A pharmacy offers customers both a patented and a generic version of a

Question

A pharmacy offers customers both a patented and a generic version of a certain drug. The pharmacy makes a profit of 20 percent of the cost on every box of the patented version, and it makes a profit of 5 percent of the cost on every box of the generic version. During a certain time period, which version of the drug yields a greater dollar profit to the pharmacy?

(1) The pharmacy pays more to the wholesaler per box for the patented version than for the generic version.

(2) The pharmacy sells 30 percent more of the generic version of the drug by weight than the patented version.

logro · Answer

Let's first break down the question stem and come up with the equations

Let the cost per box of the patented drug be Cp and of the generic version be Cg
Let the number of boxes of patented drug be Np and of generic version be Ng

We need to find which drug yield higher dollar value

Dollar profit on Patented drug = % profit per box * cost per box * no. of boxes

= 20% * Cp * Np

Dollar profit on Generic drug = % profit per box * cost per box * no. of boxes

= 5% * Cg * Ng

Statement 1:

Given that Cp > Cg

If we have Np> Ng then the patented box will result in higher dollar profit than generic

But if we have Np < Ng such that generic version may result in higher dollar profit

Hence Statement 1 alone is insufficient

Statement 2:

Let the weight of the drugs be Wp and Wg respectively

Given that Wg = (1+30%)*Wp 
In other words Wg = 1.3Wp

Wg = Ng * weight per box of the generic version
Wp = Np * weight per box of the patented version

We don't know the weight per box to be able to establish a relationship between Ng and Np

hence Statement 2 is insufficient

Combining Statement 1 and 2

The problem still persists with the unknown weight per box to establish relationship between Ng and Np

Hence IMO it is E

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

sanjitscorps18 · Answer

Let the number of boxes of patented version = p
Let the number of boxes of generic version = q

Let the cost of boxes of patented version = a
Let the cost of boxes of generic version = b

Profit on patented drugs = 0.2*pa
Profit on patented drugs = 0.05*qb

Question is whether 0.2*pa < 0.05*qb or vice versa

(1) The pharmacy pays more to the wholesaler per box for the patented version than for the generic version.
This statement informs about the variance between the purchase prices of the patented box vs the generic box
No concrete data is provided hence  Insufficient

(2) The pharmacy sells 30 percent more of the generic version of the drug by weight than the patented version.
Although we get a value of 30% morer by weight of patented vs the generic, the profit earned by the pharmacy is  per box  and not weight hence this is also  insufficient

Even together we dont get any information about which could provide more profit to the pharmacy

Option E

A pharmacy offers customers both a patented and a generic version of a

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A pharmacy offers customers both a patented and a generic version of a

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