Problem Solving

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

OA after some discussion.

Thanks Anurag, for the shorter/alternate method.OE seems to be longer than your explanation . Thanks again.

OA D

smackmartine 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

OA after some discussion.

Let the TOTAL number of upgraded sensors = 5.
Then the number of non-upgraded sensors on EACH unit = (1/5)*5 = 1.
Thus, the TOTAL number of non-upgraded sensors on the 30 units = 30*1 = 30.
Upgraded/(Upgraded+Non-upgraded) = 5/(5+30) = 1/7.

The correct answer is D.

yes got 1/7 too

Thanks Mitch!

#s are your slaves.

smackmartine 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

OA after some discussion.

--- I think this one is from one of the Manhattan tests. I agree with you, OE seems to be long and confusing.

Just choose numbers and do the question.. Total upgraded 5/unit. So total not-upgraded sensor =1
No. of unit =30. This gives us the total of 30 units (non-upgraded) = 30
So our answer will be
5/(5+30) = 1/7

The explanation by MGMAT was quite confusing. There was no need for two variables. A little reasoning through these type of problems makes them go from level 700 to level 500. Here was my thought process. (I am sleepy, so I hope I typed this all in right).

-Might need to download picture to see it full sized.

nice and easy method..
i wasnt able to get the question.
thnks..

Anurag@Gurome wrote:

smackmartine 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?

Say, total number of upgraded sensor in the satellite is x.

Hence, number of non-upgraded sensors in each unit = 1/5 of x = x/5
Hence, number of non-upgraded sensors in the satellite, i.e. 30 units = 30*(x/5) = 6x

Hence, the required fraction = (Number of upgraded sensors)/(Total number of sensors) = x/(x + 6x) = 1/7

The correct answer is D.

You can also sort this out pretty neatly with a little word translation. It isn't as short and sweet as the other answers, but it seems easier for most people to cook up under time constraints.

Call x the number of upgraded sensors on each unit.
Call y the number of non-upgraded sensors on each unit.

"The number of non-upgraded sensors on each unit"
y

"is"
=

"1/5 the total number of upgraded sensors on the entire satellite"
1/5 * (30x)

So we have y = 1/5 * 30x, which simplifies to 5y = 30x. Now we just need the ratio of upgraded sensors to total sensors:

Upgraded/Total

= 30x / 30(x+y)
= 30x / (30x + 30y)

(then substitute 5y for 30x, since they're equal)

= 5y / (5y + 30y)
= 1/7