M is a set of even numbers from 1 to 23 and odd numbers from 24 to 100. Find no. of zeroes in the sum of all values in the set.

• We have to find no of occurrence of 5.
  10-1. 35-1. 65-1. 95-1
  20-1. 45-1. 75-2
  25-2. 55-1. 85-1
  Total 12
• 9 years agoHelpfull: Yes(13) No(4)
• 12
  let's count
  all even no b/w 1-23
  2,4,6,8,10,12,14,16,18,20,22
  
  all odd no. B/w 24-100
  25,27,29.……99
  
  now
  from even we have 10 And 20 Multiple of 5 as 5*2,5*4
  
  and from odd no. We have
  25=5*5
  35=5*7
  45=5*9
  55=5*11
  65=5*13
  75=5*15=5*5*3
  85=5*17
  95=5*19
  
  now count the no. of 5 i.e.12
• 9 years agoHelpfull: Yes(13) No(3)
• 1+3+5+......+(2n-1) =n^2
  
  2+4+6+.....+2n = n(n+1)
  
  from 1 to 23 sum of even numbers is 2+4+6+...2(11)=11*12===>132
  
  
  from 24 to 100 sum of odd numbers is 25+26+...2*50 - 1= n^2- sum of odd numbers from 1 to 23
  
  50^2- 12^2
  
  =2356
  
  sum of even numbers from 1 to 23 + sum of odd numbers from 24 to 100
  
  = 132+2356
  
  =2488
  
  number of zeros in this sum 2488/5 + quotient/5+....+ until the quotient not divisible by 5
  
  2488/5 + 499/5 + 95/5 +19/5 +3
  
  =616 number of zeros in the set M
• 9 years agoHelpfull: Yes(7) No(6)
• i think 12 was the answer and the question was multiple of all set.
  
• 9 years agoHelpfull: Yes(5) No(1)
• i don't get the given solutions as in the question it is asked the no. of zeroes in "sum of all values" in the set why only 5 ,2+8 will also give zero and so on ,i think first we have to add all the values then count no. of zeroes
  
• 9 years agoHelpfull: Yes(3) No(0)
• @ Umabandekar good solution but you did a calculaion mistake....
  2488/5=497
  497/5=99
  99/5=19
  19/5=3
  
  so the no os zeros in total sum is 497+99+19+3=600 is d answer...
• 9 years agoHelpfull: Yes(2) No(0)
• if you solve according to question given here the solution is 0 zeroes cuz when you add all the numbers
  2+4+6......+97+99 = 2488
  if question is find number if zeroes in multiplication of set then , 2^19 * 5 ^12 so 12 zeroes.
• 9 years agoHelpfull: Yes(1) No(0)
• 1 to 23 .. 2,4,6,8,10,12,14,16,18,20,22..
  
  and 24 to 100 .. 25,.......35,..45..55..65..75....85..95
  
  
  8zero and 10 , 20 two zeros also .. so ans. will be is 10
  
• 9 years agoHelpfull: Yes(0) No(9)