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Collectively, the five children in the Kramer family have 30 trophies.

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Collectively, the five children in the Kramer family have 30 trophies.  [#permalink]

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New post 09 Apr 2018, 01:52
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Collectively, the five children in the Kramer family have 30 trophies. If each child has at least one trophy and no two children have the same number of trophies, what is the greatest number of trophies that the child with the second-highest number of trophies could have?

A. 10
B. 11
C. 12
D. 13
E. 14

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Collectively, the five children in the Kramer family have 30 trophies.  [#permalink]

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New post Updated on: 09 Apr 2018, 03:22
Bunuel wrote:
Collectively, the five children in the Kramer family have 30 trophies. If each child has at least one trophy and no two children have the same number of trophies, what is the greatest number of trophies that the child with the second-highest number of trophies could have?

A. 10
B. 11
C. 12
D. 13
E. 14


Let the 5 children be named M, N, P, Q and R. assign minimum possible values starting from M up to P. Q and N will then have the highest possible values.

M = 1 trophy
N = 2 trophies
P = 3 trophies

At this point M+N+P = 1+2+3 = 6. Therefore Q +R will be 30-6 = 24. Since Q and R cannot have the same number of trophies: Q will be 11 trophies and R 13 trophies.

Q = 11 trophies (second-highest number of trophies )
R = 13 trophies

Hence option B (11 trophies) is the answer.

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Originally posted by houston1980 on 09 Apr 2018, 03:17.
Last edited by houston1980 on 09 Apr 2018, 03:22, edited 1 time in total.
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Re: Collectively, the five children in the Kramer family have 30 trophies.  [#permalink]

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New post 09 Apr 2018, 03:18
Let , the number of trophies be in the order -1, 2, 3, x, y and we have to find x.
1 + 2 + 3 = 6
Therefore, x + y = 24

Now, the possible values of x and y could be -

x = 5, 6, 7, 8, 9, 10, 11
Correspondingly, y = 19, 18, 17, 16, 15, 14, 13

Thus, the greatest possible value of x = 11

Hence, option B.

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Re: Collectively, the five children in the Kramer family have 30 trophies. &nbs [#permalink] 09 Apr 2018, 03:18
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