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In the set {-1, 3, 4, 7}, which number has the greatest absolute value?

  1. -1

  2. 0

  3. 3

  4. 7

The correct answer is: 7

This set has a range of values from -1 to 7, but the absolute value of a number only looks at the distance from 0. Since 7 is the furthest from 0, it has the greatest absolute value out of the set. Option A is incorrect because -1 has a lower absolute value than 7. Option B is incorrect because 0 does not have a location or value in the set. Option C is incorrect because while 3 is a higher value than -1, its absolute value is not as great as 7's. Therefore, option D is the correct answer.