNow
Wish you health and happy.

BrentGMATPrepNow wrote:
I totally agree, TrungTiger
There are many official quantitative questions that test Reading Comprehension more than they test mathematical properties.
Great job interpreting the question as you did!


Posted from my mobile device
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Re: A satellite is composed of 30 modular units, each of which [#permalink]
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Easy algebraic way

s= total upgraded sensors
nu = total non upgraded sensors

Questions is asking what fraction of sensors has been upgraded --> s/(s+nu)

Number of non-upgraded sensors in one unit (nu/30) is 1/5 the total number of upgraded sensors (s/5)

nu/30 = s/5
nu = 6s

Now substitute in asked equation.

s / (s+6s) = s/7s

s cancels out to give 1/7
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Re: A satellite is composed of 30 modular units, each of which [#permalink]
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