D's Negativity

[housE]

Hey guys, I don't understand the below answer of C. I have tried plugging in numbers to test if it can be C and I still get E each time. Can someone explain this to me?

Or is there a shorter way to combine the two givens for C?

Thanks!
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# 34) 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.

[poojakrishnamurthy1]

Ofcourse with (A) and (B) you don't get a clear answer. I think you can do this question without plugging values. Lets see -

The equation in (1) is e + d = -12. If I multiply this equation with -1, it becomes : - e - d = 12

The equation in (2) is an inequality and let it be as it is.

Add equation in (1) with that in (2)

-e - d = +12

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

OR

d > 0

Since by combining both the equation you get a definite NO, the answer is C. Hope this helps.

(Remember that when you add an equality to an inequality, the resultant equation is an inequality)

[housE]

Thanks for this!

[esledge]

Yes, thanks Poojakrishnamurthy1!

On DS, I too prefer to do as much algebraic manipulation as possible before plugging values. As you showed, one can often manipulate to the point that you don't need to plug, and you gain absolute certainty in your answer as a result. An exception to this practice is when I suspect insufficiency on a Y/N question, and can quickly come up with a Yes case and a No case to plug. Certainly don't pick E on a problem like this unless you have either completed the algebra or plugged to get both Y and N answers.