Step 1Cut the cucumbers in half lengthwise, then slice the halves 1/4-inch thick.
Step 2Halve the jicama from top to bottom and cut off the peel. Put each half cut side down on a cutting board and cut each half in half through its "equator." Cut the pieces into slices about 1/4-inch thick. Cut the largest slices in half so they are roughly the size of the cucumber slices. (You'll need 2 2/3 to 3 cups.)
Step 3Mix the jicama, cucumbers and olives in a shallow bowl.
Step 4In a small bowl combine the olive oil, lemon juice, paprika and cumin and whisk to blend. Season to taste with salt, pepper and cayenne. Add the dressing to the salad and mix lightly.
Step 5Trim excess pith from the oranges. Halve the oranges from top to bottom. Set the cut sides down on a cutting board and cut them in crosswise slices about 1/4-inch thick. Cut each slice in half, removing any pits. Gently mix the orange pieces into the salad. Taste and adjust the seasoning. Serve cold.