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Math Expert V
Joined: 02 Sep 2009
Posts: 65785
If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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41 00:00

Difficulty:   35% (medium)

Question Stats: 64% (01:08) correct 36% (01:22) wrong based on 1249 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

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.

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Math Expert V
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Posts: 65785
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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6
17
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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4
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 24 Jan 2014, 23:46.
Last edited by arunspanda on 01 Nov 2014, 02:02, 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 22 May 2014, 23:38.
Last edited by NoHalfMeasures on 11 Nov 2015, 20:45, 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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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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2
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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1
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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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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[quote="Bunuel"]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

STEP 1 prime factorise 48 and find the other root . SO T= 8 and other root will be t=-6 .

step 2 now we know sum of roots will be -8 +6 = -2 this value is equal to - K (not just k).
hence -K = -2 => K = 2 .
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Joined: 17 Sep 2015
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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:
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: $$8^2 - 8k - 48 = 0$$ --> $$k = 2$$.

Hi,

The answer assumes that the quadratic equation equals to zero. Does this mean all quadratic equation will equal zero even though it is not stated explicitly?
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=  [#permalink]

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kanav06 wrote:
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.

Yeah that is my question too. Why do we assume all quadratic equation will equal to zero unless it is stated? I failed to solve this problem due to this issue. I did not assume the quadratic will equal to zero. Re: If (t- 8) is a factor of t^2 - kt - 48, then k=   [#permalink] 22 May 2020, 05:46

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