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Manager  Joined: 11 Jul 2010
Posts: 183
Is |a| = b - c ?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 61% (01:39) correct 39% (01:35) wrong based on 270 sessions

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Is |a| = b - c ?

(1) a + c is not equal to b
(2) a < 0

Don't get how it can be C. Shouldn't it be E? (1), (2) not sufficient. (1)+(2); lets say b = 6; c = 3; then a = -3 satisfies and gets a "Yes" but a=-10 satisfies and gets a "No"

Originally posted by gmat1011 on 25 Nov 2010, 01:40.
Last edited by gmatbusters on 23 Sep 2018, 09:13, edited 2 times in total.
Edited the OA.
Math Expert V
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Re: Is |a| = b - c ?  [#permalink]

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3
1
gmat1011 wrote:
Is |a| = b - c ?

(1) a + c is not equal to b
(2) a<0

C/right Jeff Sackmann. Just posting it here for educational purposes.

Don't get how it can be C. Shouldn't it be E? (1), (2) not sufficient. (1)+(2); lets say b = 6; c = 3; then a = -3 satisfies and gets a "Yes" but a=-10 satisfies and gets a "No"

Is $$|a|=b-c$$ true? Now, if $$a\geq{0}$$, the question becomes "is $$a=b-c$$ true?" and if $$a\leq{0}$$, the question becomes "is $$-a=b-c$$ true?".

(1) $$a+c\neq{b}$$ --> $$a\neq{b-c}$$, we cannot answer No to the question as we don't know whether $$a>0$$. Not sufficient.

(2) $$a<0$$, so the question becomes is $$-a=b-c$$, but we don't know that. Not sufficient.

(1)+(2) From: $$a\neq{b-c}$$ and $$a<0$$ we can not determine whether $$-a=b-c$$ is true. For example if $$a=-1$$, $$b=1$$ and $$c=0$$ then answer to the question will be YES but if $$a=-1$$, $$b=1$$ and $$c=1$$ then answer to the question will be NO. Not sufficient.

Answer: E.

gmat1011 wrote:
Don't get how it can be C. Shouldn't it be E? (1), (2) not sufficient. (1)+(2); lets say b = 6; c = 3; then a = -3 satisfies and gets a "Yes" but a=-10 satisfies and gets a "No"

I think that there might be a typo in statement (2) and it should read $$a>0$$ (instead of $$a<0$$), then for (1)+(2) we would have: as from (2) $$a>0$$ then the question becomes "is $$a=b-c$$ true?" and (1) ($$a\neq{b-c}$$) directly gives us the answer NO. In this case answer would indeed be C.

Hope it's clear.
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Re: Is |a| = b - c ?  [#permalink]

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yes = many thank bunuel.. that makes sense... but condition 2 is a<0 in the problem set so I think it may be a typo in the problem itself. Thanks.
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Re: Is |a| = b - c ?  [#permalink]

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2
1
Ques: Is |a| = b - c or 'Is |a| + c = b'?

1) a + c not equal to b
There are two possibilities: a is positive or 0. Then if a + c is not equal to b, |a| + c will also not be b because a = |a|.
If a is negative, then there is still a chance that |a| + c = b
e.g. a = -4, c = 2 and b = 6, then a + c is not equal to b but |a| + c = b.
But a could also be a random number e.g. a = -3, c = 2, b = 6
Then a + c is not equal to b and |a| + c is also not equal to b.

2) a < 0
As we said, if a < 0, it is not sufficient to say whether |a| + c = b.

If someone didn't put enough thought in the question, it might seem as if both statements are not sufficient together and one might mark it as (E) and still get the correct answer. But, if the second statement said a > 0, one would have to think through to get to the answer (C).
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Originally posted by VeritasKarishma on 25 Nov 2010, 22:26.
Last edited by VeritasKarishma on 26 Nov 2010, 06:29, edited 1 time in total.
Manager  Joined: 11 Jul 2010
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Re: Is |a| = b - c ?  [#permalink]

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agreed karishma, but can an OA of C go with condition 2 written as a<0? i thought bunuel's point was that that (can you have 2 'thats' in a row in the gmat world!) cannot happen and there is a typo in the problem.

