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Thread: Expectals

  1. #1
    Mar 2010


    I was given a problem on a ACT Prep course site that involved something called expectals. I've never heard of these before and I was hoping someone could either give me a break down of what to do to answer this problems or point me in the right direction to figure out how to work more problems like it. <- This is a link to a thread with the exact problem I was given. The problems are worked out but i don't fully understand what was done to get the answer. [It's the second question] Your help will be greatly appreciated. Thank you!
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  2. #2
    MHF Contributor

    Apr 2005
    The real point of the problem is to test your ability to read definitions- the problem defines "expectal", it is not a standard mathematics term.

    "Let the expectal(x) be defined for all x as the smallest prime number that is greater than x/2"

    To find the "expectal" of x, find "x/2", that is divide x by 2, then determine the smallest prime number larger than that.

    That is exactly what was said in the thread you link to!

    For example to find expectal(7), divide 7 by 2 to get 7/2= 3.5. A prime must be an integer so check integers- 4 is larger than 3.5 but is not a prime. 5 is larger than 3.5 and is a prime. It is the smallest prime larger than 7/2: expectal(7)= 5.

    expectal(14)= 11 because 14/2= 7. 7 itself is a prime but is not "larger than 7". 8, 9, and 10 are not primes but 11 is. 11 is the smallest prime larger than 14/2= 7.

    As I said initially, the point of this problem is to test your ability to understand that definition- basically to test your ability to follow directions!
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