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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Find the integers x and y such that:

equation

What is the absolute value of the product of the smallest value you found for x and the largest value you found for y?

By extracting the square root, we obtain absolute values of the expressions:

equation

Since absolute values cannot be negative numbers, we have the following possibilities:

equation

equation

or

equation

equation

or

equation

equation

or

equation

equation

The smallest value for x is -5. The largest value for y is 6. The required product is -30 and its absolute value is 30.