So the way the question stands the OA of C is wrong. So in fact if you marked C to the problem and got the 'right' answer then in fact you would be wrong as the answer should be E if a<0

you are saying the same thing, right? Thanks!
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Re: Is |a| = b - c ?  [#permalink]

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1
gmat1011 wrote:
agreed karishma, but can an OA of C go with condition 2 written as a<0? i thought bunuel's point was that that (can you have 2 'thats' in a row in the gmat world!) cannot happen and there is a typo in the problem.

So the way the question stands the OA of C is wrong. So in fact if you marked C to the problem and got the 'right' answer then in fact you would be wrong as the answer should be E if a<0

you are saying the same thing, right? Thanks!

Yes, as the question stands the OA cannot be (C). The answer will be (E). In case the second statement goes to a > 0, then the OA will be (C) and will match the official OA. That will make the question more interesting.
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Re: Is |a| = b - c ?  [#permalink]

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1
sujit2k7 wrote:
Is |a|= b - c ?

(1) a + c # b

(2) a < 0

Not satisfied with the OA..need ur inputs..I though the ans is E

Go straight to (1) and (2):
Nothing is stated about the difference $$b-c.$$ If $$b-c<0$$, the answer is a definite NO. Absolute value cannot be negative.
If $$b-c>0$$, the answer can be YES or NO. Consider the following examples:
$$a=-2, b-c=2$$ and $$a=-2, b-c=5.$$

Answer is E.
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Re: Is |a| = b - c ?  [#permalink]

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statement 1 : a=b-c here a can be positive or negative --> so insufficient

statement 2 : we know a is negative but is a=b-c ? (not given) so insuff

combing 1 and 2 :

we know a is a negative number a=-(something)
a=-(b-c) ....therefoer |a|=b-c ... hence c....
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Re: Is |a| = b - c ?  [#permalink]

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abhi398 wrote:
statement 1 : a=b-c here a can be positive or negative --> so insufficient

statement 2 : we know a is negative but is a=b-c ? (not given) so insuff

combing 1 and 2 :

we know a is a negative number a=-(something)
a=-(b-c) ....therefoer |a|=b-c ... hence c....

NO, the answer cannot be C. We know nothing about $$b-c$$, it can be positive or negative or even 0!
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Re: Is |a| = b - c ?  [#permalink]

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EvaJager wrote:
abhi398 wrote:
statement 1 : a=b-c here a can be positive or negative --> so insufficient

statement 2 : we know a is negative but is a=b-c ? (not given) so insuff

combing 1 and 2 :

we know a is a negative number a=-(something)
a=-(b-c) ....therefoer |a|=b-c ... hence c....

NO, the answer cannot be C. We know nothing about $$b-c$$, it can be positive or negative or even 0!

but from statement 2 we know that a is negative ... therefore (b-c ) has to be negative
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Re: Is |a| = b - c ?  [#permalink]

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abhi398 wrote:
EvaJager wrote:
abhi398 wrote:
statement 1 : a=b-c here a can be positive or negative --> so insufficient

statement 2 : we know a is negative but is a=b-c ? (not given) so insuff

combing 1 and 2 :

we know a is a negative number a=-(something)
a=-(b-c) ....therefoer |a|=b-c ... hence c....

NO, the answer cannot be C. We know nothing about $$b-c$$, it can be positive or negative or even 0!

but from statement 2 we know that a is negative ... therefore (b-c ) has to be negative

From (2) $$a<0$$ and from (1) $$a\neq{b-c}$$. Why should $$b-c$$ be negative?
You cannot assume that $$|a|=b-c$$ when this is the question itself: is $$|a|=b-c$$?
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Re: Is |a| = b - c ?  [#permalink]

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The answer is C... found the below explanation...
the question is asking if
a = b-c when a is positive / a = c-b and when a is negative

from option 1 we get that a != b-c and insufficient

from option 2 we get only a is negative and insufficient

when we combine both options:
-a + c != b
-b +c != a
so a!= c-b hence the second condition is also proved... therefore |a| != b-c
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Re: Is |a| = b - c ?  [#permalink]

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Since Mod a is always +ve so cant we write Is b-c>0 i.e. b>c
Hence C should be the answer
pls suggest whether my approach is right or wrong
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Re: Is |a| = b - c ?  [#permalink]

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Archit143 wrote:
Since Mod a is always +ve so cant we write Is b-c>0 i.e. b>c
Hence C should be the answer
pls suggest whether my approach is right or wrong

The correct answer is E and not C, so your approach is wrong.

