A group of students is to be divided into some rows such that all the rows have an equal number of students. When 7 students are put in each row, 3 students are left; when 8 students are put in each row, 5 students are left; and when 9 students are put in each row, 7 students are left. If 12 students are put in each row, then how many students will be left?

• @ Iqbal, Pls check.
  If 13 students are left, then 12 can be placed in another row and only 1 student will be left.
• 12 years agoHelpfull: Yes(4) No(0)
• 1
  
  there are 493 students
  
  7x+3= 8y+5= 9z+7 = p*q
  
  
  
• 12 years agoHelpfull: Yes(2) No(0)
• when divided by 7, 3 reminder=(-4)reminder
  when divided by 8, 5 reminder=(-3)reminder
  when divided by 9, 7 reminder=(-2) reminder
  similarly,
  when divided by 10=(-1) reminder
  when divided by 11=(0) reminder
  when divided by 12=(1) reminder
• 12 years agoHelpfull: Yes(2) No(1)
• 13 students will be left .
  
  Number of students Number of students are
  are putting in a row left
  
  7 3
  8 5
  9 7
  10 9
  11 11
  12 13
  
  
  
• 12 years agoHelpfull: Yes(1) No(1)
• 13 students will be left .
  for 7,8,9,10,11,12 students putting in a row correspondingly
  3,5,7, 9,11,13 students will be left.
• 12 years agoHelpfull: Yes(0) No(2)
• # Thanks Garima,
  You are right 1 student will be left
  But till now i am little bit confused so ,can you give the full solution of this puzzle from the starting........
• 12 years agoHelpfull: Yes(0) No(0)