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Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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14 Sep 2012, 22:18

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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?

Folks, please write the answer with all the steps. The answer is clear cut but the only thing I'm interested in is the interpretation of the word problem and the respective approach to solve it. Thanks. If any body used tabular approach, i will be glad to see it because i had trouble solving this problem with the same.

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.

Re: Yesterday's closing prices of 2420different stocks listed on [#permalink]

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15 Sep 2012, 01:18

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conty911 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 than yesterday was 20% greater than number that closed at lower price.How many of the stocks closed at a higher price than yesterday?

a)484 b)726 c)1100 d)1320 e)1694

Source :OG-13; Q71(PS)

Folks, please write the answer with all the steps. The answer is clear cut but the only thing I'm interested in is the interpretation of the word problem and the respective approach to solve it. Thanks. If any body used tabular approach, i will be glad to see it because i had trouble solving this problem with the same.

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

Re: Yesterday's closing prices of 2420different stocks listed on [#permalink]

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14 Sep 2012, 23:36

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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!
_________________

----------------------------------------------------------------------------------------- What you do TODAY is important because you're exchanging a day of your life for it! -----------------------------------------------------------------------------------------

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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04 May 2013, 15:15

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Can someone please help....The way this problem has been solved is correct...I arrived upon the same answer by the process of elimination but when I initially tired I used the following technique:

Total percentage of stocks = 100% All stocks changed value....therefore H + L = 100 Given that 20% stocks closed higher than those that closed lower hence H - L = 20

Hence 60% of the 2420 closed higher which gives me 1452....this was not part of the answer choice ...so I eliminated and chose 1320...but I am still confused why this thought process is wrong...

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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04 May 2013, 17:42

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tsnarendran wrote:

dave785 wrote:

tsnarendran wrote:

Can someone please help....The way this problem has been solved is correct...I arrived upon the same answer by the process of elimination but when I initially tired I used the following technique:

Total percentage of stocks = 100% All stocks changed value....therefore H + L = 100 Given that 20% stocks closed higher than those that closed lower hence H - L = 20

Hence 60% of the 2420 closed higher which gives me 1452....this was not part of the answer choice ...so I eliminated and chose 1320...but I am still confused why this thought process is wrong...

Can someone please clarify...

Naren

The correct ratio is closer to 55% - 45% not 60% - 40%

The 20% isn't based off of the total amount of stocks, it's based off of the amount that closed higher vs those that closed lower... so rather than there being a difference of 20% of the TOTAL (60-40) there's a difference of 20% of each position which is closer to only 10% of the total.

When you say that the 20% is based off of the amount that closed higher vs that closed lower.....did all stocks not change value??..so 100% changed values right? so 20% of 100% right...am sorry...I am usually not this confused...but here I am....I am waiting for that ahaa moment I guess and it all becomes clear...

any help is greatly appreciated...

the question states that there are 20% more stocks that closed higher today than stocks that closed lower today.

Stocks cannot close both higher and lower. Therefore the 20% increase is not based off of the total amount, only off of the amount that closed higher...

Therefore, (100% stocks that closed lower tody ) + (120% stocks that closed lowertoday) = 100% of ALL stocks (2420)

You're reading the question as if it read 20% more stocks closed higher today than closed higher yesterday... in which case the answer would be unsolvable because we don't know how many closed higher yesterday.

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.

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

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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04 May 2013, 15:43

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tsnarendran wrote:

Can someone please help....The way this problem has been solved is correct...I arrived upon the same answer by the process of elimination but when I initially tired I used the following technique:

Total percentage of stocks = 100% All stocks changed value....therefore H + L = 100 Given that 20% stocks closed higher than those that closed lower hence H - L = 20

Hence 60% of the 2420 closed higher which gives me 1452....this was not part of the answer choice ...so I eliminated and chose 1320...but I am still confused why this thought process is wrong...

Can someone please clarify...

Naren

The correct ratio is closer to 55% - 45% not 60% - 40%

The 20% isn't based off of the total amount of stocks, it's based off of the amount that closed higher vs those that closed lower... so rather than there being a difference of 20% of the TOTAL (60-40) there's a difference of 20% of each position which is closer to only 10% of the total.

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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04 May 2013, 16:03

1

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dave785 wrote:

tsnarendran wrote:

Can someone please help....The way this problem has been solved is correct...I arrived upon the same answer by the process of elimination but when I initially tired I used the following technique:

Total percentage of stocks = 100% All stocks changed value....therefore H + L = 100 Given that 20% stocks closed higher than those that closed lower hence H - L = 20

Hence 60% of the 2420 closed higher which gives me 1452....this was not part of the answer choice ...so I eliminated and chose 1320...but I am still confused why this thought process is wrong...

Can someone please clarify...

Naren

The correct ratio is closer to 55% - 45% not 60% - 40%

The 20% isn't based off of the total amount of stocks, it's based off of the amount that closed higher vs those that closed lower... so rather than there being a difference of 20% of the TOTAL (60-40) there's a difference of 20% of each position which is closer to only 10% of the total.

When you say that the 20% is based off of the amount that closed higher vs that closed lower.....did all stocks not change value??..so 100% changed values right? so 20% of 100% right...am sorry...I am usually not this confused...but here I am....I am waiting for that ahaa moment I guess and it all becomes clear...

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

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.
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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21 Sep 2012, 10:38

Let number of shares closed at lower price be x. Hence closed at higher price is 1.2 (this is 20% greater than closed at lower price). x+1.2x = 2420 => x = 1100 Hence shares closed at higher price = 1.2x = 1320 (D)

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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21 Feb 2014, 16:06

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.

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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06 Jun 2014, 17:49

tsnarendran wrote:

Can someone please help....The way this problem has been solved is correct...I arrived upon the same answer by the process of elimination but when I initially tired I used the following technique:

Total percentage of stocks = 100% All stocks changed value....therefore H + L = 100 Given that 20% stocks closed higher than those that closed lower hence H - L = 20

Hence 60% of the 2420 closed higher which gives me 1452....this was not part of the answer choice ...so I eliminated and chose 1320...but I am still confused why this thought process is wrong...

Can someone please clarify...

Naren

dave785 wrote:

the question states that there are 20% more stocks that closed higher today than stocks that closed lower today.

Stocks cannot close both higher and lower. Therefore the 20% increase is not based off of the total amount, only off of the amount that closed higher...

Therefore, (100% stocks that closed lower tody ) + (120% stocks that closed lowertoday) = 100% of ALL stocks (2420)

You're reading the question as if it read 20% more stocks closed higher today than closed higher yesterday... in which case the answer would be unsolvable because we don't know how many closed higher yesterday.

I just made the same mental error, so I just wanted to thank tsnarendran for asking, and dave785 for answering! (Kudos given, of course.)

Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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21 Jul 2014, 07:47

Surprised no one approached option route. Obviously the solution has to greater than 50% of the total (those who went above yesterday). And only option- D can be 20% greater than Total-Ans.

Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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11 Sep 2014, 03:43

conty911 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?

Folks, please write the answer with all the steps. The answer is clear cut but the only thing I'm interested in is the interpretation of the word problem and the respective approach to solve it. Thanks. If any body used tabular approach, i will be glad to see it because i had trouble solving this problem with the same.

convoluted thing...

let x part be higher price 2420-x be the lower price.

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