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Answer the questions on the basis of the information given below:

In an examination, there are $100$ questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries $1$ mark, each question in group B carries $2$ marks and each question in group C carries $3$ marks. It is known that questions in group A carries at least $60\%$ of the total mark.

If group B contains $23$ questions, then how many questions are there in group C?

  1. $1$
  2. $2$
  3. $3$
  4. cannot be determined
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