Recall that income elasticity = percentage change in quantity demanded / percentage change in income.

In this case, income increases by some percent, say, A percent. Since Adella always spends 30% of her income on gizmos, her total expenditure on gizmos must also increase by A percent. We are also told that price of gizmos is constant, so the quantity of gizmos Adella buy must increase by A percent. Applying the formula, income elasticity = A / A = 1.