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1985 AIME Problems/Problem 1

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Problem

Let x_1=97, and for n>1, let x_n=\frac{n}{x_{n-1}}. Calculate the product x_1x_2x_3x_4x_5x_6x_7x_8.

Solution

Since x_n=\frac{n}{x_{n-1}}, x_n \cdot x_{n - 1} = n. Setting n = 2, 4, 6 and 8 in this equation gives us respectively x_1x_2 = 2, x_3x_4 = 4, x_5x_6 = 6 and x_7x_8 = 8 so x_1x_2x_3x_4x_5x_6x_7x_8 = 2\cdot4\cdot6\cdot8 = \boxed{384}.

See also

1985 AIME (Problems • Resources)
Preceded by
First Question 		Followed by
Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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