The minutes and seconds on a 60- minute digital timer are represented by 3 or 4 digits . What is the largest product that can be obtained by multiplying the digits in one of these representations ?
(Note : when the timer displays 16:15 , the product of the digits is (1)(6)(1)(5)=30.)

Options

A. 90
B. `2,025`
C. `3,481`
D. `3,600`

Answer

To find the largest product that can be obtained by multiplying the digits in a digital timer representation (MM:SS), we will follow these steps:

### Step 1: Understand the format of the timer
The timer displays time in the format MM:SS, where MM represents minutes (00 to 59) and SS represents seconds (00 to 59). This means we have a total of 4 digits to work with.

**Hint:** Remember that the maximum values for minutes and seconds are both 59.

### Step 2: Identify the maximum possible digits
The highest digits we can use for minutes and seconds are 5 and 9. Therefore, the maximum representation we can use is 59 minutes and 59 seconds.

**Hint:** Think about how the digits in the timer can be maximized for the best product.

### Step 3: Calculate the product of the digits
For the time 59:59, we have the digits 5, 9, 5, and 9. We can calculate the product as follows:
\[ 5 \times 9 \times 5 \times 9 \]

**Hint:** Break down the multiplication step by step to avoid mistakes.

### Step 4: Perform the multiplication
1. First, calculate \(5 \times 9 = 45\).
2. Next, calculate \(5 \times 9 = 45\) again.
3. Now, multiply the two results: \(45 \times 45\).

**Hint:** Use the square of a number formula if needed: \(a^2 = a \times a\).

### Step 5: Final calculation
Calculating \(45 \times 45\):
\[ 45 \times 45 = 2025 \]

**Hint:** You can also use the distributive property to simplify the multiplication if necessary.

### Conclusion
The largest product that can be obtained by multiplying the digits in a digital timer representation is \(2025\).

**Final Answer:** 2025