Problem Solving

Mike@Magoosh wrote:A vendor sells only Product A, for $6, and Product B, for $21. If Q% of the products sold are Product B, and if T% of the total revenue comes from sales of Product B, find Q in terms of T.

I received a PM requesting that I comment.

Each A = $6, while each B = $21.
To make the math easier, let the total revenue yielded by each product = the LCM of the two prices = 42.
Since each A = $6, $42 will be yielded by product A if the number of A sold = 7.
Since each B = $21, $42 will be yielded by product B if the number of B sold = 2.

T% of the total revenue comes from sales of Product B.
Since product A and product B each yield the same amount of revenue -- $42 -- each product yields HALF the total revenue.
Thus, T = 50.

Q% of the products sold are Product B.
Since 2 of product B are sold, while 7 of product A are sold -- for a total of 9 units -- we get:
B/total * 100 = (2/9) * 100 = 200/9.

The question stem asks for the value of Q: 200/9.
This is our target.
Now plug T= 50 into the answers to see which yields our target of 200/9.
Only D works:
(40T)/(140 - T) = (40*50)/(140-50) = 2000/90 = 200/9.

The correct answer is D.

This problem appears quite closely modeled on a famous official problem about newspaper revenue that can be found here:

https://www.beatthegmat.com/newspapers-a-b-t30515.html

If anyone is keen to practice the topic, that problem would be a good follow-up.