The questions asks which option is FALSE.
So let's make sure of what the statement says:
In 1975, 35 percent of state W's workforce was employed in manufacturing jobs. That percentage dropped in each following year until in 1982 it reached 25 percent.
This statement tells us that from the total amount of jobs from W, the percentage that represents manufacturing jobs was reduced.
But how to represent this percentage?
In this way: \(\frac{Manufacturing jobs*100}{total jobs}\)
But to make it easy we'll just use this fraction: \(\frac{Manufacturing jobs}{total jobs}\)
The statement is clear: This fraction, that is proportional to the percentage, can't increase.
Let's analyze the options,

(A) The number of people in the workforce increased, while the number of people employed in manufacturing jobs decreased.
\(\frac{Manufacturing jobs}{total jobs}\)
In this case, you just need to know fractions fundamentals, if the numerator of a fraction decrease, the new one will always have less value, and adding
the fact that denominator of this new fraction is increasing, the reduction will be greater, so OPTION TOTALLY AGREES WITH THE STATEMENT:
TRUE,DISCARDED

(B) The number of people in the workforce decreased, while the number of people employed in manufacturing jobs increased.
\(\frac{Manufacturing jobs}{total jobs}\)
In this case, fraction theory says that if the denominator of a fraction (total amount of jobs) decreases, the new one will always have a greater value.
Also, adding the fact that numerator of the new fraction is increasing, the increment will be greater; that means that percentage will increase,and as a
consequence OPTION TOTALLY DISAGREES WITH THE STATEMENT: FALSE, RIGHT ANSWER

Now that we got the right one, we don't need to keep analyzing. Answer: B