1. How many two digit numbers are divisible by 3 but not by 7 ?
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By: anil on 05 May 2019 02.27 am
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, $$l=a+(n-1)d$$ => $$12+(n-1)(3)=99$$ => $$(n-1) imes3=99-12=87$$ => $$n-1=frac{87}{3}=29$$ => $$n=29+1=30$$ Similarly, two digit numbers divisible by L.C.M. (3,7) = 21 are : 21, 42, 63, 84 = 4 numbers
$$ herefore$$ Two digit numbers are divisible by 3 but not by 7 = $$30-4=26$$ => Ans - (B)
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$$ herefore$$ Two digit numbers are divisible by 3 but not by 7 = $$30-4=26$$ => Ans - (B)