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# Is |a| = b - c ?

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Intern
Joined: 24 Jul 2013
Posts: 28
Is |a| = b - c ?  [#permalink]

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Updated on: 16 Aug 2018, 23:38
00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:12) correct 49% (01:13) wrong based on 57 sessions

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Is |a| = b - c ?

(1) a + c$$\neq{b}$$
(2) a > 0

Source: Jeff Sackman

Edit: Although the question is correctly copied from the source in which statement II is a<0, teh OA is wrong and accordingly statement II has been modified

Originally posted by longranger25 on 16 Aug 2018, 11:00.
Last edited by chetan2u on 16 Aug 2018, 23:38, edited 2 times in total.
edited the question
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Joined: 22 Feb 2018
Posts: 315
Re: Is |a| = b - c ?  [#permalink]

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16 Aug 2018, 11:13
longranger25 wrote:
Is |a| = b - c ?
(1) a + c$$\neq{b}$$
(2) a < 0

Source: Jeff Sackman

add Is |a| = b - c? in question stem
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Intern
Joined: 24 Jul 2013
Posts: 28
Re: Is |a| = b - c ?  [#permalink]

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16 Aug 2018, 11:14

Princ wrote:
longranger25 wrote:
Is |a| = b - c ?
(1) a + c$$\neq{b}$$
(2) a < 0

Source: Jeff Sackman

add Is |a| = b - c? in question stem
Intern
Joined: 03 Apr 2017
Posts: 36
Re: Is |a| = b - c ?  [#permalink]

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16 Aug 2018, 11:27
longranger25 wrote:
Is |a| = b - c ?

(1) a + c$$\neq{b}$$
(2) a < 0

Source: Jeff Sackman

Can't agree here.

a = -2 b=5 c =3 s1 & s2 compliant. Answer is yes.

a = -3 b=5 c=3 s1 & s2 compliant. Answer is no.

Thus answer cannot be c, as it gives 2 different answers even when taken together.
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Joined: 02 Aug 2009
Posts: 6786
Re: Is |a| = b - c ?  [#permalink]

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16 Aug 2018, 11:38
1
1
longranger25 wrote:
Is |a| = b - c ?

(1) a + c$$\neq{b}$$
(2) a < 0

Source: Jeff Sackman

Pl recheck the question

In present state it is E..
Either
Statement I is a+b$$\neq{c}$$
Or
Statement II would be a>0

Is |a|=b-c?
If a>0, a=b-c
If a<0, a=c-b

1) $$a+c\neq{b}............a\neq{b-c}$$
But a can be equal to c-b
Insufficient

2) a<0..
So from above
a could be equal to c-b
Insufficient

Combined.
If a=c-b... Yes otherwise No
Insufficient

E

But had statement II been a>0
Combined..
a>0, so only possibility of yes is if a=b-c
But statement I gives $$a\neq{b-c}$$
So Ans is always NO
Sufficient
Then C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 24 Jul 2013
Posts: 28
Re: Is |a| = b - c ?  [#permalink]

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17 Aug 2018, 04:13
I double checked the question. It is correctly copied.

I myself could not get the twisted logic behind the official explanation and hence posted the question here.

This is what the official explanation is:

Explanation: There are two ways for the equation in the question to be
true. If a is positive, then it is true if a = b - c. If a is negative, then it is true
if -a = b - c, or put another way, a = c - b. To answer the question, we need
to know whether a is positive or negative, and if the corresponding equation is
true.

Statement (1) is insufficient. a+c $$\neq{b}$$ is the same as a $$\neq{b}$$ - c, which means
that, if a is positive, the answer is "no." However, it doesn’t tell us what the
answer is if a is negative.
Statement (2) is also insufficient: it gives us the sign of a, but nothing about
how it relates to b and c.

Taken together, the statements are sufficient. Since we know a is negative,
we know the question asks, "Is a = c - b ?" (1) tells us that that is not true,
so the answer is "no." Choice (C) is correct.

chetan2u wrote:
longranger25 wrote:
Is |a| = b - c ?

