Bunuel wrote:
Yesterday's closing prices of 2,420 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
(A) 484
(B) 726
(C) 1,100
(D) 1,320
(E) 1,694
APPROACH #1:
Say \(x\) is the number of stocks that closed at a lower price, then \(1.2x\) is the number of stocks that closed at a higher price. Since the total number of stocks is 2,420, then \(x+1.2x=2,420\) --> \(x=1,100\), so \(1.2x=1,320\).
Answer: D.
APPROACH #2:
If the number of stocks that closed at a lower price were the same as the number of stocks that closed at a higher price, then the number of stocks that closed at a higher price would be 2,420/2=1,210. Since we know that more stocks closed at a higher price than at a lower price than the answer must be greater than 1,210: eliminate A, B, and C. Now, E cannot be correct, because in this case 1,694 closed at a higher price and ~700 closed at a lower price, but 1,694 is obviously not 20% greater than ~700, so we are left with D.
Answer: D.
Hope it's clear.
Keeping the second approach in mind, we get the higher value = lower value = 1,210. Now since Higher value is 1.2 of lower value why can't we conclude that the higher value is 1.2 of 1,210? Since 1,210 is the lower value we should be able to find 20% of this and add it up to get the higher value