If twenty sweets are distributed among some boys and girls such that each girl gets two sweets and each boy gets three sweets, what is the number of boys and girls? I. The number of girls is not more than five. II. If each girl gets 3 sweets and each boy gets 2 sweets, the number of sweets required for the children will still be the same.
Explanation:
2g + 3b = 20. Since b & g should be integers the values that satisfy this equation are (g = 10 & b =0), (g = 7 and b = 2), (g = 4 & b = 4), and (g = 1 and b = 6). From the statement I, we can shortlist the last two possibilities i.e. g =4 or g = 1, but cannot get a unique answer. The statement II suggests that the number of girls and boys have to be equal. Hence we get a unique answer viz. g = 4 & b = 4. Only statement II is required to answer the question.
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