Broken Pencils Distribution

XAT 2022 · QADI · Hard · Data Interpretation

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Passage / data set

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%5\% or more than 20%20\% broken pencils.
  • Frequency table of broken pencils across the 20 boxes: 5 broken (1 box), 6 (2), 7 (4), 9 (3), 11 (1), 15 (2), 19 (1), 20 (3), 29 (1), 31 (1), 33 (1).

Question 1 of 3

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

  1. A.

    6,7,9, 11,15,19,20,20,20,29

  2. B.

    5,6,6,6,11,15,15,20,20,20

  3. C.

    7,7,7,7,11,15,15,19,20,20

  4. D.

    7,7,9,9,11,13,15,19,20,20

  5. E.

    5,7,7,7,9,11,15,20,20,20

Question 2 of 3

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

  1. A.

    No box numbered 1-6 has more broken pencils than any box numbered 17-20.

  2. B.

    A box with the highest percentage of broken pencils has 100 pencils.

  3. C.

    Four among the boxes numbered 7 to 16 have less than 10 broken pencils.

  4. D.

    Exactly three boxes have 20% broken pencils.

  5. E.

    Three among the boxes numbered 17 to 20 have 29, 31 and 33 broken pencils in some order.

Question 3 of 3

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 sufficient to uniquely know the number of defective pencils in each of the boxes numbered 17-20?

  1. A.

    Boxes no. 7-16 contains a total of 124 defective pencils.

  2. B.

    Boxes no. 17-20 contain a total of 108 defective pencils.

  3. C.

    Boxes no. 11-16 contain a total of 101 defective pencils.

  4. D.

    Box no. 17 contains more defective pencils than any box from among boxes no. 1-14.

  5. E.

    Boxes no. 7-16 contain a total of 133 defective pencils.

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