If group B contains 23 questions, then how many questions are there in group C?
Explanation:
Let there be a, b and c questions in groups A, B and C respectively.
Then, a + b + c =100
Total marks = a + 2b + 3c
Also, aa+2b+3c≥60100
b = 23
⇒ a + c = 77
⇒ a = 77 – c
⇒ aa+46+3c≥0.6
⇒ a ≥ 0.6a + 27.6 + 1.8c
⇒ 4a ≥ 276 + 18c
⇒ a ≥ 69 + 4.5c
⇒ a – 4.5c ≥ 69
⇒ 77 – c – 4.5c ≥ 69
⇒ 77 ≥ 69 + 5.5c
⇒ c ≤ 8/5.5
⇒ c = 1
Hence, option (a).
Alternatively, Evaluating options,
If C has 1 question then B and A have 23 and 76 questions respectively. The total number of marks = 125 ⇒ Group A has 60.8% marks. ⇒ Option (a) is possible.
If C has 2 questions then B and A have 23 and 75 questions respectively. The total number of marks = 127 ⇒ Group A has 59.05% marks. ⇒ Option (b) is not possible.
If C has 3 questions then B and A have 23 and 74 questions respectively. The total number of marks = 129 ⇒ Group A has 57.36% marks. ⇒ Option (c) is not possible.
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