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

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

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New post 21 Oct 2014, 22:55
Total = 2420

Lets say stocks closing on higher = x

So, stocks closing lower = (2420-x)

Setting up the equation

\(x = \frac{120}{100} (2420-x)\)

x = 1320

Answer = D
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New post 27 Oct 2014, 14:52
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 clearly understood the explanations except the highlighted part. Wouldn't it be the stocks that closed higher today?
i.e.: 100% of stocks that closed lower today + 120% of stocks that closed higher today = 100% of stocks (2420)
Please let me know if I am missing something :)

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

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New post 11 Nov 2014, 04:49
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?

(A) 484
(B) 726
(C) 1,100
(D) 1,320
(E) 1,694

[Reveal] Spoiler:
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.


Correct me if this method is wrong, If the number of stocks offered at a higher price are 20% more than ones offered at a lower price then
Stocks offered at higher price : Stocks offered at lower price
60%:40%


Since 50% of stocks are [2420][/2] =1210
Closest answer is D



I used this method, I think it saves time. :)

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

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New post 06 Aug 2015, 00:46
Bunuel 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?

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

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New post 06 Aug 2015, 04:40
BrainLab wrote:
Bunuel 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?

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

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New post 06 Aug 2015, 06:24
VeritasPrepKarishma wrote:
BrainLab wrote:
Bunuel 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?

(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.


Hi Karishma, thanks a lot, this information was usefull... I've also breinstormed the solutio yesterday and have derived on the same solution
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Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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New post 21 Aug 2015, 02:29
Alternate Solution:

Assume Stocks closing at lower price today = 100
Therefore, stocks closing at higher price = 120
Total Stocks = 100+120 = 220
Total Stocks Higher Price
220 -------------------> 120
2420------------------> x

Cross Multiply: x=(2420*120)/220 = 1,320

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

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New post 21 Aug 2015, 04:02
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?

(A) 484
(B) 726
(C) 1,100
(D) 1,320
(E) 1,694

[Reveal] Spoiler:
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.


Let x be the number of stocks that closed at a higher price today, then the number of stocks that closed lower will be 2420-x (since all stocks closed at a different price).
so, x=1.2(2420-x)
2.2x=2904
x = 1320

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

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New post 20 Feb 2016, 05:21
I have used this method. Do you think is right?

Total stocks 2,420 which is approx. 2400.
2400/2= 1200
So, yesterday there was a sort of even situation where 1200 stocks closed at higher price and 1200 didn't.

Today, we know that the 20% of the stocks closed at higher price than stocks that closed at lower price --> so 20% of 1200= 240.
240+1200= 1440.
This number is closer to answer choice D. :)

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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?

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

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New post 22 Jul 2016, 00:26
Capricorn369 wrote:
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!



Hi! please help, i am missing on something very basic. Why are we doing 120/100? Shouldn't we do 20/100L=H, which will give H=0.2L

Thanks!

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

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New post 22 Jul 2016, 01:47
Bunuel wrote:
bytatia wrote:
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.


Hi Bunuel

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

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

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New post 22 Jul 2016, 02:49
rahulkashyap wrote:
Bunuel wrote:
bytatia wrote:
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.


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

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New post 09 Aug 2016, 04:02
Bunuel wrote:
squirecreamsicle wrote:
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.



Hey!

First statement:
Total=2420
If H=x, then L=2420-x

Second statement:
x = 20/100 (2420-x) + (2420-x)
which gives me x=330 :oops:

i didnt get the question i think.
Can anyone please help?

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

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New post 20 Aug 2016, 23:31
ashutoshsh wrote:
Bunuel wrote:
squirecreamsicle wrote:
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.



Hey!

First statement:
Total=2420
If H=x, then L=2420-x

Second statement:
x = 20/100 (2420-x) + (2420-x)
which gives me x=330 :oops:

i didnt get the question i think.
Can anyone please help?


If you solve your equation for x, it gives 1320 and not 330. Try solving again.

Hope this helps.

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

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New post 21 Aug 2016, 00:02
Hi,

Isn't the language of the question faulty?

The number of stocks that closed at a higher price today than yesterday - This could mean "the number of stocks that closed at a higher price today than the price yesterday (in which case the solution makes sense)" or it could also mean "the number of stocks closed at a higher price today than the number of stocks closed at a higher price yesterday"

I interpreted the sentence in the second way and started comparing the number of stocks closed at higher prices yesterday and the number of stocks closed at higher prices today. Can someone shed some light on this?

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

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New post 21 Aug 2016, 02:37
Akashkalra wrote:
Hi,

Isn't the language of the question faulty?

The number of stocks that closed at a higher price today than yesterday - This could mean "the number of stocks that closed at a higher price today than the price yesterday (in which case the solution makes sense)" or it could also mean "the number of stocks closed at a higher price today than the number of stocks closed at a higher price yesterday"

I interpreted the sentence in the second way and started comparing the number of stocks closed at higher prices yesterday and the number of stocks closed at higher prices today. Can someone shed some light on this?


This is where sentence correction "Comparison topic" comes into picture. We are comparing the prices of the two days and not the number of stocks.

Please go through the comparisons topic first and you will get the answer. :-D
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Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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New post 03 Oct 2016, 18:12
Madrigal wrote:
Thanks Bunuel, that makes sense of course, but still leads me to ask, how do you managed to do 2420/11 in your head?

do it on a paper. You will save time and will not make a silly mistake.
you can see that 242 is definitely a multiple of 11 as we have two twos and their sum in the middle. so it will be 242*10/ 11=22*11*10/11=220

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

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New post 09 Oct 2016, 13:38
I considered this as a ratio
Ratio split of High to Low = 1.2 : 1
Since this is a ratio and we know the total shares
1.2x + 1x = 2420
x = 1100, hence High shares = 1.2x =[1100 + (11+11)] = 1320
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Re: Yesterday's closing prices of 2,420 different stocks listed [#permalink]

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New post 10 Mar 2017, 21:56
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Let us assume
stocks closed at higher price = x
stocks closed at lower price = y
as per the question stem
=> x = y + 20% of y
=> x = 1.2y

Now total stocks => x+y = 2420
=> 1.2y + y =2420
=> y = 1100
But question stem has asked about value of x
=> x = 1320

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Re: Yesterday's closing prices of 2,420 different stocks listed   [#permalink] 10 Mar 2017, 21:56

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