Notice that we are not told that |a| = b - c, we need to determine that.
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Re: Is |a| = b - c ?  [#permalink]

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Ans:

looking at 1st statement alone we get “a” not equal to b-c, therefore we can say NO for the answer, the 2nd statement does not tell us anything . Therefore the answer is (A).
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Re: Is |a| = b - c ?  [#permalink]

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priyamne wrote:
Ans:

looking at 1st statement alone we get “a” not equal to b-c, therefore we can say NO for the answer, the 2nd statement does not tell us anything . Therefore the answer is (A).

The correct answer is E, not A. Check here: is-a-b-c-1-a-c-is-not-equal-to-b-2-a-105351.html#p823428
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Re: Is |a| = b - c ?  [#permalink]

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Bunuel wrote:
gmat1011 wrote:
Is |a| = b - c ?

(1) a + c is not equal to b
(2) a<0

C/right Jeff Sackmann. Just posting it here for educational purposes.

Don't get how it can be C. Shouldn't it be E? (1), (2) not sufficient. (1)+(2); lets say b = 6; c = 3; then a = -3 satisfies and gets a "Yes" but a=-10 satisfies and gets a "No"

Is $$|a|=b-c$$ true? Now, if $$a\geq{0}$$, the question becomes "is $$a=b-c$$ true?" and if $$a\leq{0}$$, the question becomes "is $$-a=b-c$$ true?".

(1) $$a+c\neq{b}$$ --> $$a\neq{b-c}$$, we cannot answer No to the question as we don't know whether $$a>0$$. Not sufficient.

(2) $$a<0$$, so the question becomes is $$-a=b-c$$, but we don't know that. Not sufficient.

(1)+(2) From: $$a\neq{b-c}$$ and $$a<0$$ we can not determine whether $$-a=b-c$$ is true. For example if $$a=-1$$, $$b=1$$ and $$c=0$$ then answer to the question will be YES but if $$a=-1$$, $$b=1$$ and $$c=1$$ then answer to the question will be NO. Not sufficient.

Answer: E.

gmat1011 wrote:
Don't get how it can be C. Shouldn't it be E? (1), (2) not sufficient. (1)+(2); lets say b = 6; c = 3; then a = -3 satisfies and gets a "Yes" but a=-10 satisfies and gets a "No"

I think that there might be a typo in statement (2) and it should read $$a>0$$ (instead of $$a<0$$), then for (1)+(2) we would have: as from (2) $$a>0$$ then the question becomes "is $$a=b-c$$ true?" and (1) ($$a\neq{b-c}$$) directly gives us the answer NO. In this case answer would indeed be C.

Hope it's clear.

Hi Bunuel,

Just wanted to know, can we re-phrase this question as

Is -a= b- c and a=b- c?

(1) a + c is not equal to b
(2) a<0

Thanks
Mridul
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Re: Is |a| = b - c ?  [#permalink]

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Hi !

I bought a book to get some advice on the GMAT but one of the answers looks wrong to me.

Is |a| = b-c?
(1) a+c ≠ b
(2) a < 0

It says from the book that the answer is C : both statements together are sufficient, but neither statement alone is sufficient.

From (2), if A < 0, then the question becomes "Is a = c-b?"
(1) gives a ≠ b-c but it doesn't answer "Is a = c-b?", does it?

Thanks Math Expert V
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Re: Is |a| = b - c ?  [#permalink]

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ceta wrote:
Hi !

I bought a book to get some advice on the GMAT but one of the answers looks wrong to me.

Is |a| = b-c?
(1) a+c ≠ b
(2) a < 0

It says from the book that the answer is C : both statements together are sufficient, but neither statement alone is sufficient.

From (2), if A < 0, then the question becomes "Is a = c-b?"
(1) gives a ≠ b-c but it doesn't answer "Is a = c-b?", does it?

Thanks Merging topics. Please refer to the discussion above.
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Re: Is |a| = b - c ?  [#permalink]

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_________________ Re: Is |a| = b - c ?   [#permalink] 01 Dec 2018, 04:56
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