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
The OG’s solution for this is pretty straightforward with the exception of the final calculation. I’ll just sort that out real quick before moving on to the most efficient way to solve this problem.
\(n = \frac{2,420}{2.2} = \frac{24,200}{22} = \frac{{2}\times{12,100}}{{2}\times{11}} = \frac{{121}\times{100}}{11} = {11}\times{100} = 1100\)
This is the way to avoid long division – factor, cancel, factor, cancel…
Anyway, how should we really solve this problem?
Let’s approximate. What would happen is the stocks split evenly – half closing higher and half closing lower. If that were the case, then the number of stocks that close higher would be 1,210. Because we know that the number of stocks that close higher is greater than the number that close lower, the answer must be greater than 1, 210. Consequently, A, B, and C are out. Now I just need to test D or E. I’ll go with the latter. Let’s round 1,694 to 1700. If 1700 stocks closed higher, then 2420 – 1700 = 720 stocks closed lower. Clearly, 1700 is more than 100% greater than 720 (it’s more than double), so E is out.
The correct answer is D.