XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 18 : Which of the following cannot be inferred conclusively from the given information?

Explanatory Answer

For the boxes which has 50 pencils, the possible defective pencils are in the range (3 - 10)
For the boxes which has 100 pencils, the possible defective pencils are in the range (5 - 20)
For the boxes which has 200 pencils, the possible defective pencils are in the range (10 - 20)
The values of defective pencils are (5,6,6,7,7,7,7,9,9,9,11,15,15,19,20,20,20,29,31,33)
(5,6,6,7,7,7,7,9,9,9) from these, 6 values can take by 1-6 boxes and 4 values will take by 7-16
(11,15,15,19,20,20,20) → 6 values can be taken by 7-16 boxes and 1 value can be taken by 17-20 boxes.
(29,31,33) → possible only for boxes 17-20
From the above information, we can say that options A, B, and D can be concluded.
The highest number of defective pencils possible for all boxes is 10, 20, 40.
Here we don't have 10 and 40, the only value we have is 20.
At Least two of the three 20s should belong to 7-16 boxes that have 100 pencils each. Hence Option C can also be concluded.
We can't conclude Option E from the given info.
Therefore, the correct answer should be Option E

The question is " Which of the following cannot be inferred conclusively from the given information? "

Hence, the answer is 'Exactly three boxes have 20% broken pencils.'

Choice E is the correct answer.