Consider the sum of first 100 odd numbers. If every digit 7 is replaced by 2 what would be net decrease in sum and the new sum ?

• sum of n odd numbers=n^2
  sum of 100 odd nos=100^2=10000
  if 7 is replaced by 2. within 100 (7,17,27,37,47,57,67,71,73,75,77,79,87,97)
  sum decreases by(-5-5-5-5-5-5-5-5-5-50-50-50-50-50=-295
  for 100 terms which is upto 299 sum decreases by -590 new sum=10000-590=9410
• 12 years agoHelpfull: Yes(2) No(5)
• ans : 915
  no of odd number = 1 - 199 t = a + (n-1)d = 199 = 1 + (n-1)2 ;n=100
  if 7 replaced by 2 in units place = 1-70 & 80 -170 & 180 -199 = 81 * -5 = -405
  tens place 71,73,75,77,79 occurs 2 times=(-50*3)- 55 -50 =-255*2 = -510
  total = -915( it is the difference )
• 11 years agoHelpfull: Yes(1) No(1)
• Sum of first n numbers is 2n-1. s(n)=n^2.
  
  For 1-100, sum of odd numbers ranges from 1-99.
  2n-1=99;
  n=50.
  n^2=2500.
  If 7 is replaced by 2, the values that has 7 are- 7,17,27,37,47,57,67,70,77,87,97.
  
  .:. 2 x 11=22.
  
  The net decrease in sum is 22 and the new sum is 2500-22 => 2478
• 10 years agoHelpfull: Yes(1) No(1)
• 602.........
• 11 years agoHelpfull: Yes(0) No(1)
• Sum of first n numbers is 2n-1. s(n)=n^2.
  
  For 1-100, sum of odd numbers ranges from 1-99.
  2n-1=99;
  n=50.
  n^2=2500.
  If 7 is replaced by 2, the values that has 7 are- 7,17,27,37,47,57,67,70,77,87,97.
  
  .:. 2 x 11=22.
  
  The net decrease in sum is 22 and the new sum is 2500-22 => 2478
• 10 years agoHelpfull: Yes(0) No(2)