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Let A= n [100,700] N : n is neither a multiple of 3 nor a multiple of 4 . Then the number of elements in A is

Options

  1. A290
  2. B280
  3. C300
  4. D310

Correct answer

C. 300

Step-by-step solution

aligned & n (3) multiple of 3 & 102,105,108, . ., 699 & ~T _ n =699=102+( n -1)(3) & n =200 & n (3)=200 & n (4) multiple of 4 aligned aligned & 100,104,108, ., 700 & T_n=700=100+(n-1)(4) & n=151 & n(4)=151 & n(3 4) multiple of 3 & 4 both & 108,120,132, ., 696 & T_n=696=108+(n-1)(12) & n=50 & n(3 4)=50 & n(3 4)=n(3)+n(4)-n(3 4) & =200+151-50 & =301 & n( 3 4 )= Total -n(3 4)= neither a multiple & of 3 nor a multiple of 4 & =601-301=300 aligned

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