If the integers m and n are chosen at random between 1 and 100, then the probability that 7m +7n is divisible by 5 is

If the integers m and n are chosen at random between 1 and 100, then the probability that 7m +7n is divisible by 5 is

  1. A

    14

  2. B

    17

  3. C

    18

  4. D

    149

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    Solution:

    71=7,72=49,73=343,74=2401

     For each value of m in {1,2,3,,100} there are
    25 values of n as follows

    (1,3),(1,7),(1,11),,(1,99)(2,4),(2,8),(2,12),,(2,100)(3,1),(3,5),(3,9),,(3,97)

    (4,2),(4,6),(4,10),,(4,98) etc.

     Required probability =100×25100×100=14

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