PE 2 - Mathematical Reasoning | LR - Mathematical Reasoning
Answer the next 4 questions based on the information given below.
In an examination, there are 100 questions. A student is awarded 6 marks for each. He loses 2 marks for each wrong answer and loses 1 mark for each un-attempted question.
The net score of Varun in that test is 321.
The number of ways in which Varun could have attempted the exam is _____.
- A.
6
- B.
5
- C.
7
- D.
None of these
Answer: Option C
Explanation :
Let
x = Number of correct answers
y = Number of wrong answers
z = Number of unattempted questions.
Given, x + y + z = 100 …(1)
6x – 2y – z = 321 …(2)
(1) + (2) :
⇒ 7x + y = 421
⇒ y = 421 – 7x
We know y ≥ 0
Hence, 421 – 7x ≥ 0
⇒ x ≤ 421/7
⇒ x ≤ 60.14
∴ Highest value of x can be 60, for which y = 1 and z = 39
Next possible value of x = 59, for which y = 8 and z = 33
Next possible value of x = 58, for which y = 15 and z = 27
For a decrease of 1 in x, z decreases by 6.
∴ Possible values of z = 39, 33, 27, 21, 15, 9, and 3 i.e., 7 values.
⇒ Corresponding values of x = 60, 59, 58, 57, 56, 55 and 54.
⇒ Corresponding values of y = 1, 8, 15, 22, 29, 36 and 43.
∴ There are 7 ways of attempting the exam.
Hence, option (c).
Workspace:
The maximum number of questions attempted by Varun could be .
Answer: 97
Explanation :
Consider the solution to first question of this set.
We need to maximize (x + y) and hence minimize z.
The least value of z is 3, hence maximum value of (x + y) = 100 – 3 = 97.
Hence, 97.
Workspace:
What is the number of questions that Varun got wrong if the number of correct questions that he got is a multiple of 11?
Answer: 36
Explanation :
Consider the solution to first question of this set.
The number of correct questions can only be 55 (since it has to be a multiple of 11).
∴ Number of wrong questions will be 36.
Hence, 36.
Workspace:
What can be the maximum number of questions Varun left un-attempted?
Answer: 33
Explanation :
Consider the solution to first question of this set.
We need to maximize z.
The highest value of z is 33.
Hence, 33.
Workspace:
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