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:

Correct Option (B)

The mathematics test consisted of 70 problems, with each problem carrying equal marks. Assuming each question is worth 1 mark, the total possible marks for the test are 70.

To achieve a 60% passing mark, the required score is calculated as:

Passing Marks = 60% of 70 = (60/100) × 70 = 42 marks.

Anita's performance in each section is detailed as follows:

• Arithmetic: 70% of 10 problems = (70/100) × 10 = 7 problems answered correctly.
• Algebra: 40% of 30 problems = (40/100) × 30 = 12 problems answered correctly.
• Geometry: 60% of 30 problems = (60/100) × 30 = 18 problems answered correctly.

Anita's total marks obtained from correctly answered problems are:

Total Marks Obtained = 7 (Arithmetic) + 12 (Algebra) + 18 (Geometry) = 37 marks.

To determine the number of additional questions Anita needed to answer correctly to reach the passing threshold, the difference between the passing marks and her obtained marks is calculated:

Additional Questions Required = Passing Marks - Total Marks Obtained = 42 - 37 = 5 questions.

Therefore, Anita would have needed to answer 5 more questions correctly to achieve a 60% passing mark.

Incorrect Options:

Options A (1), C (7), and D (9) are incorrect. These values do not align with the precise calculation required to determine the difference between the 60% passing score (42 marks) and Anita's actual score (37 marks). The accurate calculation indicates that 5 additional correct answers were necessary.