MathRevolution wrote:
[GMAT math practice question]
Is \(1+x+x^2+x^3+x^4<\frac{1}{(1-x)}\)?
(1) \(x>0\)
(2) \(x<1\)
In case one doesn't know about or remember the GP series as explained by
chetan2u, then you can use below approach -
\(1+x+x^2+x^3+x^4<\frac{1}{(1-x)}\)---------------(1)
Case 1: \(x>1\), for eg. \(x=2\), then LHS of the above inequality will be greater than \(2\)
but RHS of inequality (1) will be negative. So we have a
NO for this case
Case 2: \(0<x<1\), for eg. \(x=\frac{1}{2}\), then LHS of inequality will be \(1+0.5+0.25+0.125+0.0625<2\)
but RHS of the inequality will be \(\frac{1}{(1-0.5)}=2\). So we have a
YES for this case
Case 3: \(x<0\), for eg. \(x=-1\), then LHS of the inequality will be \(1-1+1-1+1=1\)
but RHS of the inequality will be \(\frac{1}{(1+1)}=0.5\). So we have a
NO for this case
With these understandings, we can now check the statements
Statement 1: from this statement, both Case 1 & Case 2 are possible. Hence we have a Yes & a No.
InsufficientStatement 2: from this statement, both Case 2 & Case 3 are possible. Hence we have a Yes & a No.
InsufficientCombining 1 & 2, we have \(0<x<1\), so only Case 2 possible, hence we have a
Yes.
SufficientOption
C