If x + x^2 + x^3 = 27, then the average (arithmetic mean)

This topic has expert replies
Moderator
Posts: 2058
Joined: Sun Oct 29, 2017 4:24 am
Thanked: 1 times
Followed by:5 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + x^3 + x^4 is equal to which of the following?

A. 3
B. 3x
C. 7x
D. 9
E. 9x

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Sat Apr 06, 2019 12:55 am
M7MBA wrote:If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + x^3 + x^4 is equal to which of the following?

A. 3
B. 3x
C. 7x
D. 9
E. 9x

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
Average = (x + x^2 + x^3 + x^4)/4 = x (1 + x+ x^2 + x^3 )/4 = x(1+27)/4 = 28x/4 = 7x

Answer: Option C
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

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 » Sat Apr 06, 2019 2:25 am
GMATinsight wrote:
M7MBA wrote:If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + x^3 + x^4 is equal to which of the following?

A. 3
B. 3x
C. 7x
D. 9
E. 9x
We can PLUG IN THE ANSWERS, which represent the average of x + x² + x³ + x�.

Test B:
(x + x² + x³ + x�)/4 = 3x
Multiplying both sides by 4, we get:
x + x² + x³ + x� = 12x
Dividing both sides by x, we get:
1 + x + x² + x³ = 12
Substituting x+x²+x³=27 into 1+x+x²+x³ = 12, we get:
1 + 27 = 12
28 = 12

The right side needs to be greater.
Test C:
(x + x² + x³ + x�)/4 = 7x
Multiplying both sides by 4, we get:
x + x² + x³ + x� = 28x
Dividing both sides by x, we get:
1 + x + x² + x³ = 28
Substituting x+x²+x³=27 into 1+x+x²+x³ = 28, we get:
1 + 27 = 28
28 = 28
Success!

The correct answer is C.
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