(1) a + c$$\neq{b}$$
(2) a < 0

Source: Jeff Sackman

Pl recheck the question

In present state it is E..
Either
Statement I is a+b$$\neq{c}$$
Or
Statement II would be a>0

Is |a|=b-c?
If a>0, a=b-c
If a<0, a=c-b

1) $$a+c\neq{b}............a\neq{b-c}$$
But a can be equal to c-b
Insufficient

2) a<0..
So from above
a could be equal to c-b
Insufficient

Combined.
If a=c-b... Yes otherwise No
Insufficient

E

But had statement II been a>0
Combined..
a>0, so only possibility of yes is if a=b-c
But statement I gives $$a\neq{b-c}$$
So Ans is always NO
Sufficient
Then C
Intern
Joined: 22 Jul 2018
Posts: 10
Is |a| = b - c ?  [#permalink]

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17 Aug 2018, 05:50
chetan2u wrote:
longranger25 wrote:
Is |a| = b - c ?

(1) a + c$$\neq{b}$$
(2) a < 0

Source: Jeff Sackman

Pl recheck the question

In present state it is E..
Either
Statement I is a+b$$\neq{c}$$
Or
Statement II would be a>0

Is |a|=b-c?
If a>0, a=b-c
If a<0, a=c-b

1) $$a+c\neq{b}............a\neq{b-c}$$
But a can be equal to c-b
Insufficient

2) a<0..
So from above
a could be equal to c-b
Insufficient

Combined.
If a=c-b... Yes otherwise No
Insufficient

E

But had statement II been a>0
Combined..
a>0, so only possibility of yes is if a=b-c
But statement I gives $$a\neq{b-c}$$
So Ans is always NO
Sufficient
Then C

Hey chetan2u, why can't the answer be D?,
Statement I says $$a\neq{b-c}$$ which means it leaves us with only a+b=c, so shouldn't A be correct?
Statement ii says a>0 which leaves us with a=b-c with which we can say B is sufficient.
Are we saying C because we dont know the values of a,b and c?

Math Expert
Joined: 02 Aug 2009
Posts: 6786
Re: Is |a| = b - c ?  [#permalink]

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17 Aug 2018, 06:04
elPatron434 wrote:
chetan2u wrote:
longranger25 wrote:
Is |a| = b - c ?

(1) a + c$$\neq{b}$$
(2) a < 0

Source: Jeff Sackman

Pl recheck the question

In present state it is E..
Either
Statement I is a+b$$\neq{c}$$
Or
Statement II would be a>0

Is |a|=b-c?
If a>0, a=b-c
If a<0, a=c-b

1) $$a+c\neq{b}............a\neq{b-c}$$
But a can be equal to c-b
Insufficient

2) a<0..
So from above
a could be equal to c-b
Insufficient

Combined.
If a=c-b... Yes otherwise No
Insufficient

E

But had statement II been a>0
Combined..
a>0, so only possibility of yes is if a=b-c
But statement I gives $$a\neq{b-c}$$
So Ans is always NO
Sufficient
Then C

Hey chetan2u, why can't the answer be D?,
Statement I says $$a\neq{b-c}$$ which means it leaves us with only a+b=c, so shouldn't A be correct?
Statement ii says a>0 which leaves us with a=b-c with which we can say B is sufficient.
Are we saying C because we dont know the values of a,b and c?

The question will give a YES under two circumstances
1) a=b-c
2) a=c-b
Any other equation would give an answer NO
So the third case
So statement 1 says it is not (1), but it can still be (2), then YES OR third case then NO
Both no and yes possible.. insufficient
Statement II a>0 so case (1) or third case possible
Insufficient

Combined only third case possible, so C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

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Joined: 06 Nov 2016
Posts: 60
Location: Viet Nam
GPA: 3.54
Re: Is |a| = b - c ?  [#permalink]

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17 Aug 2018, 11:29
longranger25 wrote:
Is |a| = b - c ?

(1) a + c $$\neq{b}$$
(2) a > 0

Source: Jeff Sackman

Edit: Although the question is correctly copied from the source in which statement II is a<0, teh OA is wrong and accordingly statement II has been modified

Is |a| = b - c ? --> Is |a|+c =b ?

(1) a + c $$\neq{b}$$

If a > 0 --> |a| = a --> a + c = |a| + c
--> |a| + c $$\neq{b}$$ --> NO

If a < 0 --> -|a| = a --> a + c = -|a| + c
--> -|a| + c $$\neq{b}$$ . Since we need to compare |a| + c and $$b$$, this statement is not sufficient.
(We can test by plugging in numbers. If a=-1, b=2, c=4 --> NO, If a=-1, b=3, c=2 --> YES => Not Sufficient)

(2) a > 0
Nothing related to b, c --> not sufficient.

Combine both statements --> we can eliminate the 2nd case in the 1st statement --> Sufficient.

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Re: Is |a| = b - c ? &nbs [#permalink] 17 Aug 2018, 11:29
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