A test contains 10 true/false questions. A correct answer is awarded 2 marks, a wrong answer -1 and a question not answered is awarded 0. A student attempts 7 questions and gets 8 marks. How many questions did the student answer correctly?

Answer

To solve the problem step by step, we will define variables and set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) = number of questions answered correctly
- \( y \) = number of questions answered incorrectly

### Step 2: Set Up Equations
From the problem, we know:
1. The total number of questions attempted is 7:
\[ x + y = 7 \quad \text{(Equation 1)} \]
2. The total marks obtained by the student is 8. The marks are calculated as follows:
- Each correct answer gives 2 marks: \( 2x \)
- Each incorrect answer gives -1 mark: \( -y \)
Thus, the equation for total marks is:
\[ 2x - y = 8 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now we have two equations:
1. \( x + y = 7 \)
2. \( 2x - y = 8 \)

We can solve these equations simultaneously.

#### Adding the Two Equations
Let's add Equation 1 and Equation 2:
\[ (x + y) + (2x - y) = 7 + 8 \]
This simplifies to:
\[ 3x = 15 \]
Now, divide both sides by 3:
\[ x = 5 \]

### Step 4: Find the Number of Incorrect Answers
Now that we have \( x \), we can find \( y \) using Equation 1:
\[ x + y = 7 \implies 5 + y = 7 \implies y = 2 \]

### Conclusion
The student answered correctly \( x = 5 \) questions.

### Final Answer
The number of questions the student answered correctly is **5**.

---