In `357 xx 265 xx 239 xx 1352`, the last two digits are?

Options

A. 20
B. 33
C. 40
D. 45

Answer

To find the last two digits of the product \( 357 \times 265 \times 239 \times 1352 \), we can follow these steps:

### Step 1: Understand the Problem
We need to find the last two digits of the product, which means we need to calculate the product modulo 100.

### Step 2: Calculate Each Number Modulo 100
We will calculate each number modulo 100:
- \( 357 \mod 100 = 57 \)
- \( 265 \mod 100 = 65 \)
- \( 239 \mod 100 = 39 \)
- \( 1352 \mod 100 = 52 \)

### Step 3: Multiply the Results
Now we will multiply the results we obtained in the previous step:
1. First, multiply \( 57 \) and \( 65 \):
\[ 57 \times 65 = 3705 \]
Now, find \( 3705 \mod 100 \):
\[ 3705 \mod 100 = 05 \]

2. Next, multiply the result with \( 39 \):
\[ 5 \times 39 = 195 \]
Now, find \( 195 \mod 100 \):
\[ 195 \mod 100 = 95 \]

3. Finally, multiply the result with \( 52 \):
\[ 95 \times 52 = 4940 \]
Now, find \( 4940 \mod 100 \):
\[ 4940 \mod 100 = 40 \]

### Step 4: Conclusion
The last two digits of the product \( 357 \times 265 \times 239 \times 1352 \) are \( 40 \).

### Final Answer
Thus, the last two digits are **40**.

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