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What does 2b equal? [#permalink]
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25 Jun 2012, 12:23
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What does 2b equal? (1) b^2  b  20 = 0 (2) 2b = 3b + 25
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farukqmul wrote: Bunuel wrote: What does 2b equal?
(1) b^2b20=0. Solve quadratics for \(b\): \((b)^2b20=0\) > \(b=4\) 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^2b20=0 Considering b>0 eq. becomes b^2b20=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+b20=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]
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farukqmul wrote: Bunuel wrote: What does 2b equal?
(1) b^2b20=0. Solve quadratics for \(b\): \((b)^2b20=0\) > \(b=4\) 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 \(x^2x20=0\) > \(x=4\) 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 \(b^2+b20=0\) > \(b=5\) or \(b=4\) (not a valid solution since we are considering the range when \(b\leq{0}\)); If \(b>{0}\) then we'll have \(b^2b20=0\) > \(b=4\) (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]
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04 Jul 2013, 21:49
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(1) If b >0, eqn reduces to (b5)(b+4)=0 , since we have assumed b >0, this gives us a soln of b=5. If b <0, eqn reduces to (b+5)(b4) =0 giving us a soln of b=5 (since b <0). Since we are asked for the value of 2b it doesnt matter if b is 5 or 5. Sufficient.
(2) If b >0, it gives us 2b=3b+25 or b =25 but tht goes against our assumption. So b <0 and 2b=3b+25 or b=5. Sufficient.
Answer is (d)



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Re: What does 2b equal? [#permalink]
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26 Jun 2012, 08:09
Hey Bunuel, the original question contained b^2b20=0 but you considered it to b^2b20=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]
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26 Jun 2012, 09:03
Bunuel wrote: What does 2b equal?
(1) b^2b20=0. Solve quadratics for \(b\): \((b)^2b20=0\) > \(b=4\) 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]
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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]
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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]
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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]
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28 Jul 2012, 18:51
Bunuel wrote: What does 2b equal?
(1) b^2b20=0. Solve quadratics for \(b\): \((b)^2b20=0\) > \(b=4\) 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]
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29 Jul 2012, 01:50
alphabeta1234 wrote: Bunuel wrote: What does 2b equal?
(1) b^2b20=0. Solve quadratics for \(b\): \((b)^2b20=0\) > \(b=4\) 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? [#permalink]
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07 Jul 2013, 18:24
What does 2b equal?
(1) b^2b20=0 use quadratic formula to try and get a value for b. (b5) (b+4) = 0 b=5 OR b=4 Well, an absolute value cannot be equal to a negative number so b=5. Therefore, 2b=10 SUFFICIENT
(2) 2b=3b+25
Find positive/negative cases to try and isolate b. 2b=3b+25 If x>= 0 2b=3b+25 b=25 b=25 Not valid as 2b is not greater than or equal to zero. x<0 2b=3b+25 5b=25 b=5 Valid as 5 falls within the range of <0 SUFFICIENT (D)



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What does 2b equal? [#permalink]
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11 Aug 2014, 01:44
This is how I solved it:
1. b^2  b = 20 Since both b^2 and absolute value of b cannot be negative, b ( b  1 ) = 20 and b= 5
2. I got two solutions following the same method as Bunuel did, but the part I don't understand is why we have to discard b = 25, where does it say that we are considering b>0 ??
Can someone please explain what exactly I missed or overlooked! Thank you



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