%%

The sum of integers from 1 to 100 that are divisible by 2 or 5 is :

JEE · Math · previous-year question

  1. A.3000
  2. B.3050correct
  3. C.3600
  4. D.3250

Answer

B. 3050

Explanation

According to this question, any number between 1 to 100 should be divisible by 2 or 5 but not by 2$$ \times $$5 = 10. Possible numbers between 1 to 100 divisible by 2 are 2, 4, 6, .... , 100 This is an A.P where first term = 2, last term = 100 and total terms = 50. $$ \therefore $$ Sum of the numbers divisible by 2 = $${{50} \over 2}\left[ {2 + 100} \right]$$ = 25$$ \times $$102 = 2550 Possible numbers between 1 to 100 divisible by 5 are 5, 10, 15, .... , 100 $$ \therefore $$ Sum of the numbers divisible by 5 = $${{20} \over 2}\left[ {5 + 100} \right]$$ = 10$$ \times $$105 = 1050 And possible numbers between 1 to 100 divisible by 10 are 10, 20, 30, .... , 100 $$ \therefore $$ Sum of the numbers divisible by 10 = $${{10} \over 2}\left[ {10 + 100} \right]$$ = 5$$ \times $$110 = 550 $$ \therefore $$ Required sum = 2550 + 1050 - 550 = 3050

Practice more JEE questions

Answer thousands more real JEE previous-year questions free, get graded instantly, and climb the global ranked leaderboard.

Practice JEE free →

More JEE Math questions