exchange economy numerical

[PRACHI 214]

can someone please tell me how to solve this i am getting option d as my answer but right answer is optio c .
A and B live in an exchange economy. There are two
goods X and Y . utility functions of A and B are  
U of A(x, y) = x + y and
U of B(x, y) = x^2+y^2
, respectively. A’s endowment is 2 units of X and 1 unit
of Y , while B’s endowment is 1 unit of X and 2 units of Y . Consider the
following allocations
Allocation 1: A gets 1.5 units of X and zero unit of Y , B gets 1.5 units of X and 3 units of Y
Allocation 2: A gets 1.5 units of X and 1.5 unit of Y , B gets 1.5 units of X
and 1.5 units of Y
(a) Both the allocations are Pareto optimal
(b) None of the allocations is Pareto optimal
(c) Only allocation 1 is Pareto optimal
(d) Only allocation 2 is Pareto optimal

[Rayee]

Plot A and B's preference in an Edgeworth box. A's ICs are downward sloping straight lines, B's ICs are concave from B's POV. Clearly, there will be corner solution. Locate the first and second allocations, you will realize that only in the first allocation it is not possible to make some one better off without making the other worse off.

[Batman!]

Hey Rayee!
You’re smart. :-)

[Rayee]

Thanks batman, the joker told me the answer, he is studying exchange economy these days :-)

[PRACHI 214]

THANKS RAYEE I GOT IT....