If 3 days before yesterday was Saturday, then what day of week will it be two days after tomorrow?

Let "today" be the reference point for solving this problem.

3 days before yesterday was Saturday.

Yesterday is 1 day before today.

3 days before yesterday is:

$1 + 3 = 4$ days before today

So 4 days before today was Saturday.

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Counting forward 4 days from Saturday:

Saturday $\to$ Sunday $\to$ Monday $\to$ Tuesday $\to$ Wednesday

Therefore, today is Wednesday.

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Two days after tomorrow means:

Tomorrow is 1 day after today.

2 days after tomorrow is:

$1 + 2 = 3$ days after today

Counting forward 3 days from Wednesday:

Wednesday $\to$ Thursday $\to$ Friday $\to$ Saturday

Therefore, 2 days after tomorrow will be Saturday.

The answer is Option 3: Saturday.