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Joined: 02 Sep 2009
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If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (01:09) correct 37% (01:21) wrong based on 1084 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

Problem Solving
Question: 57
Category: Algebra Second-degree equations
Page: 69
Difficulty: 600

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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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SOLUTION

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

$$(t - 8)$$ is a factor of $$t^2 - kt - 48$$ means that $$t = 8$$ is a solution of the equation $$t^2 - kt - 48 = 0$$.

Substitute$$t = 8$$ to get the value of k: $$8^2 - 8k - 48 = 0$$ --> $$k = 2$$.

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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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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.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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Put the value of t-8=0, or t=8 in equation t^2+kt+48=0: Solving we get k=2.
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If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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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, $$k = 8 + (- 6) = 2$$

Originally posted by arunspanda on 25 Jan 2014, 00:46.
Last edited by arunspanda on 01 Nov 2014, 03:02, edited 1 time in total.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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-8 x ?? = -48
?? = 6, so the other factor is 6
(t-8)(t+6) would be the two factors
-k = -8+6
-k = -2
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If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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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 23 May 2014, 00:38.
Last edited by NoHalfMeasures on 11 Nov 2015, 21:45, edited 1 time in total.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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since (t-8) is a factor, then: (8)^2 - 8k - 48 = 0,
-8k = -16
k = 2.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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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.
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GMAT 1: 720 Q49 V40 GMAT 2: 760 Q50 V42 Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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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=  [#permalink]

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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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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

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

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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

Problem Solving
Question: 57
Category: Algebra Second-degree equations
Page: 69
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

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.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

Problem Solving
Question: 57
Category: Algebra Second-degree equations
Page: 69
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

hello Bunuel
hope my solution finds you well! 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

Ans K = 2
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