If a*b*c = 2700. (a, b, c are positive non zero). Is square root a an integer?

I. b is a perfect cube and c is an odd perfect square.
II. square root of c is not an integer.

Options: Data Suffeciency

• Only 1st is required.
  2700=2^2 * 3^3 * 5^2
  b is perfect cube so b=27
  c is odd perfect square so c=25
  and hence a should be known
• 7 years agoHelpfull: Yes(3) No(9)
• statement 1 says
  'b' is a perfect cube . now by seeing 27 on the rhs you can say that b is 27. which is 3^3 . now lets try to see what can be possible value of c and a . 'c' can be either 1^2 or 5^2 . if 'c' is 5 then a is 2^2 which contradicts the 1st condition. so we know now 'c' is 1. if 'c' is 1 it means 'a' is 10^2.
  hence sufficient.
  
  statement 2 says
  
  square root c is not an integer . since 'c' can be either 25 or 1 . it is clear with this condition that c cant be 25. hence 'c' is 1 and 'a' is 10^2. so sqaure root 'a' is 10. hence sufficient.
• 7 years agoHelpfull: Yes(0) No(1)
• ans - none
  2700 = 5^2 *3^3 * 2^2
  1. b= 1 = perfect cube
  c = 25 = odd perfect square
  a = 3^3 * 2^2. square root a is not a integer.
  2.
• 5 years agoHelpfull: Yes(0) No(0)
• The question can be answered by either of the statements a or b
• 5 years agoHelpfull: Yes(0) No(0)