let p,q,r,s,t be consecutive positive integers such that q+r+s is a perfect square & p+q+r+s+t is a perfect cube.find smallest possible value of r.

Option
(a) 575
(b) 675
(c) 125
(d) 725

• 675
  
  As q+r+s=3r which should be a square.
  so r should be multiple of 3.
  only 675 satisfies this condition from given options.
  Further check
  q+r+s=3r= 3*675= 9*225 = (3*15)^2
  p+q+r+s+t=5r = 5*675 = 125*27= (5*3)^3
• 11 years agoHelpfull: Yes(6) No(1)