XAT 2022 QADI Set 2 (3 Questions with Solutions)

A pencil maker ships pencils in boxes of size 50, 100 and 200. Due to packaging…

XAT 2022 · Quantitative Ability and Data Interpretation · 3 questions

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 (No. of broken pencils: No. of boxes): 5: 1; 6: 2; 7: 4; 9: 3; 11: 1; 15: 2; 19: 1; 20: 3; 29: 1; 31: 1; 33: 1.

Question 1

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

A. 6,7,9, 11,15,19,20,20,20,29
B. 5,6,6,6,11,15,15,20,20,20
C. 7,7,7,7,11,15,15,19,20,20
D. 7,7,9,9,11,13,15,19,20,20
E. 5,7,7,7,9,11,15,20,20,20

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Question 2

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

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

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Question 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?

A. Boxes no. 7-16 contains a total of 124 defective pencils.
B. Boxes no. 17-20 contain a total of 108 defective pencils.
C. Boxes no. 11-16 contain a total of 101 defective pencils.
D. Box no. 17 contains more defective pencils than any box from among boxes no. 1 - 14.
E. Boxes no. 7 - 16 contain a total of 133 defective pencils.

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