Problem Solving

Hey Guys,

Can you please help me understand the solution to this problem?

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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Answer

The problem tells us that the satellite is composed of 30 modular units, and there are sensors on each unit. Each unit contains the same number of non-upgraded sensors. We can use n to represent the number of sensors per unit that have not been upgraded. The problem also discusses the total number of upgraded sensors on the entire satellite; we can use u to represent this figure. The problem asks for the fraction of upgraded sensors on the entire satellite, u, among all sensors on the entire satellite, 30n + u. In other words, we want to find the fraction .

The problem tells us that the number of non-upgraded sensors on one unit, n, is 1/5 of the total number of upgraded sensors on the entire satellite, u. We can write this as a proportion and simplify:


5n = u

We can substitute this relationship into our original fraction:



This corresponds to answer choice D.

Alternately, we might consider using Smart Numbers. However, since there is a constraint in the problem (the total number of units is 30) and a specific relationship between the numbers (the number of non-upgraded sensors on each unit is 1/5 the total upgraded sensors on the satellite), it would be difficult to select Smart Numbers that work well.

The correct answer is D



I don't understand where they came up with 30n + u.. When I do this I would assume that N+U=30....

marshelle.slayton wrote:Hey Guys,

Can you please help me understand the solution to this problem?

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

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.

Thanks GMATGuruNY,

How I thought about it was based on the information given in the 3rd paragraph, 5/6 are upgraded and 1/6 are not on how ever many senors there are per unit.

I don't understand your third line item... Where in the question can we infer that? There is a satellite, it has 30 units, each of the units has some amount of sensors, of those 1/5 aren't upgraded. So upgraded units would be 5/6 (which was wrong).

I don't understand how you can add 30 units to 5? there are 30 total units as said in the problem statement so I guess I am confused by this calculation.. Where am I going wrong?