Algebra- quadratic equations question

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Troika: Master | Next Rank: 500 Posts; Posts: 136; Joined: Wed Apr 08, 2009 12:09 pm; Thanked: 4 times; Followed by:1 members

Algebra- quadratic equations question

by Troika » Sat Feb 25, 2012 7:24 pm

If (r - 4) is a factor of r^2 - kr - 36, then k =

(a) 16
(b) 5
(c) 0
(d) - 5
(e) - 16

Answer D

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Source: Beat The GMAT — Problem Solving | Sat Feb 25, 2012 7:24 pm

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 am; Location: New Delhi, India; Thanked: 130 times; Followed by:9 members; GMAT Score:720

by rijul007 » Sat Feb 25, 2012 8:28 pm

HG10 wrote:If (r - 4) is a factor of r^2 - kr - 36, then k =

(a) 16
(b) 5
(c) 0
(d) - 5
(e) - 16

Answer D

This ques can be done by plugging numbers

say r = 7

3 is a factor of 49-7k-36
13-7k

now plug each value and eliminate answer choices

(A)16
13 - 112 = 99
3 is a factor of 99
Keep it

(b)5
13-35 = -22
3 is not a factor of -22
Eliminate

(c)0
13-0
3 is not a factor of 13
Eliminate

(D)-5
13+35
48
3 is a factor of 48
Keep it

(E)-16
13+112
125
3 is not a factor of 125
Eliminate

Answer choices left A and D

Now put r= 9
(9-4) is a factor of 81-9k-36
5 is a factor of 45-9k

(A)16

45-9(16) = not divisible by 5
Eliminate

Only D is left so you can mark it and move on.
or you can check, if you want to waste time

Option D

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Feb 25, 2012 9:02 pm

HG10 wrote:If (r - 4) is a factor of r^2 - kr - 36, then k =

(a) 16
(b) 5
(c) 0
(d) - 5
(e) - 16

Answer D

For each factor of a quadratic there is a ROOT: the value that makes the factor equal to 0.
Since (r-4) is a factor here, r=4 is one of the roots of the equation rÂ² - kr - 36 = 0.
Thus, we can plug in r=4 and solve for k:
4Â² - k(4) - 36 = 0
-4k = 20
k = -5.

The correct answer is D.

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