1. How many numbers are there from 700 to 950 (including both) which are neither divisible by 3 nor by 7?
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By: anil on 05 May 2019 01.47 am
Total numbers between 700 to 950 = $$950-700+1=251$$ ----------(i) Numbers between 700 to 950 which are divisible by 3 = 702,705,708,.........,948 This is an AP with first term $$a=702$$ and common difference $$d=3$$ Last term of AP = $$a+(n-1)d$$ => $$702+(n-1)3=948$$ => $$(n-1)3=948-702=246$$ => $$(n-1)=frac{246}{3}=82$$ => $$n=82+1=83$$ -------------(ii) Similarly, numbers between 700 to 950 which are divisible by 7 = 700,707,714,.........,945 => $$700+(n-1)3=945$$ => $$(n-1)7=945-700=245$$ => $$(n-1)=frac{245}{7}=35$$ => $$n=35+1=36$$ -------------(iii) Now, numbers which are divisible by L.C.M.(3,7) = 21 are : 714,735,756,......,945 Similarly, $$n=12$$ ----------(iv) $$ herefore$$ Numbers between 700 to 950 which are not divisible by 3 or 7 = $$251-83-36+12=144$$ => Ans - (C)
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