In[15]:= set = Range[90];
 
 In[16]:= n = 6; sum = 273;
 
 In[17]:= subsets = {};
 
 In[18]:= TimeConstrained[
  Do[
   For[
   try = RandomSample[set, n]; count = 1,
   Total[try] != sum,
   count++,
   try = RandomSample[set, n]
   ];
  subsets = Append[subsets, try];
  set = Complement[set, try];
  , {15}
  ],
30]

In[19]:= subsets

Out[19]= {{44, 72, 18, 74, 25, 40}, {60, 34, 42, 24, 68, 45}, {7, 41,
  27, 82, 36, 80}, {16, 47, 52, 66, 4, 88}, {53, 56, 89, 59, 3,
  13}, {29, 55, 54, 9, 50, 76}, {67, 37, 20, 78, 43, 28}, {10, 32, 49,
   69, 26, 87}, {51, 57, 38, 23, 31, 73}, {65, 6, 22, 46, 70,
  64}, {15, 71, 39, 58, 11, 79}, {75, 86, 2, 21, 8, 81}, {5, 33, 77,
  62, 84, 12}, {1, 61, 85, 90, 17, 19}, {63, 48, 83, 35, 30, 14}}