XAT 2022 — QA & DI Question 13
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:
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Which of the following cannot be inferred conclusively from the given information?
Answer & solution
- A
No box numbered 1-6 has more broken pencils than any box numbered 17-20.
- B
A box with the highest percentage of broken pencils has 100 pencils.
- C
Four among the boxes numbered 7 to 16 have less than 10 broken pencils.
Exactly three boxes have 20% broken pencils.
- E
Three among the boxes numbered 17 to 20 have 29, 31 and 33 broken pencils in someorder.
Going by the given options :
Option A: The boxes numbered 1- 6 have a capacity of 50 pencils. The maximum number of broken pencils they can contain is 20 percent of 20 pencils = 10 pencils. For boxes numbered 17 to 20 they must contain a minimum of 5 percent which is equivalent to 5 percent of 200. Hence this is true.
Option B: Boxes with broken pencils of 29, 31, 33 must be a part of 17 - 20. There must be one box containing broken pencils in the range of 10 to 20. There are three boxes in total containing exactly 20 pencils. A maximum of only one of the three can be a part of 17 - 20. The remaining must be a part of boxes 7 - 16 because they cannot be a part of 1-6. Hence at least one box among 7 - 16 contains 20 percent of broken pencils which is the highest.
Option C: There are a total of ten boxes with less than 10 broken pencils. They can either be a part of boxes 1 - 6 or 7 - 16. Since boxes 1-6 can only take broken pencils with less than 10 in number. Hence of the 10 six must be a part of 1-6 and the remaining 4 must be a part of 7 - 16.
Option D: The only possibility for containing 20 percent of the broken pencils is only possible for 20 broken pencils which is 20 percent of 100. There must be at least 2 boxes in the range of 7 - 16 which contain 20 broken pencils which is equal to 20 percent. The third box can either be a part of (7-16) to (17-20). If this belongs to 17 - 20 then the case is not possible and hence cannot be concluded.
Option E: Boxes containing 29, 31, and 33 broken pencils must be a part of boxes 17 -20 because they are higher than the 20 percent range of boxes (1-6) and (7-16). Hence this can be concluded.