The number of 2 digit numbers n such that 3 divides n-2 and 5 divides n-3 is
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As 3 divides n-2 and 5 divides n-3 15 should divide (n-2)× (n-3) = n² -5n +6
n² -5n + 6 should have 15 as a factor that is 15 , 30 ,45, 60 ...
substituting different values for n for n = 8 we get as 30
We can substitute different values for n and if the answer is divided by 15 the following criteria is satisfied.
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