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A worker is kept on a contract for 100 days to make some toys. On any

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VP
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A worker is kept on a contract for 100 days to make some toys. On any  [#permalink]

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New post 01 Jun 2019, 17:58
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Difficulty:

  95% (hard)

Question Stats:

29% (02:10) correct 71% (02:11) wrong based on 41 sessions

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A worker is kept on a contract for 100 days to make some toys. On any of these 100 days he does not make more than 20 toys. If on any day, he makes more than 12 toys, then he makes at most 6 toys each on the next two days. What is the maximum possible number of toys that he can make over the period of 100 days?

A. 1100
B. 1109
C. 1200
D. 1202
E. 1208
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Re: A worker is kept on a contract for 100 days to make some toys. On any  [#permalink]

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New post 01 Jun 2019, 19:49
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1st day - 20 toy.
2nd day - 6 toy.
3rd day - 6 toys
total - 32 toys in 3-day max
So for 100 days 32*33 + 20. But this answer is not among the options. Is there anything that i am missing?
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Re: A worker is kept on a contract for 100 days to make some toys. On any  [#permalink]

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New post 01 Jun 2019, 20:57
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nick1816 wrote:
A worker is kept on a contract for 100 days to make some toys. On any of these 100 days he does not make more than 20 toys. If on any day, he makes more than 12 toys, then he makes at most 6 toys each on the next two days. What is the maximum possible number of toys that he can make over the period of 100 days?

A. 1100
B. 1109
C. 1200
D. 1202
E. 1208


IMO C

lets take 10 days
12* 10= 120 ( He makes 12 toys for 10 days , so he makes 120 toys )
20+ 6+ 6 +20+ 6 +6 +20 +6+ 6 +20 =116 ( He makes toys in a pattern of 20 6 6 ....)

For 100 days, multiply by a factor of 10 , so we have 1200 or 1160 , So max toys IMO C
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Re: A worker is kept on a contract for 100 days to make some toys. On any  [#permalink]

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New post 02 Jun 2019, 10:36
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We have to check 2 cases
1. When he makes 20 toys, then he makes at most 6 toys each on the next two days.
Total number of toys he build in 3 days=32
2. When he build 12 toys everyday.
Total number of toys he build in 3 days=12*3=36 which is greater than those in the first case.


The maximum possible number of toys that he can make over the period of 100 days= (12*99)+20= 1188+20=1208
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Re: A worker is kept on a contract for 100 days to make some toys. On any  [#permalink]

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New post 02 Jun 2019, 13:40
nick1816 wrote:
We have to check 2 cases
1. When he makes 20 toys, then he makes at most 6 toys each on the next two days.
Total number of toys he build in 3 days=32
2. When he build 12 toys everyday.
Total number of toys he build in 3 days=12*3=36 which is greater than those in the first case.


The maximum possible number of toys that he can make over the period of 100 days= (12*99)+20= 1188+20=1208



Right ! Great question, missed this subtle case.
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Re: A worker is kept on a contract for 100 days to make some toys. On any   [#permalink] 02 Jun 2019, 13:40
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