In a code language 'ACE' is written as 1925 and BIG' is written as '48149', then in the same language, 'DOG' will be written as:

Question

Accepted Answer

To solve the problem of determining how 'DOG' is written in the given code language, we need to understand the pattern used to encode the words 'ACE' and 'BIG'.

### Explanation of the Code Pattern:

1. **ACE = 1925:**
   - A = 1 (Position in alphabet)
   - C = 3 (Position in alphabet)
   - E = 5 (Position in alphabet)
   - The code '1925' can be broken down as follows:
     - 1 (A) is squared to get 1
     - 3 (C) is squared to get 9
     - 5 (E) is squared to get 25
   - Therefore, 'ACE' is encoded as 1925.

2. **BIG = 48149:**
   - B = 2 (Position in alphabet)
   - I = 9 (Position in alphabet)
   - G = 7 (Position in alphabet)
   - The code '48149' can be broken down as follows:
     - 2 (B) is squared to get 4
     - 9 (I) is squared to get 81
     - 7 (G) is squared to get 49
   - Therefore, 'BIG' is encoded as 48149.

### Encoding 'DOG':

- D = 4 (Position in alphabet)
- O = 15 (Position in alphabet)
- G = 7 (Position in alphabet)

Following the pattern:
- 4 (D) squared is 16
- 15 (O) squared is 225
- 7 (G) squared is 49

Thus, 'DOG' is encoded as 1622549.

### Justification for Option 3:

- **Option 3: 1622549** correctly represents the squared values of the positions of D, O, and G in the alphabet, following the pattern established by the examples.

### Explanation of Incorrect Options:

1. **Option 1: 41549**
   - This does not follow the pattern of squaring the positions of the letters. It incorrectly suggests a different encoding.

2. **Option 2: 162259**
   - This option misses the correct squared value for 'O', which should be 225, not 22.

3. **Option 4: 1622249**
   - This option incorrectly represents the squared value of 'O' as 22 instead of 225.

In conclusion, Option 3 (1622549) is the correct encoding for 'DOG' based on the established pattern of squaring the positions of the letters in the alphabet.