Bunuel wrote:
Jennifer can buy watches at a price of B dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of T by selling N watches, then in terms of B and T and N, what is the percent of the markup from her buy price to her sell price?
A. 100T/(NB)
B. TB/(100N)
C. 100TN/B
D. ((T/N) – B)/(100B)
E. 100(T – NB)/N
Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTIONAlgebraic Solution: If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (T/N)/B *100 = 100T/(NB)
Answer = (A)
That Algebraic solution was elegant if you saw it, but if not, here’s a full solution with picking numbers.
Numerical Solution: The price of each watch, I will pick B = 7, a prime number. For the percent increase, I will make this easy. Picking 100% is too easy, and too predictable, so I am going to pick 400% — 400% of 7 is 28, and the $7 watches are marked up $25, then the selling price is $35. The profit per watch is $28, and so if she sells N = 11 watches (another prime number), that would be a profit of T = 28*11 = $308. Leaving T in unmultiplied form will make it easier to cancel.
OK, now we will plug in T = 308 = 11*28, N = 11, and B = 7, and hope to get 400 as our answer.
(A) 100T/(NB) = 100*11*28/(11*4) = 100*28/7 = 110*4 = 400 = works!
(B) TB/(100N) = 11*28*7/(100*11) = 28*7/100 = doesn’t work!
(C) 100TN/B = 100*11*28*11/7 = 100*11*4*11 = doesn’t work!
(D) ((T/N) – B)/(100B) = [(11*28/11) – 7]/(7*100) = (28 – 7)/(7*100) = 21/(7*100) = 3/100 = doesn’t work
(E) 100(T – NB)/N = 100(11*28 – 11*7)/7 = 100*11*21/7 = 100*11*3 = doesn’t work!
We were lucky here. With one choice of numbers, we were able to eliminate four answer choices, leaving (A) as the only possible answer.
- See more at:
https://magoosh.com/gmat/2014/gmat-pract ... QEkpA.dpuf