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Arithmetic Percents

This topic has 4 expert replies and 8 member replies
michbuk Newbie | Next Rank: 10 Posts Default Avatar
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Arithmetic Percents

Post Sun Aug 26, 2012 4:30 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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    adthedaddy Master | Next Rank: 500 Posts
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    Post Sun Aug 26, 2012 4:59 am
    Let x be the number of stocks that closed at the lower price today.
    Stocks that closed at a higer price are 20% greater than the lower priced stocks i.e. 1.2x

    Thus, total stocks = x + 1.2x = 2420
    => 2.2x = 2420
    => x = 1100

    We need to find the higher priced stocks i.e. 1.2x = 1.2(1100) = 1320

    Ans: Option (D)

    Post Sun Aug 26, 2012 7:14 am
    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
    We can use the process of elimination (POE) to solve this question quickly.

    There are 2420 stocks in total, so the answer cannot be E, since 2694 is greater than 2420.

    Next, if the number of stocks that increased in price were EQUAL to the number of stocks that decreased in price, then the correct answer would equal 1210 (exactly half of 2420).
    However, the number of stocks that increased in price was NOT EQUAL to the number of stocks that decreased in price. The number of stocks that increased in price IS GREATER THAN the number of stocks that decreased in price.
    So, the correct answer must be greater than 1210.
    Since only D is greater than 1210 (and since we already eliminated E), the correct answer must be D

    Cheers,
    Brent

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    vijaykondepudi Newbie | Next Rank: 10 Posts Default Avatar
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    Post Sat Dec 29, 2012 9:36 pm
    When I first read the question, it confused me a lot. Especially the Bold face portion in the following lines:

    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.

    This mislead me to compare the number of stocks that closed higher between yesterday and today.

    What does the "than yesterday" part mean ? The question is much simpler, if we omit the "than yesterday" portion.

    Sapana Senior | Next Rank: 100 Posts
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    Post Tue Jan 01, 2013 9:45 am
    the language bugged me too.. What is the source of this question?

    Param800 Senior | Next Rank: 100 Posts Default Avatar
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    Post Tue Jan 01, 2013 2:29 pm
    Sapana this the question from the OG 13. Q. 71, pg 162

    Sapana wrote:
    the language bugged me too.. What is the source of this question?

    vijaykondepudi Newbie | Next Rank: 10 Posts Default Avatar
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    Post Tue Jan 01, 2013 10:04 pm
    Am I reading too much into the question or is it the way it's usually written ?

    Definitely the language is confusing. Could some experts/Native speakers comment ..

    Thank You !![/quote]

    sana.noor Legendary Member Default Avatar
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    Post Wed Jan 02, 2013 6:08 am
    Brent Could u please lend me your Brain till my gmat actual test...you are simply awesome..
    here is my explanation
    let "100x" be the number of stocks closed at lower price
    the stocks that are closed at higher price is 20% of 100x...thus we can write that stock closed at higher price is = 1.2(100x)= 120X
    now we can write an equation as "stock closed at lower price + stock closed at higher price = total number of stocks" = 100x +120x = 2420 = 220x = 2420 = x= 11
    now we wana find the number of stocks closed at higher price, x = 11= 120x = 120(11) = 1320 answer is D..

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    Last edited by sana.noor on Wed Jan 02, 2013 10:06 am; edited 2 times in total

    Post Wed Jan 02, 2013 8:16 am
    sana.noor wrote:
    Brent Could u please lend me your mind till my gmat actual test...you are simply awesome..
    here is my explanation
    let "100x" be the number of stocks closed at lower price
    the stocks that are closed at higher price is 20% of 100x...thus we can write that stock closed at higher price is = .2(100x)= 120X
    now we can write an equation as "stock closed at lower price + stock closed at higher price = total number of stocks" = 100x +120x = 2420 = 220x = 2420 = x= 11
    now we wana find the number of stocks closed at higher price, x = 11= 120x = 120(11) = 1320 answer is D..
    That looks almost perfect!
    The only issue is what looks to be a typo (above in green)
    To calculate a 20% increase, we must take 100x and multiply it by 1.2 (not 0.2)
    Your calculations are correct, I just wanted to mention this in case others were trying to follow along.

    Cheers,
    Brent

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    sana.noor Legendary Member Default Avatar
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    Post Wed Jan 02, 2013 10:09 am
    thanks Brent

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    gmattesttaker2 Legendary Member Default Avatar
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    Post Sat Apr 20, 2013 7:35 pm
    Hello,

    I was trying to solve this problems as follows:

    L = No. of stocks that closed at a lower price today than yesterday
    H = No. of stocks that closed at a higher price today than yesterday

    So, H = 1.20L

    L + H = L + 1.20L = 2.20L

    2.20L = 2420

    So L = 1100

    H = 1.20L = 1.20(1100) = 1320

    OA: D


    However, I still had the following questions:

    1) Here we add L and H. Could there be stocks that might have closed at the same price today and yesterday?

    2) "Yesterday's closing prices of 2420 different stocks listed on a certain stock exchange were all different from today's closing prices." - Do we really need this entire sentence since we are not using it anywhere? We just take 2420 out of it.

    Thanks for your help.

    Best Regards,
    Sri

    Post Tue Jun 23, 2015 3:37 pm
    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.

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    Post Tue Jun 23, 2015 5:49 pm
    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
    Seems like the easiest approach is

    x = # that closed higher
    y = # that closed lower

    x + y = 2420

    and

    x = 1.2y

    That gives us (1.2y) + y = 2420, or y = 1100. x = 2420 - 1100, or 1320, and we're done!

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