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Thread: Crazy Clock Problem

  1. #1
    Super Member harpazo's Avatar
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    Crazy Clock Problem

    A certain clock marks every hour by striking a number of times equal to the hour and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the start of the first stroke and the end stroke is 22 seconds. At 12:00, how many seconds elapse between the start of the first stroke and the end of the last stroke?


    My Effort:

    At 6:00, the clock strikes 6 times and so each stroke is
    22/6 = 11/3 seconds.

    At 12:00, the clock strikes 12 times and so
    12(11/3) = 44 seconds...my answer.

    The book's answer is 46 seconds. What did I do wrong?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Crazy Clock Problem

    At 6:00 we have 11 intervals total (strokes and in between) and that took 22 seconds, so each interval is 2 seconds long. At 12:00 there are 23 intervals, and at 2 seconds each, this is 46 seconds.
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  3. #3
    Super Member harpazo's Avatar
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    Re: Crazy Clock Problem

    Quote Originally Posted by MarkFL View Post
    At 6:00 we have 11 intervals total (strokes and in between) and that took 22 seconds, so each interval is 2 seconds long. At 12:00 there are 23 intervals, and at 2 seconds each, this is 46 seconds.
    I could not make sense of this problem. I calculated without knowing my own steps. Can you believe this is a GMAT math problem on a TIMED TEST? I'm do glad I do not have to ever take this exam.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Crazy Clock Problem

    Quote Originally Posted by harpazo View Post
    I could not make sense of this problem. I calculated without knowing my own steps. Can you believe this is a GMAT math problem on a TIMED TEST? I'm do glad I do not have to ever take this exam.
    You really just have to observe that however many strokes of the bell there are, there is one less interval in between. So, the total number of intervals $\displaystyle I$ for $\displaystyle n$ strokes is:

    $\displaystyle I=n+n-1=2n-1$

    And so the total time $\displaystyle T$ for $\displaystyle I$ intervals each having duration $\displaystyle t$ is:

    $\displaystyle T=It=(2n-1)t$
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    Super Member harpazo's Avatar
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    Re: Crazy Clock Problem

    Quote Originally Posted by MarkFL View Post
    You really just have to observe that however many strokes of the bell there are, there is one less interval in between. So, the total number of intervals $\displaystyle I$ for $\displaystyle n$ strokes is:

    $\displaystyle I=n+n-1=2n-1$

    And so the total time $\displaystyle T$ for $\displaystyle I$ intervals each having duration $\displaystyle t$ is:

    $\displaystyle T=It=(2n-1)t$
    You are the best. You are truly gifted.
    Question: If you were planning to take the GMAT or GRE or SAT, what is the best way, in your opinion, to prepare for a timed test involving tough, tricky questions?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Crazy Clock Problem

    Quote Originally Posted by harpazo View Post
    You are the best. You are truly gifted.
    Question: If you were planning to take the GMAT or GRE or SAT, what is the best way, in your opinion, to prepare for a timed test involving tough, tricky questions?
    I would likely take a look at practice tests to see what type of questions are likely to be asked.
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  7. #7
    Super Member harpazo's Avatar
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    Re: Crazy Clock Problem

    Quote Originally Posted by MarkFL View Post
    I would likely take a look at practice tests to see what type of questions are likely to be asked.
    Is this what you did before taking the ASVAB? I scored 55 percent on the ASVAB in 1995. This score qualified me for Electrician's Mate A School at NTC, Great Lakes. MarkFL, I will be 54 in April. I can't believe that my youth and the Navy will never come again. It's hard for me to accept this reality. Life is like a passing shadow. Do you agree?
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    MHF Contributor MarkFL's Avatar
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    Re: Crazy Clock Problem

    Quote Originally Posted by harpazo View Post
    Is this what you did before taking the ASVAB? I scored 55 percent on the ASVAB in 1995. This score qualified me for Electrician's Mate A School at NTC, Great Lakes. MarkFL, I will be 54 in April. I can't believe that my youth and the Navy will never come again. It's hard for me to accept this reality. Life is like a passing shadow. Do you agree?
    The ASVAB was sprung on me...I had no idea I would be given a test on the day I took it, but I wasn't surprised by it either, I mean, that there would be some testing involved. The score you get isn't a percentage of correct answers, it is a percentile based score. Your score of 55 means you did better than 55% of those who had also taken the test.
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  9. #9
    Super Member harpazo's Avatar
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    Re: Crazy Clock Problem

    Quote Originally Posted by MarkFL View Post
    The ASVAB was sprung on me...I had no idea I would be given a test on the day I took it, but I wasn't surprised by it either, I mean, that there would be some testing involved. The score you get isn't a percentage of correct answers, it is a percentile based score. Your score of 55 means you did better than 55% of those who had also taken the test.
    I know that my ASVAB score did not mean 55 percent. It was never explained to me by the recruiters.
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