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If A = B and AB =10, what is B? [#permalink]
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Updated on: 07 Mar 2016, 07:52
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If A = B and AB =10, what is B? A. 5 B. 5 C. 0 D. 5 or +5 E. 10 Source: Sravna test prep
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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 AB =10, what is B? [#permalink]
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07 Mar 2016, 07:40
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vinoo7 wrote: If A = B and AB =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 > 55 = 10. , True. KeepB. B=5 > A= B = 5 > 5+5 = 0 \(\neq\) 10. Eliminate.C. B=0 > A= B = 0 > 50 = 5 \(\neq\) 10 , False. Eliminate.D. B=5 or +5 > As mentioned in option B, 5 does not follow the given statements. EliminateE. 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 AB =10, what is B? [#permalink]
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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\(AB= 10\) and A and B have same magnitude then possible values of \(B= 5\)=> B is either 5 or 5
if B =5 =>\(A =5=5\) => \(AB = 5(5) =10\) Answer if B = 5 =>\(A=5 = 5\)=> \(AB = 5(5) =5+5 =0\)
So for\(AB =10\) => 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 AB =10, what is B? [#permalink]
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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 AB= 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 => AB = 5(5) =10 Answer if B = 5 => A=(5) =5 => AB = 5(5) =5+5 =10
So for AB =10 => value of B =5
Answer: A Hi NikkbYou 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 \(AB = 5(5) = 0\). Hence B cannot be \(5\)



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Re: If A = B and AB =10, what is B? [#permalink]
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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 AB= 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 => AB = 5(5) =10 Answer if B = 5 => A=(5) =5 => AB = 5(5) =5+5 =10
So for AB =10 => value of B =5
Answer: A Hi NikkbYou 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 \(AB = 5(5) = 0\). 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 AB =10, what is B? [#permalink]
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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 AB = 10. Only A suffices. Answer can be reached within a minute. +1 Kudos if it helped
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Re: If A = B and AB =10, what is B? [#permalink]
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19 Sep 2017, 00:45
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A=IBI AB=10 IBIB=10 BB=10 2B=10 2B=10 B=10/2=5=A



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If A = B and AB =10, what is B? [#permalink]
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01 Oct 2017, 09:24
If A = B and AB =10, what is B?
A. 5 B. 5 C. 0 D. 5 or +5 E. 10
BB=10 BB=10 2B=10 B=10/2 B=5 ANS.



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Re: If A = B and AB =10, what is B? [#permalink]
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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 > AB = 2B => 2B=10 => B=5
If A=B > AB = 0 (This is not possible since (Ab=10))
Hence, A is the correct ans



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Re: If A = B and AB =10, what is B? [#permalink]
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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 AB=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 AB =10, what is B? [#permalink]
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07 Mar 2018, 05:39
msurls wrote: If A = B and AB =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 AB=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 = (nonnegative value) = (nonpositive 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 AB =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 AB =10, what is B? [#permalink]
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08 Mar 2018, 17:56
vinoo7 wrote: If A = B and AB =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 AB =10, what is B? [#permalink]
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21 Mar 2018, 23:24
vinoo7 wrote: If A = B and AB =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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