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26 May 2017, 04:47
Kudos
Bookmarks
When 120 candies are given to 25 children and the maximum number of candies for each child is 7, what is the maximum number of children who get only 1 candy?
A. 5
B. 6
C. 7
D. 8
E. 9
A. 5
B. 6
C. 7
D. 8
E. 9
26 May 2017, 04:48
Kudos
Bookmarks
Official Solution:
When 120 candies are given to 25 children and the maximum number of candies for each child is 7, what is the maximum number of children who get only 1 candy?
A. 5
B. 6
C. 7
D. 8
E. 9
120 candies are given to children, and the maximum number of candies for each child is 7, so
\(120 = 7*17+1*1 (17 + 1 = 18)\), and this cannot satisfy the question because there are only 18 children. \(120 = 7*16+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1\) \((16+1+1+1+1+1+1+1+1=24)\), and this also cannot satisfy the question because there are only 24 children.
When \(120 = 7*15+6*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1 = 120\)
\((15+1+1+1+1+1+1+1+1+1+1 = 25)\), it satisfies the question because there are 25 children.
In other words, 15 children are each given 7 candies, 1 child is given 6 candies, and the rest of the 9 children only get 1 candy each. Hence, the maximum number of children who get 1 candy is \(1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1\), then \(1+1+1+1+1+1+1+1+1 = 9\). Therefore, the answer is E.
Answer: E
When 120 candies are given to 25 children and the maximum number of candies for each child is 7, what is the maximum number of children who get only 1 candy?
A. 5
B. 6
C. 7
D. 8
E. 9
120 candies are given to children, and the maximum number of candies for each child is 7, so
\(120 = 7*17+1*1 (17 + 1 = 18)\), and this cannot satisfy the question because there are only 18 children. \(120 = 7*16+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1\) \((16+1+1+1+1+1+1+1+1=24)\), and this also cannot satisfy the question because there are only 24 children.
When \(120 = 7*15+6*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1 = 120\)
\((15+1+1+1+1+1+1+1+1+1+1 = 25)\), it satisfies the question because there are 25 children.
In other words, 15 children are each given 7 candies, 1 child is given 6 candies, and the rest of the 9 children only get 1 candy each. Hence, the maximum number of children who get 1 candy is \(1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1+1*1\), then \(1+1+1+1+1+1+1+1+1 = 9\). Therefore, the answer is E.
Answer: E
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