The question says :
a < -1
or, a is any negative number less than -1

Statement 1 :
-b < -a
or, b > a (multiplying both sides by negative changes the inequality sign)
so, b can be any number greater than -1................. NOT SUFFICIENT

Statement 2 :
-1 < ab < 0
ab is negative fraction.
Since a < -1 so b has to be between 0 and 1 to give a negave fraction........ SUFFICIENT

Ans : B

Rezinka wrote:The question says :
a < -1
or, a is any negative number less than -1


Statement 2 :
-1 < ab < 0
ab is negative fraction.
Since a < -1 so b has to be between 0 and 1 to give a negave fraction........ SUFFICIENT

Ans : B

Great method. If you can't see why b has to a fraction for ab to be a negative fraction, use the same principle of flipping the sign when multiplying/dividing by a negative value. Since you know that a is definitely negative, you can turn -1<ab into
-1/a > b (divide by a to isolate b, flip the sign because of div by negative).

since a is negative, the fraction -1/a is positive, and since a is smaller than -1 (e.g. -2, -3, -4), -1/a must be a positive FRACTION (1/2, 1/3, 1/4, respectively). b must therefore be smaller than a fraction byt still positive, leaving b as a number between 0 and 1.

another way to look at it...

ofcourse by now u agree that statement 1 is insufficient..
so i will just concentrate on statement 2...

-1<ab<0

we already know that a<-1 and negative...

so we can divide the equation -1<ab<0 by a and keeping in mind that a is -ve...

1/a > b > 0 ... ( flip the sign because a is -ve and the negative sign is removed )

now 1/a will always be a fraction < 1 since a's absolute value is always > 1
so b will be less than 1 and greater than 0...