In the market for sweaters, suppose Green's price elasticity of demand is 0.4, Smith's price elasticity is 1.4, and the price elasticity of all the other consumers is greater than 0.4 but less than 1.4. Could the market price elasticity be less than 0.4 or greater than 1.4?

No, the market price elasticity of demand for sweaters must be between 0.4 and 1.4 because the question is telling us that all customers have a price elasticity in that range, not only Green and Smith.

This elasticity numbers means that the market for sweaters goes from moderately inelastic (the values ranging from 0.4 to 1) to moderately elastic (the values ranging from 1 to 1.4).