Vx and Vy are only meaningful as indicated airspeeds. What's the point of knowing the TAS of your best rate of climb speed, you want to know which speed to fly at, the IAS.
Uses of Vy that I can immediately think of are
1. as a target IAS for fighter pilots trying to gain height as quickly as possible for an interception.
2. as a target IAS on light twins, single engine. Vyse, otherwise known as blue line speed.
There is still an arguement, though. One can prove the EAS of Vx stays the same and the EAS of Vy decreases but, if you're talking CAS, then compressibility slightly increases the CAS of Vx as altitude increases.
In summary, I'm fairly convinced the examiners are assuming Vx and Vy are expressed as an IAS. If they assume IAS = CAS = EAS then the correct answer is that Vx stays the same and Vy decreases, if you assume IAS = CAS but that CAS and EAS are not the same then the answer is that Vx increases slightly and Vy decreases. I have to say I don't understand what is meant by 'for a given TAS' and I'm afraid I don't agree with Keith's option (b) for CAS values.