A satellite is composed of 30 modular units, each of which

This is how i solved
Let the total no of upgraded sensor in entire sat be 30 ( ie 1 per 30 modular units )
now total no of unupgraded sensor per uinit = 1/5* 30 = 6
Total no of not upgraded sensore = 6* 30 = 180
Total no of sensors = 180 + 30 = 210

Target quest
= total no of upgraded sensors / total no of sesors

= 30 / 210 = 1/7
=D

Let total number of non-upgraded sensors be y
And total number of upgraded sensors be x
y/30 = x/5
>> y/x = 6/1
>> x/(x+y) = 1/(1+6) = 1/7
Hence, Option D

Please give a kudos if you like this solution

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!

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.

Just confused by the language....!!
When we upgrade a sensors why do we add them?....shouldn't we replace the available sensors.

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

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

Thank you BrentGMATPrepNow
Wish you health and happy.



Posted from my mobile device

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.