Inequalities Problem

[pravin22jd]

This problem is from MGMAT Algebra Strategy Guide:

If AB/7 > 1/14 and A=B While of the following must be greater than 1 ?
a) A+B
b) 1-A
c) 2A^2
d) A^2-1/2
e) A

OA is C but It seems A also satisfies this condition...

I calculated it as below;
AB/7 > 1/14
multiplying both sides by 14
2AB > 1
as A=B
2A^2 >1 and 2 B^2 > 1
Option (C) is true as per this logic
While analyzing other options this is what I got...
2A^2>1
A^2>1/2
A>1/sqrt(2)
as A=B, B >1/sqrt(2)

so A+B > 1/sqrt(2) + 1/sqrt(2)
A+B > 2/sqrt(2)
A+B > sqrt(2)
This is also going to be greater than 1

[ch339]

I think A = B > 0 or A = B < 0, since all we're told is that AB must be positive and greater than 1/2. I couldn't sleep. Sorry if I'm overstepping.

[RonPurewal]

Yep. We know the product of A and B is positive, but that tells nothing about whether A and B, individually, are positive or negative. They could both be positive; they could both be negative.