Anita’s Mathematics test had 70 problems carrying equal marks i.e., 10 Arithmetic, 30 Algebra and 30 Geometry. Although she answered 70% of the Arithmetic, 40% of the Algebra and 60% of the Geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is:

The correct option is 5.

Let's break down the problem and find the step-by-step solution to understand why this is the correct answer.

Step 1: Calculate the total marks and the passing requirement.
The test has a total of 70 problems, each carrying equal marks. Let's assume each problem carries 1 mark. Therefore, the total maximum marks for the test is 70.
To pass the test, Anita needs to secure at least 60% of the total marks.
We can calculate the required passing marks as follows:
$$\text{Passing Marks}=60\%\text{of}70=\frac{60}{100}\times 70=42$$
So, Anita needs to answer at least 42 questions correctly to pass the test.

Step 2: Calculate the number of questions Anita answered correctly.
Anita answered a certain percentage of questions correctly in each of the three sections:
1. Arithmetic: She answered 70% of the 10 Arithmetic questions correctly.
$$\text{Correct Arithmetic Answers}=70\%\text{of}10=\frac{70}{100}\times 10=7$$
2. Algebra: She answered 40% of the 30 Algebra questions correctly.
$$\text{Correct Algebra Answers}=40\%\text{of}30=\frac{40}{100}\times 30=12$$
3. Geometry: She answered 60% of the 30 Geometry questions correctly.
$$\text{Correct Geometry Answers}=60\%\text{of}30=\frac{60}{100}\times 30=18$$
Now, let's find the total number of questions she got correct:
$$\text{Total Correct Answers}=7+12+18=37$$
So, Anita currently has 37 correct answers.

Step 3: Calculate the additional correct answers needed.
To find out how many more questions she would need to answer correctly to reach the passing marks (42), we subtract her current correct answers from the required passing marks:
$$\text{Additional Correct Answers Needed}=42-37=5$$
Thus, Anita needs to answer 5 more questions correctly to earn a passing score of 60%.