Put one digit before 15 and one digit after 15 and find out how many such numbers are divisible by 15

• for a no to be divisible by 15 it should be divisible by both 3 and 5 bcoz dese are its prime factors.
  A no could be divisible by 5 if it has 5 or 0 at the unit place.
  So we can put only 5 or 0 at the unit place i.e. after 15
  1)If we have put 5 then for a no to be divisible by 3 the sum of digits should be divisible by 3
  so possible cases are
  1+1+5+5=12,so we can put 1,similarly at thousand place we can put,4,7
  So total possible cases when 5 is at unit place are 3.
  2)When 0 is at unit place
  Then we can put 3,6,9 at thousand place to make it divisible by 15.
  Hence total cases and total nos divisible by 15 are 6
  1155,4155,7155,3150,6150,9150.
• 10 years agoHelpfull: Yes(26) No(2)
• ans. 7
  case 1: unit digit is 5 then we have 3 cases with 4,7,1 at thousands place
  case2: unit digit is 0 then we have 4 cases with 3,6,9,0 at thousands place
  hence total of 7 cases
  
• 10 years agoHelpfull: Yes(4) No(1)
• answer is 7.
  numbers are 1155, 4155, 5155, 3150, 6150, 7150, 9150
• 10 years agoHelpfull: Yes(2) No(8)
• Let us assume the number is x15y
  This is divisible by 3 and 5.
  As the number is divisible by 5 y should be either 0 or 5
  As the number is divisible by 3 the sum of digits should be divisible by 3
  x+1+5+y= x+y+6 is divisible by 3
  Let us say x+y+6=3n
  x+y=3n-6
  =3(n-2)-----------------(1)
  Case 1: y=0
  Substituting in (1) we get x= 3(n-2)
  n=3 x=3
  n=4 x=6
  n=5 x=9
  n=6 x=12 not possible as x is supposed to have only one digit
  The only possible one digit values of x satisfying this equation are 3, 6 and 9
  The possible nos are 3150,5150,9150
  
  Case 2:y=5
  substituting in (1) we get x=3n-11
  when n=4,x=1;
  n=5,x=4;
  n=6,x=7
  n=7,x=10 not possible as x is supposed to have only one digit.
  So the possible values of nos are 1155, 4155, 7155
  So we get totally 6 possible nos 1155, 4155, 7155, 3150, 5150, 9150
  
  
• 10 years agoHelpfull: Yes(1) No(1)
• @shubhangi why can't use the number 0150 b'cos its not given the no. must be 4 digit
• 10 years agoHelpfull: Yes(1) No(0)
• 0150
  3150
  6150
  9150
  1155
  4155
  7155
• 10 years agoHelpfull: Yes(1) No(1)
• 5 as 315, 615, 915, 155, 150
• 10 years agoHelpfull: Yes(0) No(7)
• No to be divisible by 15-should be divisible by both 3 and 5.
  A no could be divisible by 5 if it has 5 or 0 at the unit place.
  So we can put only 5 or 0 at the unit place
  1)If we have put 5 then for a no to be divisible by 3 the sum of digits should be divisible by 3
  so possible cases are
  1+1+5+5=12,so we can put 1,similarly at thousand place we can put,4,7
  So total possible cases when 5 is at unit place are 3.
  2)When 0 is at unit place
  Then we can put 0,3,6,9 at thousand place to make it divisible by 15.
  Hence total cases and total nos divisible by 15 are 7
  1155,4155,7155,0150,3150,6150,9150.
  
  
  
• 10 years agoHelpfull: Yes(0) No(0)