Answer Key for AFCAT Numerical Ability Section:

Introduction:
The AFCAT (Air Force Common Admission Test) is a highly competitive exam conducted by the Indian Air Force for the selection of officers in various branches. The numerical ability section of AFCAT assesses the quantitative aptitude of candidates. Here is the answer key for the numerical ability section with detailed solutions:

Question 1:
Find the value of x in the equation 3x + 5 = 20.

Solution:
To find the value of x, we need to isolate it on one side of the equation. Follow these steps:

1. Subtract 5 from both sides of the equation:
3x + 5 - 5 = 20 - 5
3x = 15

2. Divide both sides of the equation by 3:
3x/3 = 15/3
x = 5

Therefore, the value of x in the given equation is 5.

Question 2:
Simplify the expression (4^2 * 2^3) / (2^2 * 3^2).

Solution:
To simplify the expression, we can apply the laws of exponents. Follow these steps:

1. Simplify the numerator:
4^2 * 2^3 = 16 * 8 = 128

2. Simplify the denominator:
2^2 * 3^2 = 4 * 9 = 36

3. Divide the numerator by the denominator:
128 / 36 = 16/4 = 4

Therefore, the simplified value of the expression is 4.

Question 3:
Find the average of the numbers 12, 18, 24, and 30.

Solution:
To find the average, we need to sum up all the numbers and divide the sum by the total count. Follow these steps:

1. Add all the numbers:
12 + 18 + 24 + 30 = 84

2. Divide the sum by the total count:
84 / 4 = 21

Therefore, the average of the given numbers is 21.

Conclusion:
In this answer key, we provided solutions for three numerical ability questions from the AFCAT exam. It is essential to practice these types of questions to improve your quantitative aptitude skills. Keep practicing and refer to reliable study materials like EduRev to enhance your preparation for the AFCAT exam. Good luck!