Guide 2 (Algebra), Inequalities, p133, #2

[Josephined680]

If G^2 < G, which of the following could be G?
(A) 1
(B) 23/7
(C) 7/23
(D) -4
(E) -2

The answer is C, and the solution says that if G^2<G, then G must be positive (since G^2 will never be negative).

However I thought that if there are no parentheses around the negative sign, –2^2 = –4, and then –2>–4. Does "G^2" in the question somehow imply parentheses around G? What am I missing that invalidates options D and E? Thanks!

[Sage Pearce-Higgins]

Yes, when we're given a variable, we can assume that any operation refers to the whole variable, not just part of it. If I state G^2, we can assume that all of G is being squared, not just part of it. Conversely, if G^2 meant that only part of G were being squared, then our system of notation would break down. For that reason we don't need to write parentheses around individual variables.