Asked on 25th may 2014 in elitmus

Q. Find then sum of numbers between 1 to 200 which when divided by either 5 or 7 leaves remainder of 2?

• 6341
  
  Number which leaves remainder 2, when divided by 5 are 7,12,17,22,....,197
  So 197=7+(n-1)5, n=39,Sum of these numbers=(39/2)[2*7+38*5]=3978
  Similarly,
  Number which leaves remainder 2, when divided by 7 are 9,16,23,30,.....,198
  So 198=9+(n-1)7, n=28,Sum of these numbers=(28/2)[2*9+27*7]=2898
  
  As above both the sum includes some common numbers 37,72,107,142,177
  we have to subtract once,the sum of these common numbers(=535),to find the sum of all the numbers
  So Sum of all the numbers=3978+2898-535= 6341
  
• 10 years agoHelpfull: Yes(68) No(15)
• everything @devendra m has done is right but he forgot to include 2.so answer is 6343 not 6341
• 10 years agoHelpfull: Yes(46) No(6)
• numbers when divided by 5 leaves a reminder 2 is 2,7,12.....197 (total 40nos) and the sum is (197+2/2)*40=3980;
  numbers when divided by 7 leaves a reminder 2 is 2,9,16.....198 (total 29nos) and the sum is (198+2/2)*29=2900;
  numbers when divided by 5&7 ie 35 leaves a reminder 2 is 2,37,.....177 (total 6nos) and the sum is (177+2/2)*6=537;
  ie sum=3980+2900-537=6343
  
• 10 years agoHelpfull: Yes(45) No(2)
• TAKING LCM OF(5,7)=35 HENCE NUMBER WILL BE MULTIPLE OF 35 AND ADDING 2 AT THE END.
  FIRST NUMBER=35+2=37
  2ND- 72;
  3rd-107 , 142, 177. adding all this we get ans = 535
• 10 years agoHelpfull: Yes(13) No(4)
• Numbers leaving remainder 2 when divided by 7:
  2 9 16 23.....198
  
  using a+(n-1)d=198
  2+(n-1)7=198
  n=29
  Sn= na+d(n)(n-1)/2
  29*2+7*29*28/2
  2900
  
  
  
  Numbers leaving remainder 2 when divided by 5:
  7 12 17 22......197
  
  using a+(n-1)d=197
  7+(n-1)5=197
  n=39
  
  Sn=na+d*n*(n-1)/2
  39*7 + 5*38*39/2
  =3978
  
  total =3978+2900=6878
• 10 years agoHelpfull: Yes(3) No(6)
• MANIKANDAN I. common numbers means the numbers which give reminder =2 when divided by both 7 and 5...when u are calculating the total sum, these get added twice so u have to subtract their sum once
• 10 years agoHelpfull: Yes(1) No(0)
• hai devendra, i can't understand "common numbers 37,72,107,142,177
  we have to subtract once,the sum of these common numbers(=535"
• 10 years agoHelpfull: Yes(0) No(3)
• hey devendra and ashes i guess if the answer is 6341 or 6343 then when dividing by 7 and 5 we will not get the remainder as 2
• 10 years agoHelpfull: Yes(0) No(1)