advanced gmat guide- inequality

[agarwalva]

If a does not = 0, is 1/a > a/(b^4 + 3)

(1) a = b^2
(2) a^2 = b^4

OA A


my Only doubt.. isn't Statement I and Statement II the same

[Stuart@KaplanGMAT]

If a does not = 0, is 1/a > a/(b^4 + 3)

(1) a = b^2
(2) a^2 = b^4

OA A


my Only doubt.. isn't Statement I and Statement II the same

Hi!

The two statements aren't identical, since for (2) a could be the negative root of a^2 and for (1) a is definitely non-negative.

For example, for statement (1) we could pick a=4 and b=2 (since 4 = 2^2).
For statement (2) we could pick those same numbers (since 4^2 = 2^4), but we could also pick a=-4 and b=2 (since (-4)^2 = 2^4).

Remember: when you have an even power in DS, think about the positive and negative solutions!

[neelgandham]

Great explanation by Stuart! but my $0.02

(1) a = b^2
(2) a^2 = b^4,
Implies a^2 - b^4 = 0 .
Implies (a-b^2)*(a+b^2) = 0. [(x^2 -y^2) = (x-y)*(x+y), where x = a and y = b^2)]
Implies (a-b^2) = 0 or (a+b^2) = 0
Implies a = b^2 OR(and a BIG one) a = -b^2

See the difference??