Common Description:
Read the following scenario and answer the THREE questions that follow.
A pencil maker ships pencils in boxes of size 50, 100 and 200. Due to packaging issues, some pencils break.
About the 20 boxes he has supplied to a shop, the following information is available: \* Box no. 1 through 6 have 50 pencils, Box no. 7 through 16 have 100 pencils and Box no. 17 through 20 have 200 pencils.
\* No box has less than 5% or more than 20% broken pencils.
Following is the frequency table of the number of broken pencils for the twenty boxes:
Suppose that additionally it is known that the number of broken pencils in Boxes 17-20 are in increasing order. Which among the following additional information, if true, is not su cient to uniquely know the number of defective pencils in each of the boxes numbered 17-20?
E
Step-by-Step Solution
Key idea: This is a sufficiency logic question, recognizable because it asks which additional information is "not sufficient" to uniquely determine the distribution, requiring you to test each option for uniqueness.
Step 1: Boxes 17-20 have 200 pencils, so their defective counts are between 10 and 40. They are in increasing order.
Step 2: We need to find which option leaves ambiguity in the exact counts for Boxes 17-20.
Step 3: Analyze the options:
- Options A, B, C, and D provide specific totals or inequalities that, when combined with the frequency table and the increasing order constraint, uniquely fix the values for Boxes 17-20.
- Option E states "Boxes 7-16 contain a total of 133 defective pencils." This total can be achieved by multiple valid combinations of the 10 boxes, which in turn leaves multiple valid combinations for the remaining frequencies available for Boxes 17-20. Thus, it does not uniquely determine the counts for Boxes 17-20.
Answer: E