BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H

by BTGmoderatorDC » Tue Sep 25, 2018 3:40 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10

OA A

Source: Manhattan Prep
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Tue Sep 25, 2018 10:16 pm
BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10

OA A

Source: Manhattan Prep
Looking at the options, we can deduce that (x - 5) given in the denominator of H gets canceled.

Thus, (x - 5) must be a factor of the numerator of H = x^3 - 6x^2 - x + 30

x^3 - 6x^2 - x + 30
x^2(x - 5) - x^2 - x + 30
x^2(x - 5) - x(x - 5) - 6x + 30
x^2(x - 5) - x(x - 5) - 6(x - 5)

(x - 5)(x^2 - x - 6)

Thus,

H = (x^3 - 6x^2 - x + 30) / (x - 5)

= (x - 5)(x^2 - x - 6) / (x - 5)

= x^2 - x - 6; cancelling (x - 5)

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Paris | Shanghai | Munich | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
User avatar
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 » Wed Sep 26, 2018 2:28 am
BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10
Let x=0, with the result that H = 30/-5 = -6.
Now plug x=0 in the answers to see which yields a value of -6.
Only A works:
x² - x - 6 = 0² - 0 - 6 = -6.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Thu Sep 27, 2018 4:38 pm
BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10
We see that the numerator of H, x^3 - 6x^2 - x + 30, is not a polynomial that can be easily factored. However, since x^3/x (the first term of numerator divided by the first term of the denominator) is x^2 and 30/(-5) (the constant term of numerator divided by the constant term of the denominator) is -6, we see that if H can be simplified, the answer must be choice A: x^2 - x - 6. Now let's verify it is the case by multiplying it by (x - 5) to see if the product is x^3 - 6x^2 - x + 30.

(x - 5)(x^2 - x - 6)

x^3 - x^2 - 6x - 5x^2 + 5x + 30

x^3 - 6x^2 - x + 30

We see that (x - 5)(x^2 - x - 6) = x^3 - 6x^2 - x + 30; therefore, (x^3 - 6x^2 - x + 30)/(x - 5) = x^2 - x - 6.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1