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Intern  Joined: 16 Jun 2010
Posts: 1
If |a-b|=c ,what is the value of a?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 73% (00:50) correct 27% (00:41) wrong based on 208 sessions

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If |a-b|=c ,what is the value of a?

(1) b = 2
(2) c = 7

I know this is not a very difficult problem, but i am bit confused. I think with either of the options we can get the solution.

from 1. we get a-b= c or a-b= -c i.e 2 equations with two unknowns since b is known from this statement.
from 2 .we again get 2 equation with 2 unknowns.

Correct ans is E. Pls guide me how to go for this king of absolute DS.
Retired Moderator Joined: 02 Sep 2010
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Location: London
Re: If |a-b|=c ,what is the value of a?  [#permalink]

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rajnisht wrote:
from 1. we get a-b= c or a-b= -c i.e 2 equations with two unknowns since b is known from this statement.
from 2 .we again get 2 equation with 2 unknowns.

Thats not correct, the cases for the modulus equation, are not two independent equations.

It is EITHER a-b=c OR a-b=-c.
So if b=2, then EITHER a-2=c OR 2-a=c.
In either case, we dont have sufficient information to know what a is.

With (2) alone, we encounter the same problem.

(1+2) : b=2 & c=7
EITHER a-2=7 OR 2-a=7
EITHER a=9 OR a=-5
So we get two different values of a, clearly insufficient again, we still cant answer the question.
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Re: If |a-b|=c ,what is the value of a?  [#permalink]

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rajnisht wrote:
If |a-b|=c ,what is the value of a?
1. b=2
2.c=7

I know this is not a very difficult problem, but i am bit confused. I think with either of the options we can get the solution.

from 1. we get a-b= c or a-b= -c i.e 2 equations with two unknowns since b is known from this statement.
from 2 .we again get 2 equation with 2 unknowns.

Correct ans is E. Pls guide me how to go for this king of absolute DS.

Hiii,

This is a very simple problem if you grasp the modulus concept on GMAT.

The be low is my approcah for any modulus qtn in GMAT.

Modulus concept:
The meaning of |x-y| is "On the number line, the distance between X and +Y"
The meaning of |x+y| is "On the number line, the distance between X and -Y"
The meaning of |x| is "On the number line, the distance between X and 0".

On the # line, Left to 0 are all the -ve #s and right to 0 are all +ve #s

E.g:
|x-3|=2 ==> distand between x and 3 is 2
==> i can have a # 2 units away to the left of three and also to the right of 3 on the # line
==> x could be 1 (2 units aways from 3 to the left) or 5 (2 units aways from 3 to the right)

Original qtn:

if |a-b|=c ,what is the value of a?
1. b=2
2.c=7

qtn says, on the # line, the distance between a and B is c.
what is the value of a?

stmnt1:
b = 2
the distance between a and 2 is c.....no luck

stmnt2:
the distance between a and B is 7
==> i have a 7 units line connected between a and b
==> no fixed value for a and b as i can move this line along the #,line keeping the distance constant i.e.7
no luck..Not suff.

1&2 together:
the distance between a and 2 is 7
==> |a-2|=7
==> a could be 9 or -5
Not suff.

Regards,
Murali.

Kudos?
Manager  Joined: 08 Jun 2010
Posts: 64
Re: If |a-b|=c ,what is the value of a?  [#permalink]

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OA IS :E.

STATEment1- value of b not sufficient.
statement 2- value of c not sufficient
Both - we cant get value ,because !a-b!=c mean +c and -c.when we open the mode
so the answer is E
Intern  B
Joined: 10 Aug 2014
Posts: 4
Re: If |a-b|=c ,what is the value of a?  [#permalink]

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Hey Guys,

If |a-b|=c, isn't there only one possibility that C is always positive as |a-b| is always positive.

|a-b|=c which leads to a=b+c

from 1, B= 2 we get the value of B only. We don't know anything about C hence insuffi

from 2 C=7 we get the value of B only. We don't know anything about B hence insuffi.

But together ? B+C= 9 Hence Sufficient. Please Suggest.

Bunuel any comments ??
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Joined: 02 Sep 2009
Posts: 58381
Re: If |a-b|=c ,what is the value of a?  [#permalink]

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Alok Sharma wrote:
If |a-b|=c ,what is the value of a?

(1) b = 2
(2) c = 7

Hey Guys,

If |a-b|=c, isn't there only one possibility that C is always positive as |a-b| is always positive.

|a-b|=c which leads to a=b+c

from 1, B= 2 we get the value of B only. We don't know anything about C hence insuffi

from 2 C=7 we get the value of B only. We don't know anything about B hence insuffi.

But together ? B+C= 9 Hence Sufficient. Please Suggest.

Bunuel any comments ??

I think your doubt is already answered in the solutions above. Yes, c must be non-negative, since it equals to an absolute value, |a-b|, but a-b itself can be negative as well as positive. Notice that there are two values of a satisfying the equation -5 and 7.
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Concentration: General Management, Technology
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Re: If |a-b|=c ,what is the value of a?  [#permalink]

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rajnisht wrote:
If |a-b|=c ,what is the value of a?

(1) b = 2
(2) c = 7

|a-b|=c means
either a=b+c OR a=b-c
we see that we need value of b&c both to get the value of a. but then a can be both difference and sum of b&c, hence a will have two different values. hence insufficient. Answer is E.
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Re: If |a-b|=c ,what is the value of a?  [#permalink]

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Thanks a lot, everyone.
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Re: If |a-b|=c ,what is the value of a?  [#permalink]

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