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If A = -|B| and A-B =-10, what is B?

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Intern
Joined: 06 Jun 2014
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If A = -|B| and A-B =-10, what is B? [#permalink]

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07 Mar 2016, 06:10
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If A = -|B| and A-B =-10, what is B?

A. 5
B. -5
C. 0
D. -5 or +5
E. -10

Source: Sravna test prep
[Reveal] Spoiler: OA

Last edited by ENGRTOMBA2018 on 07 Mar 2016, 06:52, edited 1 time in total.
Reformatted the question and added the OA.
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Re: If A = -|B| and A-B =-10, what is B? [#permalink]

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07 Mar 2016, 06:40
1
KUDOS
vinoo7 wrote:
If A = -|B| and A-B =-10, what is B?

A. 5
B. -5
C. 0
D. -5 or +5
E. -10

Follow posting guidelines (link in my signatures), especially mention the source of the question and the OA.

Question is not of a good quality.

For this question, let us use the options given to us.

A. B=5 ---> A= -|B| = -5 ---> -5-5 = -10. , True. Keep
B. B=-5 ---> A= -|B| = -5 ---> -5+5 = 0 $$\neq$$ -10. Eliminate.
C. B=0 ---> A= -|B| = 0 ---> -5-0 = -5 $$\neq$$ -10 , False. Eliminate.
D. B=-5 or +5 ---> As mentioned in option B, -5 does not follow the given statements. Eliminate
E. B=-10 ---> A= -|B| = -10 ---> -10+10=0 $$\neq$$ -10. Eliminate.

Thus, A is the correct answer.

Hope this helps.
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Joined: 02 Jul 2017
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If A = -|B| and A-B =-10, what is B? [#permalink]

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16 Sep 2017, 10:44
1
KUDOS
Given $$A = -|B|$$

=> if B =-ve then $$A= -|-B|$$ = -ve
=> if B=+ve then $$A=-|B|$$ = -ve

as given$$A-B= -10$$ and A and B have same magnitude then possible values of $$|B|= 5$$=> B is either -5 or 5

if B =5 =>$$A =-|5|=-5$$ => $$A-B = -5-(5) =-10$$ Answer
if B = -5 =>$$A=-|-5| = -5$$=> $$A-B = -5-(-5) =-5+5 =0$$

So for$$A-B =-10$$ => value of B =5

Last edited by Nikkb on 16 Sep 2017, 11:49, edited 2 times in total.
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Re: If A = -|B| and A-B =-10, what is B? [#permalink]

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16 Sep 2017, 10:59
Nikkb wrote:
Given A = -|B|

=> if B =-ve then A=+ve B
=> if B=+ve then A=-ve B

as given A-B= -10 and A and B have same magnitude then possible values of |B|= 5 => B is either -5 or 5

if B =5 => A =-5 => A-B = -5-(5) =-10 Answer
if B = -5 => A=-(-5) =5 => A-B = 5-(-5) =5+5 =10

So for A-B =-10 => value of B =5

Hi Nikkb

You have got the right answer but the highlighted portions are wrong.

$$A = -|B|$$. Notice that the negative sign is outside the mod function and mod is always positive. Hence $$A$$ will be always negative irrespective of $$B$$

So if $$B=-5$$, then $$A=-|-5| = -|5| =-5$$
Hence $$A-B = -5-(-5) = 0$$. Hence B cannot be $$-5$$
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Joined: 02 Jul 2017
Posts: 288
GMAT 1: 730 Q50 V38
Re: If A = -|B| and A-B =-10, what is B? [#permalink]

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16 Sep 2017, 11:27
niks18 wrote:
Nikkb wrote:
Given A = -|B|

=> if B =-ve then A=+ve B
=> if B=+ve then A=-ve B

as given A-B= -10 and A and B have same magnitude then possible values of |B|= 5 => B is either -5 or 5

if B =5 => A =-5 => A-B = -5-(5) =-10 Answer
if B = -5 => A=-(-5) =5 => A-B = 5-(-5) =5+5 =10

So for A-B =-10 => value of B =5

Hi Nikkb

You have got the right answer but the highlighted portions are wrong.

$$A = -|B|$$. Notice that the negative sign is outside the mod function and mod is always positive. Hence $$A$$ will be always negative irrespective of $$B$$

So if $$B=-5$$, then $$A=-|-5| = -|5| =-5$$
Hence $$A-B = -5-(-5) = 0$$. Hence B cannot be $$-5$$

Hey yah thanks for pointing it out. Totally agree with you. While solving question i made correct assumptions.
while posting solution was in between 2 things so made mistake. Will update the solution.

Thanks
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If A = -|B| and A-B =-10, what is B? [#permalink]

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16 Sep 2017, 23:16
Option: A
Since the absolute value of both A and B is same, all we have to do is plug values from option in the equation A-B = -10.
Only A suffices. Answer can be reached within a minute.

+1 Kudos if it helped
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+1 Kudos if my post helps in any way

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Re: If A = -|B| and A-B =-10, what is B? [#permalink]

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18 Sep 2017, 23:45
1
KUDOS
A=-IBI
A-B=-10
-IBI-B=-10
-B-B=-10
-2B=-10
2B=10
B=10/2=5=A
Intern
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If A = -|B| and A-B =-10, what is B? [#permalink]

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01 Oct 2017, 08:24
If A = -|B| and A-B =-10, what is B?

A. 5
B. -5
C. 0
D. -5 or +5
E. -10

-|B|-B=-10
-B-B=-10
-2B=-10
B=10/2
B=5 ANS.
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Joined: 06 Apr 2016
Posts: 20
Re: If A = -|B| and A-B =-10, what is B? [#permalink]

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02 Oct 2017, 23:18
1
KUDOS
Since A=-|B|, there are two possible relations

A=-B (or) A=B

If we substitute both of them in the equation,

If A=-B ---> A-B = -2B => -2B=-10 => B=5

If A=B ---> A-B = 0 (This is not possible since (A-b=-10))

Hence, A is the correct ans
Re: If A = -|B| and A-B =-10, what is B?   [#permalink] 02 Oct 2017, 23:18
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