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(1) e+d = -12 => d = -12-e, however as we don't know anything about e, it could be 1 (thus d=-13) or -13 (thus d=1) = insufficient

(2) e-d < -12 => d > 12+e, again e can be anything => insufficient

(1) + (2) from 1: e=-12-d from 2: e<-12+d together: -12-d < -12+d => -d < +d

this is only true if d is positive.

Therefore: Answer is C

However that's not the text books answer explanation, so I thought I'd ask you guys for your opinion and if there are any flaws in the answer that I overlooked.

(1) e+d = -12 => d = -12-e, however as we don't know anything about e, it could be 1 (thus d=-13) or -13 (thus d=1) = insufficient

(2) e-d < -12 => d > 12+e, again e can be anything => insufficient

(1) + (2) from 1: e=-12-d from 2: e<-12+d together: -12-d < -12+d => -d < +d

this is only true if d is positive.

Therefore: Answer is C

However that's not the text books answer explanation, so I thought I'd ask you guys for your opinion and if there are any flaws in the answer that I overlooked.

Is d negative?

(1) e + d = -12. d can be negative as well as non-negative. For example, consider d=0 and e=-12 and d=-1 and e=-11. Not sufficient.

(2) e – d < -12. d can be negative as well as non-negative. For example, consider d=0 and e=-13 and d=-1 and e=-14. Not sufficient.

(1)+(2) From (1) we have that e = -12 - d, thus from (2) (-12 - d) - d < -12 --> -2d<0 --> d>0. Sufficient.

@e=2, d=-14 We observe that d may be negative @e=-14, d=2 We observe that d may be Positive

NOT SUFFICIENT

Statement 2: e - d < -12

@e=-15, d=1, e-d = -16 i.e. Less than -12 We observe that d may be Positive @e=-15, d=-2, e-d = -13 i.e. Less than -12 We observe that d may be Negative

NOT SUFFICIENT

Combining the Two statements

e = -12-d and e - d < -12 i.e. (-12-d)- d < -12 i.e. (-12-2d) < -12 i.e. 2d > 0 i.e. d is positive

SUFFICIENT

Answer: option C _________________

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Ans: From (1), e + d = -12, we can't tell if d is +ve or -ve ( if positive , e is -ve and more in magnitude than d by 12) From (2), e – d < -12 too, we can't tell. Hence , we put (1) into (2), => Putting e= -12 - d => (-12-d) - d < -12 => -12 - 2d < -12 => d > 0

Hence, statements 1 and 2 together are sufficient to answer the question but not alone.

Statement 1: e + d = -12 Let's TEST some values. There are several values of e and d that satisfy statement 1. Here are two: Case a: d = -6 and e = -6. Notice that e + d = (-6) + (-6) = -12. In this case, the answer to the target question is YES, d IS negative Case b: d = 1 and e = -13. Notice that e + d = (-13) + 1 = -12. In this case, the answer to the target question is NO, d is NOT negative Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: e – d < -12 There are several values of e and d that satisfy statement 2. Here are two: Case a: d = 13 and e = 0. Notice that e - d = 0 - 13 = -13, and -13 < -12. In this case, the answer to the target question is NO, d is NOT negative Case b: d = -5 and e = -20. Notice that e - d = -20 - (-5) = -15, and -15 < -12. In this case, the answer to the target question is YES, d IS negative Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that e + d = -12 Statement 2 tells us that e – d < -12 If e + d = -12, then e = -12 - d Now take e – d < -12 and replace e with -12 - d to get: (-12 - d) – d < -12 Simplify: -12 - 2d < -12 Add 12 to both sides: -2d < 0 Divide both sides by -2 to get: d > 0[since we divided by a NEGATIVE value, we REVERSED the direction of the inequality symbol] So, the answer to the target question is NO, d is NOT negative Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Since number testing is quick, it is advisable to to quickly test some scenarios:-

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We have seen above that Statement 1 & 2 are not sufficient by own. We are down to C vs E

Hence we combine the two statements. Scenario 1 satisfies the conditions but Scenario 2 does not satisfy the conditions. We need to analyse this further. We need a concrete proof before we conclude either way.

Since it is given that e + d = -12; therefore e = -12 - d Statement (2) states that e – d < -12 therefore substitute e = (-12 - d) to get: (-12 - d) – d < -12 Simplification implies that d > 0 or we get a definite "No" to the question "Is d negative?". Hence for both the equations to hold together d have to be positive therefore (C) is sufficient.
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