Macroeconomics question help

Hello, I am new here. I am having some trouble understanding this problem

If APS is .2 and MPS is .10, a simultaneous increase in both taxes and government spending of $30 billion will:

(a) reduce consumption by $27B, increase government spending by $27B, and increase GDP by $30B

(b) reduce consumption by $27B, increase government spending by $27B, and increase GDP by $27B

(c) reduce consumption by $24B, increase government spending by $30B, and increase GDP by $30B

(d) reduce consumption by $24B, increase government spending by $24B, and increase GDP by $24B

The answer in the study guide says (A) is the answer. I understand the first part (consumption goes down $27B) as well as the third part (Real GDP goes up by $30B), but I can't for the life of me understand the 2nd part.

In order for Real GDP to increase by $30B when a $30B tax is imposed, Gov't spending must increase by $30B. This is according to the Balanced Budget multiplier. I think answer (A) has a typo, but I can't be sure.

Therefore, why does the answer say Gov't spending only goes up by $27B? As far as I know, tax increase will cause Consumption to go down by $27B and Savings to go down by $3B. Gov't increasing their spending shouldn't have anything to do with MPS/MPC right?

Can anyone shed some light on this for me?

Thanks!

A large MPS means larger savings, this causes the multiplier to have a smaller effect than needed, so to off set the savings increase (which shrinks the money supply) the government must increase spending in order to boost GDP. In other words, the more people save the smaller the money supply is, so the government spends to increase GDP.