A bag is filled with blue, green, purple and red chips worth 2, 5, x

To begin, we can factor the given product of the selected chips, 13,689,000, as follows:

\(13,689,000 = \\
= 13,689 * 1000 = \\
= 13,689 * 2^3 * 5^3\)

Notice that, the sum of the digits of 13,689 is 9, indicating that it is divisible by 9:

\(= 1,521 * 9 * 2^3 * 5^3\)

Furthermore, the sum of the digits of 1,521 is also 9, indicating that it is divisible by 9 as well:

\(= 169 * 9^2 * 2^3 * 5^3 = \\
= 13^2 * 9^2 * 2^3 * 5^3\)

Therefore, we can express 13,689,000 as the product of its prime factors: \(2^3 * 3^4 * 5^3 * 13^2\). Since blue chips are worth 2 points, green chips are worth 5 points, and red chips are worth 13 points, we can deduce that 3 blue chips, 3 green chips, and 2 red chips were selected, and that the product of the points of the selected purple chips is equal to 3^4.

It is known that the point value of the purple chips is between that of the green and red chips, meaning that 5 < x < 13. Since the only power of 3 in this range is 9, we can conclude that each purple chip is worth 9 points. Finally, since 3^4 = 9^2, we can determine that 2 purple chips were selected.

Answer: B.

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Hope it helps.