In a test consisting of 120 questions, Anuradha answered 65% of the first 60 questions correctly. What percentage of the remaining questions does she need to answer correctly to sc... In a test consisting of 120 questions, Anuradha answered 65% of the first 60 questions correctly. What percentage of the remaining questions does she need to answer correctly to score 75% in the test?
Understand the Problem
The question asks how many questions Anuradha needs to answer correctly from the remaining questions in order to achieve a total score of 75% on a 120-question test. The first part of the test, consisting of 60 questions, has already been partially scored at 65%. We need to calculate the number of correct answers required from the remaining questions to meet the percentage goal.
Answer
Anuradha needs to answer correctly 85% of the remaining questions.
Answer for screen readers
Anuradha needs to answer correctly 85% of the remaining questions.
Steps to Solve
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Determine the total correct answers needed for 75% To find out how many total correct answers Anuradha needs for 75%, calculate: $$ 0.75 \times 120 = 90 $$ So, she needs 90 correct answers in total.
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Calculate the correct answers from the first part of the test Anuradha answered 65% of 60 questions correctly: $$ 0.65 \times 60 = 39 $$ Thus, she answered 39 questions correctly so far.
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Find the remaining correct answers needed Next, determine how many more questions must be answered correctly: $$ 90 - 39 = 51 $$ Anuradha needs 51 more correct answers.
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Calculate the percentage of remaining questions she needs to answer correctly There are 60 questions remaining, so find the percentage of the remaining questions: $$ \frac{51}{60} \times 100 = 85% $$ Anuradha needs to answer 85% of the remaining questions correctly.
Anuradha needs to answer correctly 85% of the remaining questions.
More Information
To achieve a score of 75% on a 120-question test, Anuradha must ensure that her correct answers from both sections total 90. This means maintaining high performance on the remaining questions is crucial.
Tips
- Confusing total correct answers with percentage calculations.
- Not accounting for how many questions were already answered correctly.
- Forgetting to convert the raw number of questions into a percentage.
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