Is |a| = b − c ?

Question

Is |a| = b − c ?

1) c = a + b

2) a < 0

IanStewart · Answer

Statement 1 is not sufficient, because maybe all the letters equal zero, and the answer to the question is 'yes', or maybe they're other things - say a = 1, b = 2 and c = 3, in which case the answer is 'no' (any numerical example with positive numbers will give a no answer, since it will make b-c negative, and |a| can never equal a negative number).

Using both statements, when a < 0, then |a| is just equal to -a. So the question becomes "Is -a = b - c"?. And if you rewrite Statement 1, we get exactly that, so the two statements together are sufficient.

Using both statements, when a < 0, then |a| is just equal to -a. So the question becomes "Is -a = b - c"?. And if you rewrite Statement 1, we get exactly that, so the two statements together are sufficient.

MahmoudFawzy · Answer

Is  |a| = b − c  ?
the question is asking: is  0\leq{b-c}  ?? ... Is  c\leq{b}  ??

statement 1 :   c = a + b 
 a = c - b 
if  a > 0 , then  c>b  so  NO 
if  a\leq{0} , then  c\leq{b} , so  Yes .
since we don't know the sign of " a " , then   Insufficient

Statement 2:   a < 0 
it gives no info regrading b or c, so   Insufficient  .

but when combining , statement 2 clearly addresses the uncertainty in statement 1, directing to " Yes " --->   Sufficient

IanStewart · Answer

Be careful with how you rephrase DS questions. The question is not  only  asking if b-c is greater than or equal to zero -- that's something that needs to be true for the answer to the question to be 'yes', but it's not the only thing we need to know. We also need to know if b-c is precisely equal to |a|. If instead, the question read:

Is |a| = b - c ?

1. b - c > 0
2. a = 5

Statement 1 would not be sufficient, even though it ensures that b-c is positive. We still wouldn't know if it was exactly equal to |a|, and in fact the answer here would be E, because we don't know if b-c is equal to 5 or to something else.

Chethan92 · Answer

|a| = b-c
If a>0, then |a| = +a = b-c
If a<0, then |a| = -a = c-b

From S1:

c = a+b
or a = c-b.
But, No info about a.
Hence Insufficient.

From S2:

a<0.
No info about b and c.
Insufficient.

Combining both
a<0 and a = c-b.
Sufficient.

C is the answer.

MahmoudFawzy · Answer

Thanks IanStewart for the note. I totally agree with you. You are the Expert

Your strategy is based on picking smart numbers, which is perfect approach. I just wanted to share alternative approach, not to repeat what others already wrote. My approach was to deal with context of the question and highlight the constrain in it, that is, "b-c" must be >= 0 (while "a" has no clue constrain). Anyways, you are right that the constrains may not always be helpful or all used. but if the question is: Is |a| = b - c ? 1. b - c < 0 2. a = 5 the answer would be A, regardless of the value of "a".

CAMANISHPARMAR · Answer

Statement 2 is easier to start with and clearly insufficient.

Statement 1 says that a = c - b and is not sufficient because a < 0 or a = 0 or a > 0. If a = 0 then the statement is true but if a < 0 then the statement is not true.

Combining the two statement gives clarity and gives a definite no. Hence C is the right answer.

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Is |a| = b − c ?

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Is |a| = b − c ?

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