askhokha
Is b greater than 1?
(1) b^2 is greater than b
(2) b is positive
According to Kaplan practice set solution the correct answer is 'Together', but I'm leaning towards 'Neither'. As after 1 and 2 are eliminated, To test the statements Together, I picked b=1/2 which yields a 'No' as (1/2)^2 is not greater than 1/2, however if i select another positive such as 2 it yields (2)^2>2 a 'Yes' so in the case of 'Together' the statement produces a 'yes' and 'no' with positive selections for b leading to insufficiency. Can you please explain in detail why Together was selected as the correct answer? I would really appreciate the help!
\(b=\frac{1}{2}\) does not satisfy the first statement so you cannot pick that number when testing whether both statements are sufficient: \((\frac{1}{2})^2=\frac{1}{4}<\frac{1}{2}\).
Is b greater than 1?(1) b^2 is greater than b --> \(b^2>b\)--> \(b(b-1)>0\) --> \(b<0\) or \(b>1\). Hence \(b\) may or may not be greater than 1. Not sufficient.
(2) b is positive --> \(b>0\). Clearly insufficient.
(1)+(2) From the ranges above we have that \(b>1\). Sufficient.
Answer: C.
Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.htmldata-suff-inequalities-109078.htmlrange-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535everything-is-less-than-zero-108884.html?hilit=extreme#p868863P.S. Please read and follow:
rules-for-posting-please-read-this-before-posting-133935.html (rule #3)