|
Author |
Message |
|
TAGS:
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 65785
|
If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
 24 Jan 2014, 02:53
Question Stats:
64% (01:08) correct 36% (01:22) wrong based on 1249 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf (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 ProjectEach 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: 1. Please provide your solutions to the questions; 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!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
|
|
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 65785
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
24 Jan 2014, 02:53
SOLUTIONIf (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: \(8^2 - 8k - 48 = 0\) --> \(k = 2\). Answer: C.
_________________
|
|
|
|
|
|
|
|
Manager
Joined: 11 Jan 2014
Posts: 85
Concentration: Finance, Statistics
GMAT Date: 03-04-2014
GPA: 3.77
WE: Analyst (Retail Banking)
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
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.
|
|
|
|
|
|
Intern
Joined: 25 Apr 2013
Posts: 14
Location: India
GPA: 4
WE: Engineering (Transportation)
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
24 Jan 2014, 22:27
Put the value of t-8=0, or t=8 in equation t^2+kt+48=0: Solving we get k=2.
|
|
|
|
|
|
Manager
Joined: 04 Oct 2013
Posts: 148
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
|
If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
Updated on: 01 Nov 2014, 02:02
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.
|
|
|
|
|
|
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1705
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
25 Feb 2014, 18:44
-8 x ?? = -48
?? = 6, so the other factor is 6
(t-8)(t+6) would be the two factors
-k = -8+6
-k = -2
k=2 Answer = C
|
|
|
|
|
|
Retired Moderator
Joined: 29 Oct 2013
Posts: 245
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
|
If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
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
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
|
|
|
|
|
|
Senior Manager
Joined: 28 Jun 2015
Posts: 272
Concentration: Finance
GPA: 3.5
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
30 Jun 2015, 21:27
since (t-8) is a factor, then: (8)^2 - 8k - 48 = 0, -8k = -16 k = 2.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
|
|
|
|
|
|
Intern
Joined: 07 Jul 2015
Posts: 26
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
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.
|
|
|
|
|
|
SVP
Joined: 23 Feb 2015
Posts: 2008
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
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.
|
|
|
|
|
|
Manager
Joined: 05 Nov 2016
Posts: 81
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
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
|
|
|
|
|
|
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11392
Location: United States (CA)
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
08 Feb 2017, 18:39
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf (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 Answer: C
_________________
★
★
★
★
★
250 REVIEWS
5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
|
|
|
|
|
|
Current Student
Joined: 23 Dec 2013
Posts: 131
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44
GPA: 3.76
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
23 May 2017, 20:41
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf (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 ProjectEach 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: 1. Please provide your solutions to the questions; 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.
|
|
|
|
|
|
VP
Joined: 09 Mar 2016
Posts: 1261
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
26 Aug 2017, 11:22
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf (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 ProjectEach 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: 1. Please provide your solutions to the questions; 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
|
|
|
|
|
|
Manager
Joined: 01 Dec 2018
Posts: 135
Concentration: Entrepreneurship, Finance
GPA: 4
WE: Other (Retail Banking)
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
29 Sep 2019, 23:08
[quote="Bunuel"] The Official Guide For GMAT® Quantitative Review, 2ND EditionIf (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 .
|
|
|
|
|
|
Intern
Joined: 17 Sep 2015
Posts: 21
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
22 May 2020, 05:35
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: \(8^2 - 8k - 48 = 0\) --> \(k = 2\).
Answer: C. 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?
|
|
|
|
|
|
Intern
Joined: 17 Sep 2015
Posts: 21
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
Show Tags
22 May 2020, 05:46
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. Did anyone reply to your question or do you know the answer already?
|
|
|
|
|
|
|
Re: If (t- 8) is a factor of t^2 - kt - 48, then k=
[#permalink]
22 May 2020, 05:46
|
|
|
|
|
|
|
close
