Question
Elena wrote an objective testin English language,mathematics and science
The total number of questions for each of the subjects are 60,40 and 30 respectively
1. If she had 80% in mathematics, how many questions did she answer in all
2. Elena was able to answer two-thirds of the science questions correctly
What will be her percentage score to the nearest whole number?
3. She scored 45 out of 60 in English language. What percentage of questions did she get wrong in English language?
4. How many science questions did Elena score wrong
Find the value of n given that 4n-3 =1/256
The total number of questions for each of the subjects are 60,40 and 30 respectively
1. If she had 80% in mathematics, how many questions did she answer in all
2. Elena was able to answer two-thirds of the science questions correctly
What will be her percentage score to the nearest whole number?
3. She scored 45 out of 60 in English language. What percentage of questions did she get wrong in English language?
4. How many science questions did Elena score wrong
Find the value of n given that 4n-3 =1/256
Answers
GPT-4o mini
Let’s solve the problem step by step.
### 1. Total number of questions answered by Elena in Mathematics
Elena scored 80% in Mathematics, with a total of 40 questions.
To find out how many questions she answered correctly:
\[
\text{Correct answers} = 80\% \text{ of } 40 = 0.80 \times 40 = 32
\]
If she answered 32 questions correctly, she likely attempted all the questions in Mathematics as it is common for objective tests. So, we assume she answered all 40 questions.
**Total questions answered in Mathematics = 40**
### 2. Percentage score in Science
Elena was able to answer two-thirds of the science questions correctly. The total number of science questions is 30.
To find the number of questions she answered correctly:
\[
\text{Correct answers in Science} = \frac{2}{3} \text{ of } 30 = 20
\]
To find her percentage score in Science:
\[
\text{Percentage} = \left(\frac{\text{Correct answers}}{\text{Total questions}}\right) \times 100 = \left(\frac{20}{30}\right) \times 100 = \frac{2000}{30} \approx 66.67\%
\]
Rounding to the nearest whole number gives her a score of **67%**.
### 3. Percentage of questions answered incorrectly in English Language
Elena scored 45 out of 60 in English Language. To find out how many questions she got wrong:
\[
\text{Wrong answers in English} = 60 - 45 = 15
\]
To find the percentage of questions she got wrong:
\[
\text{Percentage wrong} = \left(\frac{\text{Wrong answers}}{\text{Total questions}}\right) \times 100 = \left(\frac{15}{60}\right) \times 100 = 25\%
\]
### 4. Number of Science questions scored wrong
From question 2, we know that she correctly answered 20 science questions out of 30. Thus, the number of wrong answers in Science is:
\[
\text{Wrong answers in Science} = 30 - 20 = 10
\]
### Solving for \( n \)
Given the equation:
\[
4n - 3 = \frac{1}{256}
\]
First, we add 3 to both sides:
\[
4n = 3 + \frac{1}{256}
\]
We can express 3 as a fraction:
\[
3 = \frac{768}{256}
\]
So,
\[
4n = \frac{768 + 1}{256} = \frac{769}{256}
\]
Next, divide both sides by 4:
\[
n = \frac{769}{4 \times 256} = \frac{769}{1024}
\]
Thus, the value of \( n \) is:
\[
\boxed{\frac{769}{1024}}
\]
### 1. Total number of questions answered by Elena in Mathematics
Elena scored 80% in Mathematics, with a total of 40 questions.
To find out how many questions she answered correctly:
\[
\text{Correct answers} = 80\% \text{ of } 40 = 0.80 \times 40 = 32
\]
If she answered 32 questions correctly, she likely attempted all the questions in Mathematics as it is common for objective tests. So, we assume she answered all 40 questions.
**Total questions answered in Mathematics = 40**
### 2. Percentage score in Science
Elena was able to answer two-thirds of the science questions correctly. The total number of science questions is 30.
To find the number of questions she answered correctly:
\[
\text{Correct answers in Science} = \frac{2}{3} \text{ of } 30 = 20
\]
To find her percentage score in Science:
\[
\text{Percentage} = \left(\frac{\text{Correct answers}}{\text{Total questions}}\right) \times 100 = \left(\frac{20}{30}\right) \times 100 = \frac{2000}{30} \approx 66.67\%
\]
Rounding to the nearest whole number gives her a score of **67%**.
### 3. Percentage of questions answered incorrectly in English Language
Elena scored 45 out of 60 in English Language. To find out how many questions she got wrong:
\[
\text{Wrong answers in English} = 60 - 45 = 15
\]
To find the percentage of questions she got wrong:
\[
\text{Percentage wrong} = \left(\frac{\text{Wrong answers}}{\text{Total questions}}\right) \times 100 = \left(\frac{15}{60}\right) \times 100 = 25\%
\]
### 4. Number of Science questions scored wrong
From question 2, we know that she correctly answered 20 science questions out of 30. Thus, the number of wrong answers in Science is:
\[
\text{Wrong answers in Science} = 30 - 20 = 10
\]
### Solving for \( n \)
Given the equation:
\[
4n - 3 = \frac{1}{256}
\]
First, we add 3 to both sides:
\[
4n = 3 + \frac{1}{256}
\]
We can express 3 as a fraction:
\[
3 = \frac{768}{256}
\]
So,
\[
4n = \frac{768 + 1}{256} = \frac{769}{256}
\]
Next, divide both sides by 4:
\[
n = \frac{769}{4 \times 256} = \frac{769}{1024}
\]
Thus, the value of \( n \) is:
\[
\boxed{\frac{769}{1024}}
\]