Please answer true or false with explanation

Consider a standard Keynesian model but with two types of consumers, first type who have low marginal propensities to consume and second type who have high marginal propensities to consume.

The government wants to stimulate the economy while balancing the budget. If spending is targeted equally on both types of consumers, but taxes are levied in greater amount on second type consumers, then the balanced-budget multiplier will be greater than one.

Answer true or false. Please briefly explain your answer.