"Exact Powers" problem

[am.harel]

Problem reads:
Is x > 10^10?

(1) x > 2^34

(2) x = 2^35

In the explanation, it reasons that because 2^10=1024, which is greater than 10^3, you can substitute 10^3 for it. I do not understand why that is a logical step to take. Why should you be able to substitute a smaller number for a bigger one, especially when the question is telling you that x is greater than that number?

Thanks

[tim]

if you know that x > 2^10, then you can definitely say that x > 10^3. use the transitive property if you need to:

x > 2^10
AND
2^10 > 10^3
THEREFORE
x > 10^3

now sub in as many 10^3's as you need for 2^10's, and if you get a yes you're fine. in a substitution like this though, you need to watch out for inconclusive results though..