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What does |2b| equal? [#permalink]
 25 Jun 2012, 12:23
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What does |2b| equal? (1) b^2-|b|-20=0 (2) |2b|=3b+25 it should be easy to solve - but i didn't see the necessary data at first glance may be some of you will offer easier way to understand this issue 
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Re: What does |2b| equal? [#permalink]
25 Jun 2012, 12:55
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Re: What does |2b| equal? [#permalink]
26 Jun 2012, 08:09
Hey Bunuel, the original question contained b^2-|b|-20=0 but you considered it to |b|^2-|b|-20=0 I know it does not matter that if it is |b|^2 or b^2 But it does matter especially when it is not mentioned that b is positive number...
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Re: What does |2b| equal? [#permalink]
26 Jun 2012, 08:13
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Re: What does |2b| equal? [#permalink]
26 Jun 2012, 09:03
Bunuel wrote: What does |2b| equal?
(1) b^2-|b|-20=0. Solve quadratics for |b|: (|b|)^2-|b|-20=0 --> |b|=-4 or |b|=5. Since absolute value cannot be negative then we have that |b|=5 and |2b|=10. Sufficient.
(2) |2b|=3b+25. Two cases:
If b\leq{0} then we would have that -2b=3b+25 --> b=-5.
If b>0 then we would have that 2b=3b+25 --> b=-25, but since we are considering the rangeo when b>{0} then discard this solution.
So, we have that b=-5, hence |2b|=10. Sufficient.
Answer: D.
Hope it's clear. Hi, can you make the solution more clear?in case of (1) why you didn't consider the negative value of b? When b is positive, b^2 -b = 20 and when b is negative b^2 + b =20..then we will find 4 values of b...I am confused ..Can you explain? and in case of (2) how you discard the 2nd value? Thanks
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Re: What does |2b| equal? [#permalink]
26 Jun 2012, 09:21
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farukqmul wrote: Bunuel wrote: What does |2b| equal?
(1) b^2-|b|-20=0. Solve quadratics for |b|: (|b|)^2-|b|-20=0 --> |b|=-4 or |b|=5. Since absolute value cannot be negative then we have that |b|=5 and |2b|=10. Sufficient.
(2) |2b|=3b+25. Two cases:
If b\leq{0} then we would have that -2b=3b+25 --> b=-5.
If b>0 then we would have that 2b=3b+25 --> b=-25, but since we are considering the rangeo when b>{0} then discard this solution.
So, we have that b=-5, hence |2b|=10. Sufficient.
Answer: D.
Hope it's clear. Hi, can you make the solution more clear?in case of (1) why you didn't consider the negative value of b? When b is positive, b^2 -b = 20 and when b is negative b^2 + b =20..then we will find 4 values of b...I am confused ..Can you explain? and in case of (2) how you discard the 2nd value? Thanks OK. Say x=|b|, then we have that x^2-x-20=0 --> x=-4 or x=5. Now, x=|b|=-4 is not possible, since an absolute value of a number ( |b|) cannot be negative. So, we have that |b|=5 and |2b|=10. Now, you can solve this statement considering two ranges: b\leq{0} and b>0, which will lead you to the same. If b\leq{0} then we'll have b^2+b-20=0 --> b=-5 or b=4 (not a valid solution since we are considering the range when b\leq{0}); If b>{0} then we'll have b^2-b-20=0 --> b=-4 (not a valid solution since we are considering the range when b>{0}) or b=5; So, only two valid solutions: b=-5 or b=5 --> |2b|=10. As for (2), it's explained in the post: If b>0 then we would have that 2b=3b+25 --> b=-25, but since we are considering the rangeo when b>{0} then discard this solution. Hope it's clear.
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Re: What does |2b| equal? [#permalink]
26 Jun 2012, 09:22
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farukqmul wrote: Bunuel wrote: What does |2b| equal?
(1) b^2-|b|-20=0. Solve quadratics for |b|: (|b|)^2-|b|-20=0 --> |b|=-4 or |b|=5. Since absolute value cannot be negative then we have that |b|=5 and |2b|=10. Sufficient.
(2) |2b|=3b+25. Two cases:
If b\leq{0} then we would have that -2b=3b+25 --> b=-5.
If b>0 then we would have that 2b=3b+25 --> b=-25, but since we are considering the rangeo when b>{0} then discard this solution.
So, we have that b=-5, hence |2b|=10. Sufficient.
