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Thread: two questions about: Let x,y,z be distinct, non-zero, one-digit numbers.

  1. #1

    two questions about: Let x,y,z be distinct, non-zero, one-digit numbers.

    This simple problem is from a series of review problems:
    problem.jpg

    Here is the book's solution:
    solution.PNG

    Here is what I did:
    my solution.jpg

    Question 1) Where did the author get the 4? The two largest numbers are 5 and 7 and the difference can only be 2 or -2.

    Question 2) Is there a way to solve this problem using algebra? Or is that even expected here?

  2. #2
    Elite Member
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    Quote Originally Posted by allegansveritatem View Post
    This simple problem is from a series of review problems:
    problem.jpg

    Here is the book's solution:
    solution.PNG
    Here is what I did:
    my solution.jpg
    Question 1) Where did the author get the 4? The two largest numbers are 5 and 7 and the difference can only be 2 or -2.
    Question 2) Is there a way to solve this problem using algebra? Or is that even expected here?
    There are four one digit prime numbers: [tex]2,~3,~5,~\&~7[/tex]
    Read again carefully the wording. Then repost.
    [tex][/tex]
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

  3. #3
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    Quote Originally Posted by allegansveritatem View Post
    This simple problem is from a series of review problems:
    problem.jpg

    Here is the book's solution:
    solution.PNG

    Here is what I did:
    my solution.jpg

    Question 1) Where did the author get the 4? The two largest numbers are 5 and 7 and the difference can only be 2 or -2.

    Question 2) Is there a way to solve this problem using algebra? Or is that even expected here?
    This is not an algebra problem. I'd say it's just testing general reasoning skills.

    You can't assume the numbers are 2, 5, 7. What other possibilities are there for the three numbers?

  4. #4
    Quote Originally Posted by Dr.Peterson View Post
    This is not an algebra problem. I'd say it's just testing general reasoning skills.

    You can't assume the numbers are 2, 5, 7. What other possibilities are there for the three numbers?
    I'm afraid I ASSUMED that the two digits, the ones other than 2, had to be contiguous. Don't ask me why. I suppose it is because there is a category of word problem where we are asked to find contiguous even or odd digits that have such and such addends and/or subtrahends. A good motto when dealing with word problems: Assume nothing!

  5. #5
    Quote Originally Posted by pka View Post
    There are four one digit prime numbers: [tex]2,~3,~5,~\&~7[/tex]
    Read again carefully the wording. Then repost.
    [tex][/tex]
    I catch your drift. I assumed certain conditions that did not warrant assumption.

  6. #6
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    Quote Originally Posted by allegansveritatem View Post
    I catch your drift. I assumed certain conditions that did not warrant assumption.
    Each of the three numbers is prime & one is even.
    Thus the selection is [tex]\{2,3,5\},~\{2,3,7\},\text{ or }\{2,5,7\}[/tex]

    [tex]7-3=4,\text{ or }7-5=2[/tex]
    Last edited by pka; 12-06-2018 at 01:14 AM.
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

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