At RW Press, the advertising rate, a, is inversely proportional to the productivity measure, b, which, in turn, is inversely proportional to the labor cost, c. Is the labor cost at least 200 when the productivity measure is at least 100?

(1) When \(C\geq{100}\), \(B\geq{50}\)

(2) When \(C=100\), \(a=100\)

Until the OA is posted, this answer will be based on my own understanding, therefore susceptible to be incorrect.

The wording of this problem seems off to me. Anyway, let's solve this.

First of all, we need to understand and rephrase the problem.

We are told that the advetising rate "a" is inversely proportional to the productivity measure "b". Algebraically it means that there's a constant C such as : \(a=\frac{C}{b}\) (1)
Likewise, we are told that the productivity measure "b" is inversely proportional to the labor cost "c". Algebraically it means that there's a constant D such as : \(b = \frac{D}{c}\) (2)

So we're told that to see whether the labor cost is at least 200 when the productivity measure is at least 100. Meaning that we need to find the value of the constant D.

Statement 1 : when\(c >=100\) then \(b >=50\)

Using equation (2), we get : \(D = b*c\) which means that given the statement, \(D >= 5000\).
If we consider the lowest possible value of D, i.e 5000, we get for \(b >= 100\), \(\frac{D}{c} >= 100\), meaning that \(\frac{5000}{c} >=100\), therefore
\(c <= 50\).

Which means that the labor cost will be at most 50 when the productivity measure is at least 100 given \(D = 5000\). In fact the more D increases, the more c decreases. So statement 1 is sufficient.

Statement 2 : when \(c = 100\) then \(a = 100\)

Since a and c are not directly linked, then using both equations 1 & 2, we can find the link between the two variables :

We have : \(a=\frac{C}{b}\)
and \(b = \frac{D}{c}\)
Therefore, by putting b's expression in a, we get \(a = c*\frac{C}{D}\)

Since a = c, then we get C = D. And since there's no further information to be gained from this statement (remember that we're looking for D's value), then this statement is insufficient.

The final answer is A.

Hope that helped

At RW Press, the advertising rate, a, is inversely proportional to the productivity measure, b, which, in turn, is inversely proportional to the labor cost, c. Is the labor cost at least 200 when the productivity measure is at least 100?

(1) When c=>100, b=>50.

(2) When c=100, a=100.



---what I struggled with the question---

I think the correct choice should have been E because,

let's take c= 1000 and b=50, then if b= 100; c=500 that is greater than 200
let's take c= 100 and b=50, then if b= 100; c=50 that is less than 200, this inconsistency make the first stament insufficient.

Also, both together are not sufficient.

we are told that a=1/b, and b=1/c, or a=c.
B and D we can eliminate right away, because we are told the same information. C=100 while A=100.
Thus, it must be A, C, or E.
C is highly unlikely, as there is no much new information given
picked A...but confused with the terms used here...
i think it should be specified that big letters are constants..

Bunuel

Please help. Why is everyone plugging the value of C= 100 and b=50 for option A, we can try c=100000 and b=50. From this option A can be both true or false. NO?