Find the largest 4-digitnumber, which gives the remainder 7 and 13 when divided by 11 and 17?

• LCM of 11 and 17 is 187
  when divided by 11 remainder 7,so difference 4
  when devided by 17 remainder 13,so difference 4
  Largest no exactly devide by 11 & 17=9911(because 9999/187=quotient53 and remainder 88
  so 9999-88=9911)
  the no is 9911-4=9907
  
  ans=9907
• 8 years agoHelpfull: Yes(40) No(0)
• let N be such number satisfying given conditions
  i.e. N = 11a + 7 where a is any whole number
  &N = 17b + 13 where b is any whole number
  Here remainder is not same but the difference between the remainder and the divisor is same i.e. 11-7 =17-13=4
  Hence N must be of the form
  N=(LCM of 11, 17) p – 4where p is any whole number
  Since LCM of 11 and 17 is 187so the number must be in the form
  N=187 p – 4
  The largest value of “p” possible so that the N remains 4-digit number is 53.
  Therefore, 187p= 187 x 53=9911.
  Hence the largest 4-digitnumber, which gives the remainder 7 and 13 when divided by 11 and 17, is 9907.
• 8 years agoHelpfull: Yes(3) No(0)
• 9992
  solving 9999/11=909 so 9999-9=9992
• 8 years agoHelpfull: Yes(0) No(13)
• it will be 9907.
  
• 8 years agoHelpfull: Yes(0) No(1)
• l.c.m of two num is 187
  remainder diff is 4
  so 9911 s exactly divisble by 187
  to get 4 has we should add 4 not sub
  so the ans is 9911+4=9914
  
• 8 years agoHelpfull: Yes(0) No(5)