Sequence And Series Question 495
Question: The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is
[MP PET 2000]
Options:
A) 2489
B) 4735
C) 2317
D) 2632
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ S=1+2+3+………..+100 $ $ =\frac{100}{2}(1+100)=50(101)=5050 $ Let $ S_1=3+6+9+12+………+99 $ = $ 3(1+2+3+4+………+33) $ = $ 3.\frac{33}{2}(1+33)=99\times 17=1683 $ Let $ S_2=5+10+15+……..+100 $ = $ 5(1+2+3+……..+20) $ = $ 5.\frac{20}{2}(1+20)=50\times 21=1050 $ Let $ S_3=15+30+45+……..+90 $ = $ 15(1+2+3+……..+6) $ = $ 15.\frac{6}{2}(1+6)=45\times 7=315 $ \ Required sum = $ S-S_1-S_2+S_3 $ = $ 5050-1683-1050+315 $ = 2632.
BETA
