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mikemcgarry
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.

(A) \(1501T - 15T^2\)

(B) \(\frac{15T}{615 - 6T}\)

(C) \(\frac{21T}{621 - 6T}\)

(D) \(\frac{40T}{140 - T}\)

(E) \(\frac{60T}{160 - T}\)


For the OE on this problem, and more practice Word Problems, see:
https://magoosh.com/gmat/2014/gmat-prac ... -problems/

Mike :-)
Let toatal number of product A=A and product B=B
total no. of products sold=(A+B)
total revenue= 6A+21B
As per stem
Q%(A+B)=B -------(a)
T%(6A+21B)=21B-------(b)
from(b) we get
6AT+21BT=2100B
B=6AT/(2100-21T)----(c)
from (a)
QA+QB=100B
B=QA/(100-Q)----(d)
equating (c)&(d)
2100Q-21QT=600T-6QT
Q(2100-15T)=600T
Q=600T/(2100-15T)
dividing by 15 to num. & denom.
Q=40T/(140-T)
Ans D
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These questions always throw me for a loop, but picking smart numbers works best for me. Granted, this STILL took me 4 minutes:

If we buy 2 of each product, Q = 50%, and T = 42/54, or 7/9, or 77% (let's round this to 80% and save ourselves the headache).

I begin plugging in for each answer choice:

A: 1501(80) - 15(80)^2 = 1501(80) - 15(640)...no way this is 50!

B: 15(80) / 615-6(80) = ~1000 / ~200...no way this is 50!

C: 21(80) / 621-6(80) = ~1600/ ~140...no way this is 50!

D: 40(80) / 140-(80) = ~3200 / 60 ... A little over 50, THIS SEEMS PRETTY CLOSE!

E: 60(80) / 160-(80) = ~4800 / 80 ... ~60, this is definitely close too, but D is closest!

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Let Total products Sold = 100

Let Q=60%
Number of B sold = 60

Therefore, Number of A sold = 40
Total Revenue = 40(6) + 60(21) = 1500
T% = 60(21)/1500% = 84%

Use the above values in options, find Q
Answer D
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