A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16?

Options

A. 2
B. 4
C. 6
D. 8

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the given information
We know that when a number \( n \) is divided by 192, it gives a remainder of 54. This can be expressed mathematically as:
\[ n = 192x + 54 \]
where \( x \) is some integer.

**Hint:** Remember that the remainder is what is left after division, and it must be less than the divisor.

### Step 2: Substitute the expression for \( n \)
Now, we need to find the remainder when this number \( n \) is divided by 16. We can substitute our expression for \( n \):
\[ n = 192x + 54 \]

### Step 3: Divide by 16
Now we will divide the entire expression by 16:
\[ n \div 16 = (192x + 54) \div 16 \]

### Step 4: Simplify the expression
We can separate the terms:
\[ n \div 16 = \frac{192x}{16} + \frac{54}{16} \]
Calculating each part:
- \( \frac{192x}{16} = 12x \)
- \( \frac{54}{16} = 3 + \frac{6}{16} \) (since \( 54 = 48 + 6 \))

So, we can rewrite it as:
\[ n \div 16 = 12x + 3 + \frac{6}{16} \]

### Step 5: Identify the remainder
The term \( 12x \) is an integer, and when we look at \( 3 + \frac{6}{16} \), we can see that:
- The integer part is 3.
- The remainder from \( \frac{6}{16} \) is simply 6.

Thus, when \( n \) is divided by 16, the remainder is:
\[ 6 \]

### Final Answer
Therefore, the remainder when the number is divided by 16 is **6**.

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