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please solve it

by soumya_joy » Fri Nov 23, 2012 1:22 pm
In an examination, there are 150 questions divided into three groups A, B and C such that
each group contains at least one question. Each question in group A carries 2 mark, each
question in group B carries 3 marks and each question in group C carries 5 marks. It is
known that the questions in group A together carry at least 40% of the total marks. If
group B contains 20 questions, then
A. C ≤ 21 B. C ≤ 31 C. C ≤ 41 D. C ≤ 51
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by Anurag@Gurome » Sat Nov 24, 2012 8:19 am
soumya_joy wrote:In an examination, there are 150 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 2 mark, each question in group B carries 3 marks and each question in group C carries 5 marks. It is known that the questions in group A together carry at least 40% of the total marks. If group B contains 20 questions, then
A. C ≤ 21 B. C ≤ 31 C. C ≤ 41 D. C ≤ 51
Group B contains 20 questions of 3 marks each --> 20*3 = 60 marks

Let us assume group A contains x questions and group C contains y questions.
Hence, (x + y) = (150 - 20) = 130

Total marks of the 150 questions = (2x + 60 + 5y)

Now, the questions in group A together carry at least 40% of the total marks.
Hence, 2x/(2x + 60 + 5y) ≥ 40/100
--> x/(2x + 60 + 5y) ≥ 1/5
--> 5x ≥ (2x + 60 + 5y)
--> 3x ≥ (60 + 5y)
--> 3(130 - y) ≥ (60 + 5y) ............... Replacing x = (130 - y)
--> (390 - 60) ≥ (5y + 3y)
--> 8y ≤ 330
--> y ≤ 41.(something)

Hence, number of questions in group C is less than or equal to 41.
It is not defined in the question what C is in the options. I assume it means the number of questions in group C.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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