Is |a| = b – c? (1) c = a + b (2) a

Question

Is |a| = b – c?

(1) c = a + b

(2) a < 0

Bunuel · Accepted Answer

If a<0 it must be true that -a=b-c ; If a\geq{0} it must be true that a=b-c . (1) c=a+b --> -a=b-c . But we don't know whether a<0 . Not sufficient. (2) a<0 . Question becomes is -a=b-c ? We don't know that. Not sufficient. (1)+(2) Form 2: a<0 , question becomes is -a=b-c ? Statement 1 confirms this. Sufficient. Answer: C. (similar topic: abs-equation-from-gmatprep-84821.html)

zisis · Answer

why not (A)?

-a = b-c 
therefore b-c = |a|......

sk818020 · Answer

If b-c=-a, then lal=-(b-c), or c-b=lal, which does not answer our original question, b-c=lal.

Thanks,

Jared

karun0109 · Answer

Is this approach correct?

For ┃a┃ = b – c to be true , (b - c ) >=0 ie positive

(1) c = a + b : for (b - c ) >=0 to be true a needs to be <=0. Not given, hence insufficient
(2) a < 0, says nothing about (b - c ) >=0 Hence insufficient
(1)+(2) proves b - c>=0. Sufficient.

hatemnag · Answer

Hi Bunuel
Actually, I did not understand the concept of statement 2 confirms statement 1.
if the two statements confirmed each other, it means that answer C.
please clarify more regarding the concept. I always fall in the traps of absolute value DS questions.

fiel9882 · Answer

Hi Bunuel, I know this is an old question, but if statement 2 says a is negative can we not answer it because we plug the negative a back into the absolute value in the stem? My thought was that since lal=b-c is either a=b-c or -a=c-b we could say b is sufficient since statement 2 says a is negative. I just don't fully understand the concept.

Bunuel · Answer

The question asks: Is ┃a┃ = b – c.

From (2) we know that a is negative. How this can be sufficient to answer the question whether┃a┃ = b – c?

KrishnakumarKA1 · Answer

Prompt analysis
a ,b, c are real numbers.

Superset
The answer to this question will be either yes or no.

Translation
In order to find the answer, we need:
1# exact value of a, b, c
2# condition or equation, so that we can infer the answer.

Statement analysis
St 1: c = a+b or b-c = -a. The condition might be true if a is negative. But nothing as such is given. INSUFFICIENT

St 2: a<0. Nothing can be said about b and c. Insufficient.
ST 1 &St 2: if a<0, that mean -a is positive and b-c is positive.ANSWER

Option C

AkshdeepS · Answer

Bunuel  : Isn't the question a bit unclear, Bunuel.

It is asking +/- a = b - c. Can a question ask for both positive and negative values.

From 1 we know that b - c = -a, NS as " a" can be positive.

From 2, if we know "a" is negative, isn't it understood that it is equal to "b - c" because it is given in in question?

If b - c = -a , then how statement 2 is adding a new info?

Please help.

Basshead · Answer

Is  |a| = b – c?

(1)  c = a + b 
 -a = b - c 
 \frac{-a}{-1} = \frac{b - c }{ -1} 
 a = - (b - c)

Insufficient.

(2)  a < 0

Noting about b or c. Insufficient.

(1&2) a < 0
thus -(-a) = b - c
|a| = b – c

Sufficient. Answer is C.

CEdward · Answer

Is |a| = b – c?

(1) c = a + b
a = c-b --> | c - b | = b - c
c = 3, b = 1 VIOLATES
c = 1, b = 1 WORKS
Insufficient

(2) a < 0
Clearly insufficient.

Combo:
a = -1, c = 3, b = -4 |a| will never equal b - c
Sufficient.

bumpbot · Answer

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Is |a| = b – c? (1) c = a + b (2) a < 0

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