Sequence And Series Question 412
Question: The sum of integers from 1 to 100 that are divisible by 2 or 5 is
[IIT 1984]
Options:
A) 3000
B) 3050
C) 4050
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
The sum of integers from 1 to 100 that are divisible by 2 or 5 = sum of series divisible by 2 + sum of series divisible by 5 - sum of series divisible by 2 and 5. $ =(2+4+6+……+100)+(5+10+15…….+100) $ $ -(10+20+30+……..+100) $ $ =\frac{50}{2}{ 2\times 2+(50-1)2 }+\frac{20}{2}{ 2\times 5+(20-1)5 } $ $ -\frac{10}{2}{ 10\times 2+(10-1)10 } $ $ =2550+1050-550=3050 $ .
BETA
