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Intern  Joined: 05 Mar 2014
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Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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Question Stats: 66% (01:44) correct 34% (01:48) wrong based on 302 sessions

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Is d negative?

(1) e + d = -12

(2) e – d < -12

(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.

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 61508
Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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jumli wrote:
Is d negative?

(1) e + d = -12

(2) e – d < -12

(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.

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.

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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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jumli wrote:
Is d negative?

(1) e + d = -12

(2) e – d < -12

Question : Is d < 0?

Statement 1:e + d = -12

@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

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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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(1) e + d = -12
(2) e - d < -12

1 and 2 alone are not possible.

Together e - d<e + d since -12 = e + d
0<2d or 0<d is positive . Ans C
Intern  Joined: 25 Aug 2015
Posts: 5
Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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(1) is not enough

(2) e+12<d is not enough

(1)&(2) we know from (1) that e+12+d=0 and we know from (2) e+12<d. Therefore, we can say that d+d>0=> d>0

In my opinion, the answer is c

I may have simplified the question too much, but this is how I solved it
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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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the problem is not hard, and since I have completed all set of quantitative quiz from one of members in the forum, i can solve this problem easily.
Intern  B
Joined: 15 May 2017
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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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

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.

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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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jumli wrote:
Is d negative?

(1) e + d = -12

(2) e – d < -12

Is $$d$$ negative? (Its a YES/NO Question.)

(1) $$e + d = -12$$

$$e = -12 - d$$ -------- (i)

We cannot find value of $$e$$ or $$d$$. Hence I is Not Sufficient.

(2) $$e – d < -12$$

We cannot find value of $$e$$ or $$d$$. Hence II is Not Sufficient.

Combining (1) and (2)

Substituting value of $$e$$ from (i) in (2), we get;

$$-12 -d -d < -12$$

$$-2d < 0$$

$$2d > 0$$

$$d > 0$$

Therefore $$d$$ is positive.

Combining (1) and (2), we get the Answer to question is $$d$$ negative is NO.

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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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Both statements alone are not sufficient. If you plug in statement one in statement you get -2d<0. Therefore d is >0. Answer c is correct.
Math Expert V
Joined: 02 Aug 2009
Posts: 8257
Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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shringi87 wrote:
Is d negative?

(1) e + d = -12
(2) e – d < -12

1) e+d=-12
If e <-12, d will be >0....and NO
If e>-12, d Will be negative...YES
Insufficient

2) e-d<-12
d>e+12..
If e=-12, d>0
If e=-15, d can be > or <0..
Insufficient

Combined..
From 1) e=-d-12..
So -d-12-d<-12.......-2d<0....2d>0..
Sufficient as and is NO
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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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Top Contributor
jumli wrote:
Is d negative?

(1) e + d = -12

(2) e – d < -12

Target question: Is d negative?

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

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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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Both I and II statements are not giving answers...

Only after combining two
Putting equation 1 in 2
We get
-2d<0

I.e. d>0

Give kudos if it helps

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Joined: 11 Feb 2015
Posts: 1036
Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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This is a Yes/No question.

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

Attachment: 2018-06-27_23-48-51.jpg [ 184.98 KiB | Viewed 2240 times ]

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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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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(1) e=1; d=-13
e=-13; d=1
Insufficient

(2) e=-13; d=1
e=-14; d=-1
Insufficient

(1) and (2)
-12-d-d < -12
-2d < 0
d>0
Sufficient
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Re: Is d negative? (1) e + d = -12 (2) e – d < -12  [#permalink]

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