Options Weekly Tests 100 Anjali started conducting weekly tests on Friday evening. The marks in this test was used as a metric to judge 80 student’s grasp over concepts discussed in this week. To discourage students from making wild guesses, she 85 awarded +4 for correct responses and -1 for incorrect responses. No marks were awarded or deducted for 90 unattempted questions. The top scorer of last weekly test was Afzal. Afzal scored 250 marks. If he attempted all the 200 questions, then can you tell us how many questions were answered correctly by him.
pls solve within 30 mins
The correct answer and explanation is:
Let’s break down the problem systematically to find how many questions Afzal answered correctly.
Given Information:
- Afzal’s total score = 250 marks.
- Total number of questions = 200.
- The scoring system:
- +4 marks for each correct answer.
- -1 mark for each incorrect answer.
- 0 marks for unattempted questions.
Variables:
Let:
- xx = the number of questions answered correctly.
- yy = the number of questions answered incorrectly.
- zz = the number of unattempted questions.
We know that:
- Total questions = 200. So: x+y+z=200(Equation 1)x + y + z = 200 \quad \text{(Equation 1)}
- Afzal’s total score = 250. Based on the scoring rules: 4x−y=250(Equation 2)4x – y = 250 \quad \text{(Equation 2)}
Step 1: Solve the system of equations
From Equation 1, we know: z=200−x−yz = 200 – x – y
But, we don’t need the value of zz directly for our calculations. We’ll use the two main equations.
From Equation 2, rearrange it for yy: y=4x−250y = 4x – 250
Now substitute this expression for yy into Equation 1: x+(4x−250)+z=200x + (4x – 250) + z = 200
Simplify the equation: x+4x−250+z=200x + 4x – 250 + z = 200 5x−250+z=2005x – 250 + z = 200 5x+z=450(Equation 3)5x + z = 450 \quad \text{(Equation 3)}
Step 2: Analyze the possible values for xx and yy
From Equation 3, for xx and zz to be valid, zz must be a non-negative integer. Let’s try different values of xx.
Case 1: Try x=50x = 50
Substitute x=50x = 50 into Equation 3: 5(50)+z=4505(50) + z = 450 250+z=450250 + z = 450 z=200z = 200
This means Afzal answered 50 questions correctly, 0 incorrectly, and left 200 unattempted.
Verification:
- From Equation 2, substitute x=50x = 50 into y=4x−250y = 4x – 250: y=4(50)−250=200−250=−50y = 4(50) – 250 = 200 – 250 = -50 Since yy cannot be negative, x=50x = 50 is not a valid solution.
Case 2: Try x=60x = 60
Substitute x=60x = 60 into Equation 3: 5(60)+z=4505(60) + z = 450 300+z=450300 + z = 450 z=150z = 150
This means Afzal answered 60 questions correctly, 0 incorrectly, and left 150 unattempted.
Verification:
- From Equation 2, substitute x=60x = 60 into y=4x−250y = 4x – 250: y=4(60)−250=240−250=−10y = 4(60) – 250 = 240 – 250 = -10 Again, yy is negative, so this is also not a valid solution.
Case 3: Try x=70x = 70
Substitute x=70x = 70 into Equation 3: 5(70)+z=4505(70) + z = 450 350+z=450350 + z = 450 z=100z = 100
This means Afzal answered 70 questions correctly, 0 incorrectly, and left 100 unattempted.
Verification:
- From Equation 2, substitute x=70x = 70 into y=4x−250y = 4x – 250: y=4(70)−250=280−250=30y = 4(70) – 250 = 280 – 250 = 30 This yields y=30y = 30, which is positive and valid.
So, Afzal answered 70 questions correctly.
Final Answer:
Afzal answered 70 questions correctly.
Explanation:
We analyzed the problem step-by-step by using the given scoring system and equations. The key challenge was balancing the total score with the constraints of the number of correct, incorrect, and unattempted questions. Through solving the system of equations, we determined that Afzal answered 70 questions correctly.