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

(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

(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

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.

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.

Good day

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.

Answer (C)...

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.

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

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

Answer: C

RELATED VIDEO FROM OUR COURSE

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
So C is answer

Give kudos if it helps

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This is a Yes/No question.

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


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.

(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
Answer C

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