Hi,

The following points will hold you in good stead while solving questions on inequalities.

1. Always break down the question stem

2. Keep the right hand side of the inequality as 0 (This helps in an analysis and will save you the tedious task of plugging in values)

The question here is

'Is 1/(a + b) > b - a?'. Let us break down the question stem by keeping the right hand side 0 and simplifying.

1/(a + b) - (b - a) > 0 Simplifying the left hand side we get

(1 - (b - a)(b + a))/(a + b) > 0 ------>

(1 - (b^2 - a^2)/(a + b)) > 0So now the question can be rephrased as

'Is (1 - (b^2 - a^2)/(a + b)) > 0'Statement 1 : a + b > 0 Here the denominator a + b in (1 - (b^2 - a^2)/(a + b)) is positive, but we have no information whether the numerator is positive or negative. So it is possible for us to get a YES and a NO.

Insufficient.

Statement 2 : b^2 – a^2 > 1The numerator 1 - (b^2 - a^2) will always be negative since b^2 - a^2 is greater than 1, but we have no information about the denominator a + b.

Insufficient.

Combining 1 and 2 :We know that the numerator is negative and the denominator is positive, so the entire term

(1 - (b^2 - a^2)/(a + b)) will always be negative. This gives us a definite NO. Sufficient.Hope this helps!

CrackVerbal Academics Team

_________________

For more info on GMAT and MBA, follow us on @AskCrackVerbal