How many two digit numbers are divisible by 3 but not by 7 ?

Two digit numbers divisible by 3 are : 12, 15, 18, ......., 96, 99

The above series follows an A.P. with first term $$a=12$$, common difference $$d=3$$ and last term $$l=99$$. Let number of terms be $$n$$

Thus, $$l=a+(n-1)d$$

=> $$12+(n-1)(3)=99$$

=> $$(n-1)\times3=99-12=87$$

=> $$n-1=\frac{87}{3}=29$$

=> $$n=29+1=30$$

Similarly, two digit numbers divisible by L.C.M. (3,7) = 21 are : 21, 42, 63, 84 = 4 numbers

$$\therefore$$ Two digit numbers are divisible by 3 but not by 7 = $$30-4=26$$

=> Ans - (B)