" ...
In cryptography, the RSA scheme has the following pair of
characteristics:
     a. asymmetric cipher system
     b. a public key encryption algorithm system
... "

A 'system' is usually understood to be the practical implementation of a
'scheme' which makes use of one or more algorithms.

(b) implies that a given system is a characteristic of a given scheme,
which, taken literally, is nonsense. Therefore one must conclude that the
writer of the question has not a good command of english. Overt
syntactical idiosyncracies tend to confirm this conclusion, e.g.
'algorithm system', and the word 'characteristic', which is often (mis)used
in place of a more precise word.

However, whether you encrypt with the public key or with the private key
depends on whether you want to encrypt a text or to 'sign' it using a
cryptographic checksum. Both are applications of cryptography. Rightly or
wrongly I believe the RSA 'scheme' foresaw both applications right from the
first publication. So I found myself wondering whether the intent of the
question was to pick up on this, but for various reasons I concluded that
it was probably not.

When a candidate is drawn to consider what the question author intended,
rather than simply what is written, s/he is disadvantaged, if time is a
limiting factor. Yes, it is a poorly phrased question, although it's not
the worst example I have seen. For a candidate it can be worse if a
question is simply ambiguous without any clues.
  Alice couldn't help smiling as she took out her memorandum-book, and
worked the sum for him:
365
  1-

---
364
---
   Humpty Dumpty took the book, and looked at it very carefully. "That seems to be done right -- -" he began.
  "You're holding it upside down!" Alice interrupted.
  "To be sure I was!" Humpty Dumpty said gaily, as she turned it round for
him. "I thought it looked a little queer. As I was saying, that seems to be
done right -- though I haven't time to look it over thoroughly just now --
and that shows that there are three hundred and sixty-four days when you
get un-birthday presents -- -"
  "Certainly," said Alice.
  "And only one for birthday presents, you know. There's glory for you!"
"I don't know what you mean by 'glory'", Alice said.
  Humpty Dumpty smiled contemptuously. "Of course you don't -- till I tell
you. I meant 'there's a nice knock-down argument for you!'"
  "But `glory' doesn't mean `a nice knock-down argument'", Alice objected.
  "When I use a word," Humpty Dumpty said in a rather a scornful tone, "it
means just what I choose it to mean -- neither more nor less".
... from "Through the Looking Glass", by Lewis Carroll.

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