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

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If |a-b|=c ,what is the value of a? [#permalink]

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New post 19 Dec 2010, 23:45
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If |a-b|=c ,what is the value of a?

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

[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA
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Re: If |a-b|=c ,what is the value of a? [#permalink]

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New post 20 Dec 2010, 00:34
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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New post 21 Dec 2010, 03:15
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.

Hence Answer "E".

Regards,
Murali.

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

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New post 31 Dec 2010, 10:40
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
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Re: If |a-b|=c ,what is the value of a? [#permalink]

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New post 10 Jun 2016, 03:57
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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Re: If |a-b|=c ,what is the value of a? [#permalink]

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New post 10 Jun 2016, 06:24
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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Re: If |a-b|=c ,what is the value of a? [#permalink]

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New post 10 Jun 2016, 09:08
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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New post 11 Jun 2016, 00:54
Thanks a lot, everyone.
Re: If |a-b|=c ,what is the value of a?   [#permalink] 11 Jun 2016, 00:54
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