D's Negativity (Positives & Negatives )

[alecm666]

Is d negative?

(1) e + d = -12

(2) e – d < -12
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Explanation:
The question asks about the sign of d.

(1) INSUFFICIENT: When two numbers sum to a negative value, we have two possibilities:

Possibility A: Both values are negative (e.g., e = -4 and d = -8)
Possibility B: One value is negative and the other is positive.(e.g., e = -15 and d = 3).

(2) INSUFFICIENT: When the difference of two numbers produces a negative value, we have three possibilities:

Possibility A: Both values are negative (e.g., e = -20 and d = -3)
Possibility B: One value is negative and the other is positive (e.g., e = -20 and d = 3).
Possibility C: Both values are positive (e.g., e = 20 and d = 30)

(1) AND (2) SUFFICIENT: When d is ADDED to e, the result (-12) is greater than when d is SUBTRACTED from e. This is only possible if d is a positive value. If d were a negative value than adding d to a number would produce a smaller value than subtracting d from that number (since a double negative produces a positive). You can test numbers to see that d must be positive and so we can definitively answer the question using both statements.
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My questions:
1# Is d negative? (I have changed the -12 to +12)

1. e+d = +12
2. e-d < +12

Should the answer be C still?
=> my interpretation: d must be positive, and e can be positive or negative.


2# If I switch the "<" to ">",
1. e+d = +12
2. e-d > +12
is it true that e must now be positive and d must be negative?

[RonPurewal]

My questions:
1# Is d negative? (I have changed the -12 to +12)

1. e+d = +12
2. e-d < +12

Should the answer be C still?
=> my interpretation: d must be positive, and e can be positive or negative.

you're correct about the sign of "d", which, of course, is the only thing that matters here.

as for "e", it's true that "e" can have any sign (positive, zero, or negative)-- but "e" has to be less than 12. (it's not clear from your wording whether you figured this out, although, since "e" is immaterial to the actual problem, it's ok if you didn't.)

[RonPurewal]

2# If I switch the "<" to ">",
1. e+d = +12
2. e-d > +12
is it true that e must now be positive and d must be negative?

yes.

in fact, "e" is further restricted: it must be greater than 12. (again, this is immaterial to the problem at hand, though it's instructive to consider when reviewing.)