Aptitude Test Question:

In an aptitude test, a student must answer 65% of the questions correctly to qualify. If a student has answered 7 questions correctly out of the first 14, what is the minimum number of questions in the paper?

Solution:

To qualify, the student must answer 65% of the total questions correctly. If the student has answered 7 questions correctly out of 14, this means they have answered 50% of the questions correctly so far.

Let the total number of questions in the paper be x.

Given that 7 questions out of 14 have been answered correctly, the remaining number of questions to answer correctly for qualification = 65% of (x-14).

Equating the number of questions answered correctly so far with the remaining questions needed to answer correctly for qualification:

7 + 0.5(x-14) = 0.65x

Solving the above equation, we get:

7 + 0.5x - 7 = 0.65x

0.5x = 0.65x - 7

0.15x = 7

x = 7 / 0.15

x = 46.67

Therefore, the minimum number of questions in the paper for a student to qualify in the aptitude test is 47 questions.