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D is corrent because in the third-party donee beneficiary contract, the donee beneficiary can assert rights to the contract if the beneficiary can prove that the terms of the contract and surrounding circumstances manifest a clear intent to benefit her.
A is incorrect because a donee beneficiary does not have to establish that she gave consideration for the benefit conferred in the agreement. The nature of a third-party donee beneficiary contract is such that a gift is being conferred on the donee beneficiary, with no consideration being given in exchange.
B is incorrect because the donee beneficiary can assert rights to the contract if the beneficiary can prove that the terms of the contract and surrounding circumstances manifest a clear intent to benefit her. The donee beneficiary need not prove that the contract specifically named her as beneficiary.
C is incorrect because a donee beneficiary need not prove that she is related to the promisee by blood or marriage. This has no relevance in deciding whether a third-party donee beneficiary can enforce the contract.