Answer: D.
Hope it's clear. Hi, can you make the solution more clear?in case of (1) why you didn't consider the negative value of b? When b is positive, b^2 -b = 20 and when b is negative b^2 + b =20..then we will find 4 values of b...I am confused ..Can you explain? and in case of (2) how you discard the 2nd value? Thanks hey farukqmul I also had the same doubt but then i tried to solve it properly and i found out that there is no need to do it the long way but i will post here to clear your doubt b^2-|b|-20=0 Considering b>0 eq. becomes b^2-b-20=0 which gives us solution b=-4 and 5 since we assumed b>0 so b=-4 is rejected Considering b<0 eq. becomes b^2+b-20=0 which gives us solution b=4 and -5 since we assumed b<0 so b=4 is rejected In both the cases |2b|=10Now for the 2nd part (copying Buenel's explanation) |2b|=3b+25. Two cases: If b>0 then we would have that -2b=3b+25 --> b=-5. If b>0 then we would have that 2b=3b+25 --> b=-25, but since we are considering b>0 then discard this solution. Hope it's all clear now.
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Re: What does |2b| equal? [#permalink]
27 Jul 2012, 03:32
Hi, I am wondering why |b| cannot be other numbers greater than 5. What if |b| was to equal 16? This would also allow us to solve the quadratics right? in this case (1) would have multiple answers, 5 and 6, therefore causing (1) to be insufficient?
Please let me know if I misunderstand something. Thank you
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Re: What does |2b| equal? [#permalink]
27 Jul 2012, 04:20
Solving the equation x^2 - x - 20 = 0 gives you two possible solution which are -4 and +5
In our case x = |b| so x cannot be negative.
That let x = 5 the only possible solution
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Re: What does |2b| equal? [#permalink]
27 Jul 2012, 07:43
hi Arthur, I understand your point. However, I do not understand why "16" cannot be another possible answer. Since if we allow |b| to be 16, we can also solve the quadratics.
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Re: What does |2b| equal? [#permalink]
27 Jul 2012, 08:20
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Re: What does |2b| equal? [#permalink]
28 Jul 2012, 18:51
Bunuel wrote: What does |2b| equal?
(1) b^2-|b|-20=0. Solve quadratics for |b|: (|b|)^2-|b|-20=0 --> |b|=-4 or |b|=5. Since absolute value cannot be negative then we have that |b|=5 and |2b|=10. Sufficient.
(2) |2b|=3b+25. Two cases:
If b\leq{0} then we would have that -2b=3b+25 --> b=-5.
If b>0 then we would have that 2b=3b+25 --> b=-25, but since we are considering the rangeo when b>{0} then discard this solution.
So, we have that b=-5, hence |2b|=10. Sufficient.
Answer: D.
Hope it's clear. Hey Bunuel, I have always been meaning to ask you. I know that (1) |x|=x if x>0 and (2) |x|=-x if x <0. But the "=" of the (less than or equal to) or (greater than or equal to), where does it go? I noticed that you put it on equation 2, while others place it on equation (1). Its Driving me nuts!!
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Re: What does |2b| equal? [#permalink]
29 Jul 2012, 01:50
alphabeta1234 wrote: Bunuel wrote: What does |2b| equal?
(1) b^2-|b|-20=0. Solve quadratics for |b|: (|b|)^2-|b|-20=0 --> |b|=-4 or |b|=5. Since absolute value cannot be negative then we have that |b|=5 and |2b|=10. Sufficient.
(2) |2b|=3b+25. Two cases:
If b\leq{0} then we would have that -2b=3b+25 --> b=-5.
If b>0 then we would have that 2b=3b+25 --> b=-25, but since we are considering the rangeo when b>{0} then discard this solution.
So, we have that b=-5, hence |2b|=10. Sufficient.
Answer: D.
Hope it's clear. Hey Bunuel, I have always been meaning to ask you. I know that (1) |x|=x if x>0 and (2) |x|=-x if x <0. But the "=" of the (less than or equal to) or (greater than or equal to), where does it go? I noticed that you put it on equation 2, while others place it on equation (1). Its Driving me nuts!! First of all: |x|=-x when x\leq{0}; |x|=x when x\geq{0}. Next, as for "=" sign in the solution: you could include it either in the first case or in the second, it doesn't matter at all.
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Re: What does |2b| equal?
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29 Jul 2012, 01:50
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