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

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

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New post 07 Mar 2016, 07:10
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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, 07:52, 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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New post 07 Mar 2016, 07:40
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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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If A = -|B| and A-B =-10, what is B? [#permalink]

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New post 16 Sep 2017, 11:44
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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

Answer: A

Last edited by Nikkb on 16 Sep 2017, 12:49, 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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New post 16 Sep 2017, 11:59
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

Answer: A


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

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New post 16 Sep 2017, 12:27
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

Answer: A


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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New post 17 Sep 2017, 00:16
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.

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

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New post 19 Sep 2017, 00:45
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A=-IBI
A-B=-10
-IBI-B=-10
-B-B=-10
-2B=-10
2B=10
B=10/2=5=A

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

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New post 01 Oct 2017, 09:24
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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Re: If A = -|B| and A-B =-10, what is B? [#permalink]

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New post 03 Oct 2017, 00:18
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

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Re: If A = -|B| and A-B =-10, what is B?   [#permalink] 03 Oct 2017, 00:18
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