A carpenter has to build 71 wooden boxes in one week (7 days). He can

Question

A carpenter has to build 71 wooden boxes in one week (7 days). He can build as many per day as he wants but he has decided that the number of boxes he builds on any one day should be within 4 off the number he builds on any other day. What is the greatest number of boxes that he could have build on Saturday?

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

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hinasingh · Answer

A carpenter has to build 71 wooden boxes in one week (7 days). He can build as many per day as he wants but he has decided that the number of boxes he builds on any one day should be within 4 off the number he builds on any other day. What is the greatest number of boxes that he could have build on Saturday?

Total number of boxes to be built in one week = 71.
Let x be the number of boxes he build's on any one day, then the number of boxes for other days must be in the range of x+4 or x-4.
Let's plug in values - 
Say, he builds 14 boxes on Saturday, then, he has to build 10 boxes on 3 days and 9 boxes on balance 3 days - 
total is 14 + 30 + 27 = 71.
but here, the condition is violated - since, 14 - 9 =5.
Hence, there is no way that the maximum value could be 14.

Now, let's say, he builds 13 boxes on Saturday, then, he has to build 10 boxes on 4 days and 9 boxes on balance 2 days
which is withing the given condition. 13-9 =4.
Answer D

wickedvikram · Answer

Total Box 71
 if sat max is 14, then for other days minimum is 6*10=60; total 74
However, if max is 13, for other days minimum is 9*6=54; total 67, However, he can fit 4 other boxes in 6 minimum days to get to 71

Rabab36 · Answer

Bunuel  sir can you pls post explanation

Bunuel · Answer

In order to maximize the number of boxes built on a specific day, we should minimize the number of boxes built on all other days. Let's assume that on 6 days, he builds x boxes each day, and on Saturday he builds x + 4 boxes. In this scenario, we'd have the equation x + x + x + x + x + x + (x + 4) = 71, which gives us x = 67/7 ≈ 9.something and x + 4 ≈ 13.something. Therefore, the maximum number of boxes he can build on Saturday is 13. The distribution of boxes built can be 9, 9, 10, 10, 10, 10, and 13.

Note that the maximum number cannot be 14 because, in this case, 9*6 + 14 > 71 and none of the days can have fewer than 9 boxes built. This is because, if that were the case, the difference between the boxes built on Saturday (14) would be more than 4 greater than on some other day, which is not allowed.

Answer: D.

14. Min/Max Problems 
     Theory   
 Maximizing/Minimizing Strategies on the GMAT - All in One Topic! 
     Questions   
 Worst Case Scenario Questions  
 DS Questions 
 PS Questions

Hope it helps.

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A carpenter has to build 71 wooden boxes in one week (7 days). He can

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A carpenter has to build 71 wooden boxes in one week (7 days). He can

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