The question

Today was my mathematics examination. It went of ok, I wasn't able to do some question. But there was this one question which I had done correctly and most of the people of my class had done wrong. The question was

A student taking a test consisting of 10 questions in that each question after the first is worth 2 marks more than the preceding quesiotn. If the third question of the test is of 5 marks, what is the maximum score that the student can obtain by attempting only 8 questions?

Now this is the way that most of the people had solved it -

d=2 (Difference of marks)
a₃=5 (Weightage of the third question)
a₂=a₃-d=5-2=3
Thus,
a₁=a₂-d=3-2=1
Now, that a₁=1 and d=2
The maximum marks that one can obtain will be S₈. So they solved
S₈=(n/2)(2a+(n-1)d)
S₈=(8/2)(2+(8-1)2))
S₈=4(2+(7*2))
S₈=4*16
S₈=64
Answer: 64 Marks

But the thing is that the question never said that the student attempted the first 8 questions. He attemtep any 8 questions. Now, we can say that who are we to determine which question he would have done. The fisrt 8 seems to be the obvious choice. But then again, the question has clearly asked what are the maximum marks one can get by attempting 8 questions. So the correct way to solve it would be -

d=2 (Difference of marks)
a₃=5 (Weightage of the third question)
a₂=a₃-d=5-2=3
Thus,
a₁=a₂-d=3-2=1
We will assume that he did the last 8 questions as it would fetch him the maximum marks. Thus thhe maximum marks would be-
S₁₀-(a₂+a₁)
Which is-
(n/2)(2a+(n-1)d)-(a₂+a₁)
=(10/2)(2+18)-(3+1)
=(5)(20)-4
=100-4
=96
Answer: 96

Get it?