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Math Help - problem i need to solve

  1. #1
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    problem i need to solve

    The first digit of a 4 digit number is 7 and the last digit is 4. If the first and last digits are swapped, then the new number would be:
    a)made larger by 2997
    b)made smaller by 2997
    c)made larger by 3003
    d)not enough information
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by kl050196 View Post
    The first digit of a 4 digit number is 7 and the last digit is 4. If the first and last digits are swapped, then the new number would be:
    a)made larger by 2997
    b)made smaller by 2997
    c)made larger by 3003
    d)not enough information
    7xy4 = 7*10^3 + x*10^2 + y*10 + 4...............1

    4xy7 = 4*10^3 + x*10^2 + y*10 +7...................2

    1-2

    = 3*10^3 -3

    = 2997
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  3. #3
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    Hello, kl050196!

    The first digit of a four- digit number is 7 and the last digit is 4.
    If the first and last digits are swapped, then the new number would be:

    (a) made larger by 2997
    (b) made smaller by 2997
    (c) made larger by 3003
    (d) not enough information
    Set up the subtraction problem . . .


    The number has the form: . 7\,a\,b\,4

    The new number would be: . 4\,a\,b\,7

    Obviously, the number becomes smaller . . . Eliminate choices (a) and (c).


    Then we have: . \begin{array}{ccccc}& 7 & a & b & 4 \\ - & 4 & a & b & 7 \\  \hline<br />
& ? & ? & ? & ?<br />
 \end{array}

    The last (rightmost) digit is 7.
    The next digit is 9 . . .
    [Think about it!]
    The next digit is 9.
    And the leftmost digit is 2.

    The difference is 2997 . . . answer (b).

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