XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 17 : Which of the following can possibly be the sequence of the number of broken pencils in Boxes 7-16?

Explanatory Answer

For the boxes which have 50 pencils, the possible defective pencils are in the range (3 - 10)
For the boxes which have 100 pencils, the possible defective pencils are in the range (5 - 20)
For the boxes which have 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
Option B is not possible because even 20% of 100 is just 20, but we have 29 in this option.
Option C is also not possible because we don't have 13 defective pencils in any box.
Option E is not possible because we don’t have a chance for three 6’s
Option D is not possible because the boxes from 1-6 should only take the values from (5,6,6,7,7,7,7,9,9,9) The 7-16 boxes will only take 4 values. But option D has five values from this range.
Therefore Option A is the correct choice.

The question is " Which of the following can possibly be the sequence of the number of broken pencils in Boxes 7-16? "

Hence, the answer is '7,7,7,7,11,15,15,19,20,20'

Choice A is the correct answer.