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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 Updated on: 07 Mar 2016, 07:52
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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

Originally posted by vinoo7 on 07 Mar 2016, 07:10.
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 Updated on: 16 Sep 2017, 12:49
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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

Originally posted by Nikkb on 16 Sep 2017, 11:44.
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
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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]

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New post 07 Mar 2018, 05:29
I understand the solutions above and now understand why the answer must be 5.

But I think what tripped me up is that I think that because A=-|B| that A has to be negative. Because if we make B=5, then A=-5. If we make B=-5, then A=-5.

I understand that because A-B=-10, that B has to be 5, but using the first equation in the questions I feel like 5 doesn't work because that makes it ==> A=-|B| ==>5=-|5|==>5=-5, which is not true. Can someone explain? Why are we allowed to make A a positive number when the equation makes it seem like A has to be negative.
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Re: If A = -|B| and A-B =-10, what is B?  [#permalink]

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New post 07 Mar 2018, 05:39
msurls wrote:
If A = -|B| and A-B =-10, what is B?

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

I understand the solutions above and now understand why the answer must be 5.

But I think what tripped me up is that I think that because A=-|B| that A has to be negative. Because if we make B=5, then A=-5. If we make B=-5, then A=-5.

I understand that because A-B=-10, that B has to be 5, but using the first equation in the questions I feel like 5 doesn't work because that makes it ==> A=-|B| ==>5=-|5|==>5=-5, which is not true. Can someone explain? Why are we allowed to make A a positive number when the equation makes it seem like A has to be negative.


A = -|B| = -(non-negative value) = (non-positive value). So, A = -|B| means that A is positive or 0.
Now, if B = 5, then A = -|B| = -|5| = -5 = negative.

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

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

A = -|B| and A - B = -10, thus:

-|B| - B = -10;
B + |B| = 10.

If B is negative or 0, then we'd have B - B = 10 --> 0 = 10, which is not true.
If B is positive, then we'd have B + B = 10 --> B = 5.

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

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New post 08 Mar 2018, 17:56
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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


Sine A = B - 10, we have:

B - 10 = -|B|

When B is positive we have:

B - 10 = -B

2B = 10

B = 5

When B is negative we cannot get a solution for B. So B must be 5.

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

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New post 21 Mar 2018, 23:24
vinoo7 wrote:
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


A = - |B|

means A = B or A = -B

A - B = -10 --------(I)

Replace A with B,

B - B = -10

0 = -10 (Not true)

Replace A with -B,

-B -B = -10

B = 5

Hence (A)
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Re: If A = -|B| and A-B =-10, what is B?   [#permalink] 21 Mar 2018, 23:24
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