If in a certain code, '753' means 'books are old', '365' means 'old and rare' and '473' means 'books and pens', which digit stands for 'rare'? MCQ with Answer and Explanation

From first and second, old =5 or 3. From first and third, books =7 or 3. Common analysis: first and second share 5 and 3, old common. Second and third share 3, but second has and rare old, third books and pens. 'and' common in second and third =3. Then from second, old and rare =3 6 5, and =3 so old/rare =6,5. From first, books are old =7 5 3, and =3 so books/are/old =7,5. Thus old =5, then rare =6.