Halve jicama from top to bottom and cut off peel. Put each half, cut side down, on a board and cut it in half through its “equator.” Slice about 1/4-inch thick. Cut largest slices in half so they are roughly the size of the cucumber slices (you’ll need 2 2/3 to 3 cups). Mix jicama, cucumbers and olives in a shallow bowl.
In a small bowl, combine oil, lemon juice, paprika and cumin and whisk to blend. Season to taste with salt, pepper, and cayenne. Add to salad and mix lightly.
Trim excess pith from oranges. Halve oranges from top to bottom. Set, cut side down, on a board and cut in crosswise slices about 1/4-inch thick. Cut each slice in half, removing any pits. Gently mix orange pieces into salad. Taste and adjust seasoning. Serve cold.
Makes four servings.