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MGMAT a satellite is composed of

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by rommysingh » Thu Sep 03, 2015 12:08 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?



5/6


1/5


1/6


1/7


1/24
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by Brent@GMATPrepNow » Thu Sep 03, 2015 12:14 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)1/2
Since we're asked to find a certain FRACTION, we can plug in some nice values that meet the given conditions.

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
= [spoiler]1/7[/spoiler]
= D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Poisson » Sat Jun 11, 2016 6:18 am
Hello,

I'm having a hard time following the calculations for this. Could someone share an algebraic approach to answering this question? Thanks so much
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by Gmatasap » Sat Jun 11, 2016 8:15 am
Poisson wrote:Hello,

I'm having a hard time following the calculations for this. Could someone share an algebraic approach to answering this question? Thanks so much
Let N be the number of Non Upgraded sensors in each unit. Total Non upgraded sensors will be 30N
Let T.U be the total Upgraded sensors, then

N=1/5(T.U)
or 5N= T.U

Now ratio of Total upgraded to Total sensors is,

T.U/(TU+30N)
=5N/(5N+30N)
=[spoiler]1/7[/spoiler]

IMO D
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