data sufficiency :two spheres are melted to form a combined sphere x. Find the diameter of x.
St 1)the radius of 2nd sphere was given
St2) the weight of sphere 1 is 8 kg and sphere 2 is 10 kg and they are made of same material

• General Info:
  4*pi*r1 ^3 /3 + 4*pi*r2 ^3 /3 =4*pi*rc ^3 /3.................................(1)
  
  s1) 4 pi (r2) ^3 /3 =m/d (density = mass/volume) ........(2)
  here we need value of m and d to get the value of r2 ..But these values are not available so not possible to find r2.. Thus we can not find x as at least two variable values are required to solve equation of three variable ...(1) alone not possible
  
  s2)m1/d + m2/d = mc/d ----> 8/d + 10/d = mc/d -------> mc=18 ........(3)
  
  also for combined sphere:
  4*pi*rc ^3 /3 = mc/d...... here we need value of d to find rc so alone not possible
  
  Now s1 + s2:
  for 2nd sphere ----> 4*pi*r2^3 /3 = m/d ----> 4*pi*r2^3 /3 = 10/d.....(4) now r2 value is given so find d.
  
  fOR COMBINED SPHERE:
  4*pi*rc^3 /3 = m/d------>4*pi*rc^3 /3 = 18/d----> putting the value of d from equation (4) rc value can be calculated.
• 8 years agoHelpfull: Yes(2) No(1)
• As we know the resultant sphere was made by mixing of the two spheres.So the volume of sphere x is sum of the volume of the both sphere.
  i.e r1^3+r2^3=x^3 ------------------------------------------(1)
  now according to the statement one:
  its given the radius of the 2nd sphere but i dont know the value of r1.so from eq 1 i get different value of x as i change the value of r1
  so statement 1 is insufficient
  i know the weight will be same after mixing both the spheres because both the sphere are of the same material
  so the weight of x=18=4/3(pir^3) from here i can find the value of r and also the diameter.thus it gives a unique value for the diameter,
  so statement 2 alone is sufficent.
• 2 years agoHelpfull: Yes(1) No(0)