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by j_shreyans » Wed Mar 11, 2015 8:57 am
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


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by Brent@GMATPrepNow » Wed Mar 11, 2015 9:09 am
j_shreyans 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)1/2
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

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by DavidG@VeritasPrep » Wed Mar 11, 2015 9:11 am
Let's take the simplest possible scenario: we'll say that each of the 30 units has 1 non-upgraded sensor, giving us a total of 30 non-upgraded sensors on the satellite. We're told that the number of non-upgraded sensors on one unit is 1/5 the total of upgraded sensors on the entire satellite. If each unit has 1 non-upgraded unit, and '1' is 1/5 of the total upgraded sensors, then we must have a total of 5 upgraded sensors on the satellite.

In sum, on our satellite we have:

5 upgraded sensors
30 non-upgraded sensors
35 sensors total

So the fraction of upgraded to total is 5/35, or 1/7.
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by DavidG@VeritasPrep » Wed Mar 11, 2015 9:20 am
And I suspect the inspiration for this question was the following official question:

Alice's take home pay last year was the same each month and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of her monthly take home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take home pay did she save each month?

a. 1/2
b. 1/3
c. 1/4
d. 1/5
e. 1/6
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