Is substative test direct related or inversely related to detection risk?

These two MC Questions confuses me, pls help

As the acceptable level of detection risk decreases, the assurance directly provided from:

(a)     Tests of controls should increase.

(b)     Tests of controls should decrease.

(c)     Substantive tests should increase.

(d)     Substantive tests should decrease.

The acceptable level of detection risk is inversely related to the:

(a)     Assurance provided by substantive tests.

(b)     Risk of misapplying auditing procedures

(c)     Preliminary judgment about materiality levels.

(d)   Risk of failing to discover material misstatements.

I would think the 2nd question is (D), in my book it says

Audit Risk = Risk of material misstatement * Detection Risk

So detection risk would be inverse to that.

Think about it like this, If Detection risk is high, it is set high because you have more assurance of the substantive tests, This is because Control risk and inherent risk are LOW. Another way to look at is is you have more assurance from the substantive tests performed when control risk and inherent risks are low.

 So Detection risk is directly related to Substantive tests.

The first question is substantive tests should increase, but you are not getting more assurance from the individual substantive tests performed. That is why you have to do more of them.

What is the correct answer for the 2nd quetion anyway?

According to the Becker material cpa2008 is correct Question 1 is C and Question 2 is A.

For the second question I thought it was D but that wasn't right and that is why I was confused. So this means Detection Risk is inversely related to Substantive and directly related to RMM

Can't say I agree, I would write becker directly, they do make mistakes.  maybe someone else can put in their input.