OG Query - Quantitative review 2nd edition

I am preparing for Quant using the 2nd edition of Quantitative review 2nd edition.

Could someone please explain the solution for the 75th problem?

Question - Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, Sam and Tina are all alive 4 years from today, which of the following must be true on that day?
1. Rose is twice as old as Sam.
2. Sam is 3 years younger than Tina
3. Rose is older than Tina

My understanding is both 2 and 3 must be true.

OG solution

Let R, S and T be the ages of Rose, Sam and Tina.
Today
Rose - 2S
Sam - S
Tina - S + 3

4 years from today
Rose - 2S + 4
Sam - S + 4
Tina - S + 3 + 4 = S + &

Four years from today, Rose will be older than Tina only if 2S + 4 > S + 7 or only if S > 3. Therefore, depending on how old Sam is today, option 3 need not be true

But my understanding is that Sam must be at least 4 years old 4 years from now and hence option 3 must also be true.

Someone please confirm this for me.

Regards,
Bala