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

 It is currently 16 Jul 2018, 19:10

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

A soccer team scores x goals the first game then averages twice as man

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47019
A soccer team scores x goals the first game then averages twice as man [#permalink]

Show Tags

02 Jan 2018, 01:29
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:31) correct 0% (00:00) wrong based on 14 sessions

HideShow timer Statistics

A soccer team scores x goals the first game then averages twice as many goals for the next 5 games. The team averages two goals less than the average (arithmetic mean) of the previous 5 games over their next four games. How many goals will the team have scored after 10 games?

A. 19x − 8
B. 15x
C. 12x
D. 19x/10
E. 27x

_________________
SC Moderator
Joined: 22 May 2016
Posts: 1825
A soccer team scores x goals the first game then averages twice as man [#permalink]

Show Tags

02 Jan 2018, 15:10
Bunuel wrote:
A soccer team scores x goals the first game then averages twice as many goals for the next 5 games. The team averages two goals less than the average (arithmetic mean) of the previous 5 games over their next four games. How many goals will the team have scored after 10 games?

A. 19x − 8
B. 15x
C. 12x
D. 19x/10
E. 27x

Attachment:

soccergoals.png [ 11.82 KiB | Viewed 223 times ]

Algebra
There are three groups of games.
Each group has
• A, an average number of goals
• n, a number of games and
• S, Sum (A * n), total number of goals for that group

There are 1 + 5 + 4 = 10 games
Total number of goals? Sum the sums for each group

$$A*n = S$$
1) first game: team scores x goals
A = x, n = 1, S = x

2) next 5: average is twice that of first game
A = 2x, n = 5, S = 10x

3) next 4: 2 goals less than average for the previous 5 games
A = 2x - 2, n = 4
S = 4(2x - 2) = 8x - 8

The total number of goals after 10 games: sum the sums
$$x + 10x + 8x - 8$$ =

$$19x - 8$$

Assign values

• Let first week = 1 goal
1 game * average of 1 goal = 1 goal total

• Next 5 weeks, team averages twice as many goals as the first week

5 games * average of 2 goals = 10 goals

• Next 4 weeks, team averages 2 less than average (arithmetic mean) of previous 5 games' average

4 games * average of 0 goals = 0 goals total

• Total number of goals scored after 10 games?

Number of games? 1 + 5 + 4 = 10
Total number of goals: (1 + 10 + 0) = 11 goals total

• Using x = 1, find the answer choice that yields 11 goals
Eliminate D (not an integer) and E immediately (it's huge)

A. 19x − 8: (19)(1) - 8 = 11. MATCH

B. 15x: (15)(1) = 15. NOT A MATCH

C. 12x (12)(1) = 12. NOT A MATCH

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

A soccer team scores x goals the first game then averages twice as man   [#permalink] 02 Jan 2018, 15:10
Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.