Problem Solving

sana.noor wrote:The s subjects in an experiment are divided into 4 groups: 3 test groups and a control. If each group is further divided into units consisting of u subjects each, with each unit assigned to a different researcher, how many researchers are assigned to units?
(A) s/u
(B) u/s
(C) 3s/u
(D) 4s/u
(E) 4u/s
A

The trick here is that you don't need the "4 groups" part at all.
Since "each unit is assigned to a different researcher", we just need to find the number of "units". To find that, the "breaking into four groups" step is unnecessary. (In fact, you can't use that step -- even if you want to -- because there's no information about the sizes of the groups. In particular, there are no grounds for assuming that the 4 groups contain equal numbers of subjects.)

Algebraically:
There are a total of s students.
So, if there are u students in each unit, then the total number of units is s/u. Done.

Pick your own numbers:
Let there be 100 subjects total, and let u = 5.
Then we're breaking 100 people into units of 5 people each, so that's 20 units.
Plug s = 100 and u = 5 into the choices: (A) 20, (B) less than 1, (C) 60, (D) 80, (E) less than 1.
So it's (a).

sana.noor wrote:The s subjects in an experiment are divided into 4 groups: 3 test groups and a control. If each group is further divided into units consisting of u subjects each, with each unit assigned to a different researcher, how many researchers are assigned to units?
(A) s/u
(B) u/s
(C) 3s/u
(D) 4s/u
(E) 4u/s

Since there are s people and there are 4 groups, each group has s/4 people. Since each group is divided into units consisting of u people each, we divide the number of people in each group by the number of people in each unit to get the number of units in each group:

(s/4)/u = s/(4u)

So, there are s/(4u) units in each group. However, we have 4 groups, so the total number of units is:

4 x s/(4u) = 4s/(4u) = s/u

Since each unit is assigned to a different researcher, we need s/u researchers.

Answer: A