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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
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24 Jan 2014, 04:55
Factoring the expression: (t - 8) (t - ?), since (t - 8) is a factor, the other bracket has to be (t + 6). The net result is -2. So (B)? Not sure of the answer because I got lost with the signs a bit.
If (t- 8) is a factor of t^2 - kt - 48, then k=
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Updated on: 01 Nov 2014, 02:02
1
2
If (t- 8) is a factor of \(t^2 - kt - 48\), then k=
(A) - 6 (8) - 2 (C) 2 (0) 6 (E) 14
It is given that \((t - 8)\) is a factor of the quadratic expression \(t^2 - kt - 48\) Hence, we need to find the other factor of \(-48\) such that the sum of factors is\(-(\frac{-k}{1})=k\).
Thus, \((8) * x = -48\)
Or, \(x = -6\)
So, \(k = 8 + (- 6) = 2\)
Answer: (C)
Originally posted by arunspanda on 24 Jan 2014, 23:46.
Last edited by arunspanda on 01 Nov 2014, 02:02, edited 1 time in total.
If (t- 8) is a factor of t^2 - kt - 48, then k=
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Updated on: 11 Nov 2015, 20:45
Vieta's formulas applied to quadratic: x1+x2= -b/a & x1*x2=c/a From what is given in the question: -8+x2=-k and -8*x2=-48 so, x2=6 and thus -8+6=-k i.e. k=2
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Originally posted by NoHalfMeasures on 22 May 2014, 23:38.
Last edited by NoHalfMeasures on 11 Nov 2015, 20:45, edited 1 time in total.
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
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15 May 2016, 10:04
In this question, I didn't understand this step:
(t−8)(t−8) is a factor of t2−kt−48t2−kt−48 means that t=8t=8 is a solution of the equation t2−kt−48=0t2−kt−48=0.
Why do we assume both equations are equal to 0? What is the rationale of this step? It would be great if someone could explain with examples, or with videos.
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
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03 Feb 2017, 02:00
gjonrexha wrote:
If (t-8) is a factor of t^2 - kt - 48, then k =
A(6) B(-2) C(2) D(6) E(14)
Can someone explain how the answer isnt 6?
(t-8)(t+6) = t^2 - 14 -48
---->Your red part is somewhat mistake; you can't find (t-8)(t+6) = t^2 - 14 -48. Actually, (t-8)(t+6)=t^2-2t-48. ***Can someone explain how the answer isnt 6? ---->if you put put the value of k=6 in t^2 - kt - 48, then you can't find (t-8) as a factor. So, that's why it wrong. But, if k=2, then t^2 - kt - 48=t^2 - 2t - 48=>t^-8t+6t-48=>t(t-8)+6(t-8)=>(t-8) (t+6). So, the green part is the factor according to question stem.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
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03 Feb 2017, 19:13
gjonrexha wrote:
If (t-8) is a factor of t^2 - kt - 48, then k =
A(6) B(-2) C(2) D(6) E(14)
Can someone explain how the answer isnt 6?
(t-8)(t+6) = t^2 - 14 -48
We were asked to find the value of k but not the factors of the given expression. -6 will be a factor of the expression, apart from 8. If you want to know k, substitute 8 in the value of t or -6, both will give you the value of K as 2. Here by using 8 directly, gives us the result quicker.
Hope this helps
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Since (t - 8) is a factor of t^2 - kt - 48, t = 8 must be a root of the equation t^2 - kt - 48 = 0. We can substitute 8 for t and determine a value for k.
8^2 - 8k - 48 = 0
64 - 8k = 48
-8k = -16
k = 2
Answer: C
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This problem is a good one in a few ways because it has a trap that's useful to learn from and it can be solved in two ways.
The simplest method is to realize that t = 8 is a root of the quadratic (as given), plug it into the equation and solve for k directly.
8^2 - k(8) - 48 = 0 K =2
The other method involves breaking up the quadratic into its roots: (t-8)(t+6) = 0 -Kt = -8t + 6t by FOIL -k = -2 k = 2
However, it's common to set kt = -2t and thus set oneself up for the trap k = 2, one of the answer choices. So it's important to remember that -kt is an entire term, not just kt itself, so you need to set the entire term = -2t.
Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.
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I would appreciate if you could let me know if my solution is correct!
t-8 = k t = k+8 Plug in T into t^2 - kt – 48 - k^2+8^2 – k(k+8) – 48 -k^2+8^2 – K^2-8k– 48 After i eliminate k^2; and – K^2 I get this 64-8k-48 -8k= -64+48 -8k= -16 then k = 2
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
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