# 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.

**PE 2 - Mathematical Reasoning | LR - Mathematical Reasoning**

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:

**PE 2 - Mathematical Reasoning | LR - Mathematical Reasoning**

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:

**PE 2 - Mathematical Reasoning | LR - Mathematical Reasoning**

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:

**PE 2 - Mathematical Reasoning | LR - Mathematical Reasoning**

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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