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

Question

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

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

nick1816 · Accepted Answer

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

rishabhshreyas14 · Answer

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?

stne · Answer

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

stne · Answer

Right ! Great question, missed this subtle case.

Sakshi516B · Answer

Question asks - 
he makes more than  12  toys, then he makes at most 6 toys each on the next two days

why is everyone reading 12 as 20?
it is obvious though

Regor60 · Answer

People are discussing 20 because it is one of the two limiting cases, the other being 12.

20 is the absolute limit of toy production per day.

12 is the limit of toy production beyond which the next two days are limited to 6 each.

Without the second condition the answer would be trivial as 100*20.

The goal is to maximize each 3 day period.

Posted from my mobile device

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