Consider a number n=21 P 5 3 Q 4.
The number of values of Q so that the number 'N' is divisible by 8, is

Options

A. 4
B. 3
C. 2
D. 6

Answer

To determine how many values of \( Q \) make the number \( N = 21P53Q4 \) divisible by 8, we need to focus on the last three digits of the number, which are \( 3Q4 \). A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

### Step-by-Step Solution:

1. **Identify the last three digits**: The last three digits of the number \( N \) are \( 3Q4 \).

2. **Set up the divisibility condition**: We need to check for which values of \( Q \) the number \( 3Q4 \) is divisible by 8.

3. **List possible values of \( Q \)**: Since \( Q \) is a digit, it can take values from 0 to 9. Therefore, we will check \( Q = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 \).

4. **Check divisibility for each value of \( Q \)**:
- For \( Q = 0 \): \( 304 \div 8 = 38 \) (divisible)
- For \( Q = 1 \): \( 314 \div 8 = 39.25 \) (not divisible)
- For \( Q = 2 \): \( 324 \div 8 = 40.5 \) (not divisible)
- For \( Q = 3 \): \( 334 \div 8 = 41.75 \) (not divisible)
- For \( Q = 4 \): \( 344 \div 8 = 43 \) (divisible)
- For \( Q = 5 \): \( 354 \div 8 = 44.25 \) (not divisible)
- For \( Q = 6 \): \( 364 \div 8 = 45.5 \) (not divisible)
- For \( Q = 7 \): \( 374 \div 8 = 46.75 \) (not divisible)
- For \( Q = 8 \): \( 384 \div 8 = 48 \) (divisible)
- For \( Q = 9 \): \( 394 \div 8 = 49.25 \) (not divisible)

5. **Count the valid values of \( Q \)**: From the checks above, the values of \( Q \) that make \( 3Q4 \) divisible by 8 are:
- \( Q = 0 \)
- \( Q = 4 \)
- \( Q = 8 \)

Thus, there are **3 valid values of \( Q \)**.

### Final Answer:
The number of values of \( Q \) such that \( N \) is divisible by 8 is **3**.