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Math Help - Mental calculation

  1. #1
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    Mental calculation

    Find the digit represented by ? in the following problem: 37? 35 = 13090. No calculators, please.
    Last edited by Sigyn3; October 7th 2009 at 06:10 AM. Reason: Typo
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  2. #2
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    Quote Originally Posted by Sigyn3 View Post
    Find the digit is represented by ? in the following problem: 37? 35 = 13090. No calculators, please.
    37? * 7 * 5 = 13090

    37? * 7 = twice 13090/10 = twice 1309 = 2618 (easy w/o calculator)

    only 4 * 7 possible: 2[8], 261[8]

    So red? = 4
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  3. #3
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    Thanks Wilmer. Your method is much better than the one I had in mind!
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  4. #4
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    Hello, Sigyn3!

    Find the digit is represented by {\color{red}?} in the following problem: . 37{\color{red}?} \times 35 \:=\: 13,\!090.
    No calculators, please.
    I did it "mentally", but then my brain is cluttered with various trivia . . .


    I saw that: . 37 \times 35 \:=\:(36+1)(36-1) \:=\:36^1 - 1^2 \:=\:1296 - 1 \:=\:1295

    . . So that: . 370 \times 35 \:=\:12,\!950 . . . which is 140 short of 13,090

    . . Hence, we need four more 35's.


    Therefore: , 37{\color{red}4} \times 35 \:=\:13,\!090

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