2 NOL Carryforward questions

I have a 2 part question that I could not understand from Becker/Wiley and I hope someone can explain it to me please.

Company A has the following income and losses and chose to apply carryforward,

Y2 (400) loss

Y3 1,200 income

tax rate is 30% for all years.

for the carryforward to apply to Y3 is Y2 (400) * .30 = 120 DTA

Y2 DTA 120

Benefit due to carryforward 120

Question 1, what is the Y3 total tax expense, had company feels its more like than not that all DTA will be used? (no valuation allowance)

Im told the answer is 360 because its Y2 DTA 120 + Y3 (1200-400) * .30 = 360

Tax expense Now 360

Benefit used 120

DTA 120

Tax payable 360

Why is it that the answer 360, it is because Y2 DTA 120 was used and Y3 240 expense was used?

Are my entries correct?

Question 2, what is the Y3 total tax expense, had company feels its not more likely than not that all DTA will be used? (w/ valuation allowance)

Im told answer is 240, because valuation allowance was used in Y2 that made the 120 DTA obsolete.

Y2 DTA 120

Benefit due to carryforward 120

Benefit due to carryforward 120

Valuation allowance 120

so in Y3, the valuation is reversed and DTA is again, usable.

Tax expense NOW 360

DTA 120

Tax payable 240

Valuation allowance 120

Benefit due to CF 120

WHY is the answer 240 this time? Y2 DTA 120 and Y3 240 current tax ARE used right? shouldnt it be 360 eventhough the valuation reversed?