Motivation and IQ scores

Thought experiment

If we had a group of kids from a poorer part of town and we offered a reward to be distributed only to the kids who scored high on an IQ test, would the IQ test results rise in the poorer part of town?

How important is motivation to not just IQ test scores but any test score? If we set up a system where people are given cash rewards for achieving high scores would this be more effective for measuring competence than to rely on cultural bias toward intrinsic motivation?