Choice "A" is correct. In asymmetric encryption, a public key is used to encrypt messages. A private key (which is never transmitted) is used to decrypt the message at the other end. There are two keys. Effectively, anyone can encrypt a message, but only the intended recipient can decrypt the message.
Choice "b" is incorrect. Data encryption is, in fact, based on the concept of keys. However, the length of the key is extremely important in data encryption. The longer the key is, the harder it is to crack the key. There are a number of different encryption algorithms, and sooner or later, they are almost always discovered, even if the developers attempt to keep them secret (and these days, many of the more popular algorithms are public). The algorithm is important, but the length of the key is more important.
Choice "c" is incorrect. In asymmetric encryption, a public key is used to encrypt messages. However, the public key is not transmitted along with the message (if it were, why have it in the first place?). The private key of the recipient is used to decrypt the message. There is always a problem of how to transmit the key (when there is only one key such as in symmetric encryption).
Choice "d" is incorrect. Asymmetric encryption techniques are much more computationally intensive than symmetric encryption techniques and thus are considerably slower because a different key is used to decrypt the message than the one used to encrypt it. This requires more time and resources to accomplish.