p,q,r are distinct single digit no,such that
(10p+q)^2=110r+q
such that each side is greater than 310..ten what is the value of q?

• value of q is 1.
  p=2,q=1,r=4 => (10*2 +1)^2 = 110*4 +1 => 21^2 = 440 +1 => 441 = 441.
• 12 years agoHelpfull: Yes(71) No(11)
• So before going into the solution , let me tell you for this sum you have to open up your mind, your brains for sharper ways. Firstly without just getting into some calculation like squaring the left side and other stuffs… think a bit logically…
  Left Hand Side : Firstly look into 10*p .. p being any single digit.. the last digit will always come as 0.And if we add q to it.. the last digit of the resultant no. will be q only [q is single digit]
  Right Hand Side: 110*r so r being any single digit, 0 will be the last digit of the product. And if we add q the last digit will e q.
  
  Now see in the left side the last digit of the no. is q which is to be squared. And the resultant no. in the right side will have a last digit of the same number q only [RHS]
  Now think how many cases are there that you square a single digit no. and get the same digit back in the units place.
  Three cases possible 0,1 and 5 right?
  
  Case q=0 :
  Think fast. Left side is a square no. In right side 110r+0.. NO such single digit available for r such that 110r + 0 will be a perfect square [simple reason is 11 is a divisor of 110.. To become a perfect square there should be another 11 needed. But r varies from 0 to 9. So no chance]. So 0 dismissed
  
  Case q=5:
  Only one case possible if p=1 and r=2, then each side is 225 but its given each side is greater than 310, so 5 dismissed
  
  Case q=1:
  Its possible if p=2 and r=4, each side becomes 441.
  SO Q=1 …. ANS
• 7 years agoHelpfull: Yes(12) No(0)
• value of q is 1.
  p=2,q=1,r=4 => (10*2 +1)^2 = 110*4 +1 => 21^2 = 440 +1 => 441 = 441.
  
  value of q is 10 or 15
  p=2,q=1,r=4 => (10*2 +1)^2 = 110*4 +1 => 21^2 = 440 +1 => 441 = 441.
  p=2,q=15,r=11 => (10*2 +15)^2 = 110*11 +15 => 35^2 = 1210 +15 => 1225 =1225.
  
• 10 years agoHelpfull: Yes(3) No(2)
• leave this question
• 9 years agoHelpfull: Yes(3) No(1)
• (10p+q)^2=110r+q
  
  (pq)^2 =rrq
  
  21^2 = 441
• 8 years agoHelpfull: Yes(1) No(0)
• 2^9-1= 511 answer
• 10 years agoHelpfull: Yes(0) No(7)
• (10x2+1)^2=110x4+1
  
  q=1
• 10 years agoHelpfull: Yes(0) No(3)