MGMAT a satellite is composed of

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rommysingh: Master | Next Rank: 500 Posts; Posts: 112; Joined: Thu Mar 22, 2012 9:33 amFollowed by: 1 member; Thanked: 1 times

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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Source: Beat The GMAT — Problem Solving | Thu Sep 03, 2015 12:08 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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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Poisson: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Sat Aug 11, 2012 1:31 am

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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Gmatasap: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Mon Apr 04, 2016 3:20 am

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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