Explanation:

Let’s break this down:

- We’re looking for the smallest number “N” that gives a remainder of 13 when divided by 16, 21 when divided by 24, and 25 when divided by 28.

- In math speak,

N = 13 (mod 16)

N = 21 (mod 24)

N = 25 (mod 28)

- Notice a pattern: 13 is 16-3, 21 is 24-3, and 25 is 28-3.

- So, N is always 3 less than a multiple of each divisor.

- That means: N+3 is divisible by 16, 24, and 28.

- Find the LCM of 16, 24, and 28:

16 = 2^4

24 = 2^3 × 3

28 = 2^2 × 7

LCM = 2^4 × 3 × 7 = 336

- Now, N + 3 = 336 ? N = 333

- Let’s check your options:

1. 333 (fits perfectly)

2. 336 (gives remainder 0, not the right pattern)

3. 320 (doesn’t match remainder pattern)

4. 348 (doesn’t match)

- The correct answer is Option 1: 333.

-