GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Aug 2019, 02:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# M31-04

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 57229

### Show Tags

07 Jun 2015, 08:46
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:13) correct 23% (02:52) wrong based on 31 sessions

### HideShow timer Statistics

If $$1 + x^4 + x^3 + x^2 + x = 80$$, then the average (arithmetic mean) of $$x$$, $$x^2$$, $$x^3$$, $$x^4$$ and $$x^5$$ is equal to which of the following?

A. $$12x$$
B. $$13x$$
C. $$14x$$
D. $$16x$$
E. $$20x$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 57229

### Show Tags

07 Jun 2015, 08:46
1
Official Solution:

If $$1 + x^4 + x^3 + x^2 + x = 80$$, then the average (arithmetic mean) of $$x$$, $$x^2$$, $$x^3$$, $$x^4$$ and $$x^5$$ is equal to which of the following?

A. $$12x$$
B. $$13x$$
C. $$14x$$
D. $$16x$$
E. $$20x$$

The average (arithmetic mean) of $$x$$, $$x^2$$, $$x^3$$, $$x^4$$ and $$x^5$$ is $$\frac{x + x^2 + x^3 + x^4 + x^5}{5} = \frac{x(1 + x + x^2 + x^3 + x^4)}{5} = \frac{80x}{5} = 16x$$.

_________________
Intern
Joined: 20 Aug 2015
Posts: 6

### Show Tags

02 Feb 2016, 02:26
Hey Bunuel!

I do not see how x(1+x+x^2+x^3+x^4) = 80x. Can you please explain?

Many thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 57229

### Show Tags

02 Feb 2016, 03:02
marcoelmanchi wrote:
Hey Bunuel!

I do not see how x(1+x+x^2+x^3+x^4) = 80x. Can you please explain?

Many thanks!

We are given that $$1 + x^4 + x^3 + x^2 + x = 80$$, thus $$x(1+x+x^2+x^3+x^4) = x*80=80x$$.
_________________
Intern
Joined: 29 Jul 2017
Posts: 35
Location: India
Concentration: Operations, Finance
GPA: 3.94
WE: Design (Manufacturing)

### Show Tags

02 Aug 2019, 23:43
I think this is a high-quality question and I agree with explanation.
Re M31-04   [#permalink] 02 Aug 2019, 23:43
Display posts from previous: Sort by

# M31-04

Moderators: chetan2u, Bunuel