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

I get the explanation given in the test solution. However, if I do it my way I cannot figure out where I'm going wrong. It has happened to me before as well when I try to rephrase an inequality type DS question and things fall apart. Is there a rule which I'm missing -- can we not rephrase a DS inequality question?

My method when trying to solve for (C)

1) d = -12 -e
2) -d < -12 - e which is
d > 12 + e

Let's assume if e = 15 then
st1 is -ve and st2 is + ve


If e is -15 then
st1 is +ve and d>-3

Hence I chose "E". Ans is C. Please explain.

e + d = -12 doesn't tell much
e-d < -12 , not suff.

From 1, e = -12-d, replace in 2

12-d-d < -12
-2d < -12+12
-2d < 0

So d is positive. C is the answer.

Problem is process: if you're looking at both statements together, you have to accept that both statements are true. So it's fine to try random numbers, but you can only try numbers that make both statements true and you have to use the same numbers for d and e for both equations.

If you pick e = 15, then according to the first equation, that makes d = -27. We have to now keep those exact same values for statement 2 - we have set those values now and the variables don't change. So that would make statement 2 read: -27 > 12 + 15. Which is not true, so the combination of e=15 and d=-27 is not a valid combo to try for the two statements together.

Make sure you have this straight before you take the test or it will cost you a lot of points!

Also, the better way to approach this one, in my opinion, is the algebraic approach anadi showed, so that you can get a definitive answer. It's always harder to try random numbers when you are dealing with multiple equations rather than simpler expressions - too easy to make the kind of conceptual mistake you made, and not terribly easy to pick number combos that are valid (in terms of making both statements true).