michbuk wrote:Yesterday's closing prices of 2420 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% 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. 1100
d. 1320
e. 2694
Solution:
Although this problem may seem wordy, it is actually a pretty basic word problem. We are asked to determine the number of stocks that closed at a higher price today than yesterday.
Initially, we are given that there are 2,420 different stocks. It follows that the TOTAL NUMBER of stocks is 2,420. We are also given that the number of stocks that closed at a higher price today than yesterday was 20% greater than the number that closed at a lower price. Let’s define two variables and then create two equations using those variables. We can say:
H = number of stocks that closed at a higher price today than yesterday
L = number of stocks that closed at a lower price today than yesterday
With these two variables we can create two equations:
1) H + L = 2,420
2) H = 1.2L
We can now substitute 1.2L, from equation 2, for H in equation 1. So we have:
1.2L + L = 2,420
2.2L = 2,420
22L = 24,200
L = 24,200/22
L = 1,100
Since we are solving for variable H, we can plug 1,100 for L, in equation 1.
H + 1,100 = 2,420
H = 1,320
Answer:
D
Note: Be careful of the trap in the answer choices. Notice that 1,100 was actually an answer choice. Arguably, it was put there for you to jump on, after getting 1,100 for variable L. Partial answers and answers that represent values other than the one you are being asked to find are common trap GMAT answers; don’t fall for them.
Additionally, if you were running out of time and had to use a guessing strategy, there is an interesting pattern to look at as far as these answer choices go. The method I’ll describe can be used in many cases in which we are given a TOTAL value in a word problem. With this problem, we are first given that the total number of stocks in question is 2,420. If we look at our answer choices, we will find two sets of answers that, when summed, equal 2,420.
a. 484
b. 726
c. 1100
d. 1320
e. 1694
Notice that:
answer c + answer d = 1,100 + 1,320 = 2,420
and
answer b + answer e = 726 + 1,694 = 2,420
So at a bare minimum we can consider eliminating choice A because there is a slim likelihood that it is going to be the correct answer. So now we are down to 4 choices. We are also told that the number of stocks that closed at a higher price today was 20% greater than the number that closed at a lower price. This means that the value we are trying to determine, THE HIGHER PRICE, is greater than the lower price. So when we look at our two pairs of answer choices, we know the correct answer has to be the higher of the two numbers in each pair, so either 1,320 or 1,694 will be correct. Finally, we see that 1,320 is less than twice 1,110, but 1,694 is more than twice 726. However, the problem says that the higher price is only 20% greater than the lower price. Since the higher price is less than twice the lower price, the answer must be 1,320.
To be clear, the guessing tip is just that – a guessing tip. It’s far better to work a problem out in the most straightforward way possible, and leave this type of guessing for a time when you truly need it.
