Can You Solve This Logic Puzzle? -

Can You Solve This Logic Puzzle?

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This is from a sample paper for the Online Mathematics Challenge 2020.



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  1. 3+5= 16( 3×5 + 1)
    4+7 = 30( 4×7 + 2)
    1+1= 4 ( 1×1 + 3)

  2. 3a + 5b + c = 16
    3(3a + 5b + c) = 3×16
    9a + 15b + 3c = 48 (1)
    4a + 7b + c = 30
    2(4a + 7b + c) = 2×30
    8a + 14b + 2c = 60 (2)
    Subtract (2) from (1)

  3. I interpreted it as (3×5) + 1=16
    (4×7) + 2=30
    Therefore 1+1 is (1×1) +3=4

    Though the solution was awesome 😎😘 and great 👍🏼👌🏼✌️😃

  4. there's a pattern.

    3 and 5 make 16
    4 and 7 make 30

    the first integer goes up by 1 and the second integer goes up by 2. the equated number goes up by 14

    therefore 1 and 1 make -12

  5. First approaches that came into my head:

    (3*2) + (5*2) = 16
    (4*4) + (7*2) = 30
    (1*6 or 8) + (1*2) = 8 or 10
    ^ It could also be (1*2) + (1*2) by following the pattern *x-1, *x, *x+1
    For the first number.

    (3*5)+1 = 16
    (4*7)+2 = 30
    (1*1)+3 = 4

    The answer was interesting though.

  6. what's the need of that +c…? you cold just treat it like xa+yb and from it you get a= -38 and b= 26, and so 1*-38+1*26=-12

  7. 3 x 5 = 15, plus 1 = 16
    4 x 7 = 28, plus 2 = 30
    1 x 1 = 1, plus 3 = 5
    I know I bent the rules a bit, but seeing as your numbers don't add up to your answers, I can assume that the addition signs can be messed around with as well. (I hope)

  8. Seems to me like people are taking all kinds of liberties with the meaning of "+".

  9. I am very disappointed at this solution. Actually it is just a logical puzzle and does not require any profound algebraic methodology. The correct answers as per the two samples is ZERO. By adding 1 to the first number and multiplying it to the number you get after deducting 1 from the second number. Check it out please. It was not expected of you Sir…. Regarda

  10. Did anyone point out, the problem is only soluble because the left-hand sides 3a+5b+c, 4a+7b+c and a+b+c are linearly dependent. This is because the determinant of the 3×3 coefficient matrix is zero. Given that, we know there will be a nulling vector (A,B,1) such that A(3a+5b+c)+B(4a+7b+c)+(a+b+c)=0 regardless of a, b and c. Thus 3A+4B+1=0, 5A+7B+1=0, A+B+1=0. Solve any two of these for A=-3, B=2. Then 16A+30B+x=0, x=48-60=-12.

  11. wait why do yo0u suddenly multiply the second equation by -5!? That's a huge leap I don't understand

  12. 3+5 =/= 16
    4+7 =/= 30
    So therefore,
    1+1 = 2

  13. We can just take c=0 as a, b and c are any real numbers that add upto a certain real number(-12 in this case) and we will get the same answer ; )

  14. We have 2 equation on our hands therefore we must have 2 unknowns. So we must eliminate the c. Eliminate it then you'll find a+2b is 14. Multiply by 4 and you'll see 4a+8b is just one more b away from second equation. Work on that you'll find b. Rest is history. Did in my mind.

  15. 3 ( square of first number + 2* Second number)

  16. From the thumbnail, thought the rule was:

    a + b = (a+1)(b-1), giving
    1 + 1 = 2(0) = 0

    Obviously then I realised the video had a question itself nothing to do with this

  17. Sir I don't understood why you multiple with 5🤔🤔🤔😒

  18. Correct answer is 0.
    Let x be the first number and y the second number.
    The formula to find the correct answer would then be xy+x-2.
    Note that this formula satisfies both the given equations.
    So the answer is 1*1+1-2=0

  19. The way this man solves these problems,he can never pass a competitive exam
    Where you have to solve 100 ques. In 2 hrs.

  20. I set the equation 3x+5y=16 and 4x+7y=30 and got the same answer.

  21. I think at least three clues are needed to get a single function.

  22. why did you choose -5 out of all other numbers?

  23. I did
    And solved for a and b
    And got a+b=-12

  24. Do you really have to do such hard math to just solve 1 logic reasoning riddle?

  25. Because/explanation/logical reasoning

    ([3×5]=15+1) so
    ([4×7]=28+2) so

  26. The reason these puzzles are given with 3 or more statements because there are infinite possibilities what ans will come depending upon nature of the polynomial… Here you did with a linear function which is not mentioned in the question… Anyother person can try in a quadratic form or even xy+c form..

  27. (4a+7b+c)-(3a+5b+c)=30-16
    That is equal to a+2b=14
    And since 3a+5b+c=16
    Then (3a+5b+c)-(2*(a+2b))=16-(2*14)
    Which is equal to
    Therefore 1©1=-12
    I solved it this way 🙃

  28. Afterall you can just build a simple system with 3 equations, and the result is a=14 b=0 and c=-26

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