The equation 11x + 67y = 133 has

1. two integral solutions for 0 < x < 50
2. no integral solutions for 10 < y < 20
3. an integral solution for 100 < x < 200
4. no integral solutions for y < 0

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      1. Abhishek Tandon

        Raman Sir,
        While solving again I got it where I went wrong. Please correct me if I am wrong.
        I tried this way

        (x,y):……..(-61,12), (6,1), (6+67,1-11),….
        (x,y): (6,1), (73,-10), (130,-21), (197,-32)…..

        From above values I eliminated options
        Option 1: eliminated because there is only one integral solution in that x range

        Option2: eliminated because for y=12 x=-61 hence it is in range so there is an integral solution

        Option 3: satisfying because there are 2 integral solutions in that range

        Option 4: eliminated because there are many integral solutions for y<0

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