DS- equal and less than

[monal1234]

Is d negative? (1) e + d = -12 (2) e - d < -12

Source- GMAT private tutor question.
I am not sure how to deal with = and < sign. wondering if this could be typo. I researched this over online but never found any DS question like this.

[LazyNK]

Hey Monal,
Such questions can be tackled by converting the inequality to equality by using notations like lt (less than) or gt(greater than) or lte (less than or equal to) or gte (greater than or equal to). I illustrate this in the problem you have provided :

1) e+d=-12 --> Not sufficient as possible if e=-13, d=1 aswell as when e=1, d=-13, so d could be both positive or negative.
2.) e-d < -12 --> Not sufficient as possible when e=-12 and d=1 as well as when e=-14 and d=-1 .

Looking at both statements together :
we need to convert the second inequation to equation.
so e-d< -12 --> e-d=lt(-12) where lt(-12) is a number less than -12.
Thus looking at the equations e+d=-12 and e-d=lt(-12),
we get 2d=-12-lt(-12)=-12 + gt(12), where similar to definition of lt(-12), gt(12) is a number greater than 12. [Note that -lt(-12) = +gt(12)]
-> 2d= gt(12) - 12 > 0 since if we subtract 12 from a number greater than 12, we get a number > 0
-> d> 0
So, both together are sufficient.
-NK

[monal1234]

thank you lot!

[jnelson0612]

Excellent LazyNK! Thanks for helping!