Yesterday's closing prices of 2,420 different stocks listed

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.
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No. of share closed at higher price than yesterday = X
No. of share closed at lower price than yesterday = Y
X = 1.2Y
so,
1.2Y + Y = 2420
Y = 1100

So, X = 1320

Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 2420 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)

Solve eq (1) & (2) to get H = 1320.
D is my answer.

Questions, Pls let me know. Cheers!
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Can someone please explain how to get 1.2x? Where does 1.2 come from/ how do you calculate that??

We are told that "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".

20 percent greater is 1.2 times as many. So, if \(x\) 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.

Hope it's clear.
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I'm having a huge problem understanding the solution for some reason. I do not understand why 1.2x+x=2420

So there are 2 420 stocks. Yesterday X were sold at lower price and Y and higher price.

So today I know that stocks sold at a higher price are 20 percent more than stocks sold at a lower price yesterday. Which would indeed give me 1.2X but! Don't I need to have another unknown? 1.2X + z = 2 420. as Z would represent number of stocks sold at higher price today. So I do not see why we get 1.2x + x as we did not use X for today's number of stocks sold at lower price.

I must be missing the important point. If someone could explain I'd be very thankful.

There are total of 2,420 stocks, out of them the number of stocks that closed at a higher price than yesterday was 20% greater than number that closed at lower price.

Say \(x\) is the number of stocks that closed at a lower price TODAY, then \(1.2x\) is the number of stocks that closed at a higher price TODAY. Since the total number of stocks is 2,420, then \(x+1.2x=2,420\) --> \(x=1,100\), so \(1.2x=1,320\).

Hope it's clear.
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Can I ask how people quickly divide 2420/2.2 in their head?

\(2.2x = 2,420\);

\(\frac{11}{5}x=2,420\);

\(x= \frac{2,420*5}{11}=220*5=1,100\).
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Thanks Bunuel, that makes sense of course, but still leads me to ask, how do you managed to do 2420/11 in your head?

Sometimes you have to do actual math...
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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.

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.
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Hi Bunuel

arent we assuming that there were no stocks whose price remained constant over the 2 days?

Read the first sentence of the stem: Yesterday's closing prices of 2420 different stocks listed on a certain stock exchange were all different from today's closing prices.
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Hi all,

X = Higher Price

Y = Lower Price

X is 20% greater than Y => X = 1.2Y . This first thought is straightforward. I got it.

BUT, [ X is 20% greater than Y ] is equivalent to [ Y is 20% less than X ]

So, Y = 0.8X. This second thought will give a different answer.

Kindly clarify why the second thought, Y = 0.8X, is wrong.

Many thanks.

If X is 20% greater than Y, it is not the same as Y is 20% less than X.
Note that the base is different in the two cases.

When you say "X is 20% greater than Y", the base is Y
X = Y + 20% of Y
X is 20% greater than Y
Say Y = 100
X = 100 + 20% of 100 = 120

When you say Y is 20% less than X, the base is X
Y = X - 20% of X
Y is 20% less than X
Say Y = 100
100 = X - 20% of X
100 = 0.8X
X = 125

Note that the value of X in the two cases is different.

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