BrainLab
Bunuel
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.
Hi Bunuel, can you recommend some similiar problems to solve, in order one can distinguish between such cases as here --> I've almost got trapped and solved it this way--- H=60% Low=40% etc.... , actually I've solved it this way, but didn't receive the correct answer and solved it another way 1,2x+x
In percentage questions, always notice what comes after "than" very carefully. The thing that comes after "than" is the base. So you need to take a percentage of the thing that comes after "than".
"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."
You are comparing the number of stocks that closed higher with the number of stocks that closed lower. The number of stocks that closed higher are 20% more than the number of stocks that closed lower. So if L stocks closed lower, 1.2L stocks closed higher.
If you did consider values 60 and 40, you should have verified them: is 60 20% more than 40? 60 is 20 more than 40. 20 is 50% of 40. So 60 is 50% more than 40, the base. Hence 60 and 40 are incorrect values.