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CAT 2004 — QA Question 25

PercentageEasy
Passage / Data

Answer the following question based on the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?

Answer & solution

  • A

    11 or 12

  • B

    12 or 13

  • 13 or 14

  • D

    14 or 15

Solution

c = 8
∴ a + b = 92   ...(1)

Also, 2ba+2b+3c≥0.2

⇒ 2b92-b+2b+24≥0.2

⇒ 2b ≥ 23.2 + 0.2b

⇒ b≥23218

⇒ b ≥ 13   ...(2)

Also, as group A carries at least 60% of the total marks,

aa+2b+3c≥0.6

⇒ aa+2(92 - a)+24≥0.6

⇒ aa ≥ 0.6a + 110.4 - 1.2a + 14.4

⇒ 1.6a ≥ 124.8

⇒ a ≥ 78  ...(3)

From (1), (2) and (3)
⇒ b can be 13 or 14.

Hence, option (c).

Alternately,
Consider options.

For c = 8 and b = 11, a = 81. The total marks = 127.
Group B has 17.32% marks, which is not possible.

For c = 8 and b = 12, a = 80. The total marks = 128.
Group B has 18.75% marks, which is not possible.

For c = 8 and b = 13, a = 79. The total marks = 129.
Group B has 20.15% marks and group A has 61.24% marks, which is possible.

For c = 8 and b = 14, a = 78. The total marks = 130.
Group B has 21.53% marks and group A has 60% marks, which is possible.

For c = 8 and b = 15, a = 77. The total marks = 131.
Group B has 22.9% marks and group A has 58.77 marks, which is not possible.

Hence, option (c).

CAT 2004 QA Q25: If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following be — Solution | TheCATExam