Solving a Complex Math Problem: How Many Questions Did Sakshee Omit?

In a recent mathematics challenge, a quiz posed a challenging problem to participants: a quiz with 25 questions, each worth 7 points for a correct answer, 2 points deducted for a wrong answer, and 0 points for omitted questions. Sakshee scored a total of 113 points. How many questions did she omit? This article will guide you through the reasoning and mathematical calculations to find the answer.

Defining the Variables and Establishing Equations

To solve this problem, we need to define the variables and set up the equations.

Variables

Let C represent the number of correct answers, W represent the number of wrong answers, and M represent the number of omitted questions.

From the given information, we know that: C W M 25, the total number of questions. 7C – 2W 113, based on the scoring system.

Step-by-Step Calculation

Let's break down the problem into manageable steps to find the correct values for C, W, and M.

Step 1: Determine the Value of M (Omitted Questions)

From the equation:

C W M 25,

we can test different values of M to see which value satisfies the scoring equation.

Step 2: Check for Consistency with the Scoring Equation

If M 5, then:

C W 20,

and the scoring equation becomes:

7C – 2W 113.

Solving this, we find:

9C 153, and C 17.

17C – 3W 0M 119 – 60 113.

Correct.

Thus, Sakshee omitted 5 questions, got 17 correct answers, and 3 wrong answers.

Generalization and Verification

Let's generalize the problem with variables x (correct answers), y (wrong answers), and z (omitted questions).

Equation for Scoring

The scoring equation is:

7x – 2y 0z 113,

and the total questions constraint is:

x y z 25.

To verify the solution, we consider:

The maximum number of correct answers is 113 / 7 16.

Given that:

7x – 2y 113,

and knowing that:

The correct answers must be more than or equal to 17, making 7n to be an odd number.

7n – 113 must be even, so n can be 17, 19, 21, 23.

When n 19, 7n 133, which is not a solution since it exceeds 113.

When n 17, 7n 119, and 119 – 113 6.

Therefore, 2y 6, y 3.

Thus, x 17, y 3, and z 25 – 17 – 3 5.

Hence, Sakshee omitted 5 questions.

Conclusion

In conclusion, Sakshee omitted 5 questions, with 17 correct answers and 3 wrong answers, scoring a total of 113 points.