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

 It is currently 23 Oct 2019, 09:55

### 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

# One-third of a barrel's contents is emptied with each turn of the whee

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58464
One-third of a barrel's contents is emptied with each turn of the whee  [#permalink]

### Show Tags

11 Jan 2018, 21:54
00:00

Difficulty:

25% (medium)

Question Stats:

82% (01:16) correct 18% (01:37) wrong based on 15 sessions

### HideShow timer Statistics

One-third of a barrel's contents is emptied with each turn of the wheel. If the barrel begins full, what fraction of the barrel remains after 2 turns of the wheel?

A. 1/9

B. 4/7

C. 4/9

D. 2/3

E. 8/9

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3581
One-third of a barrel's contents is emptied with each turn of the whee  [#permalink]

### Show Tags

12 Jan 2018, 11:22
1
Bunuel wrote:
One-third of a barrel's contents is emptied with each turn of the wheel. If the barrel begins full, what fraction of the barrel remains after 2 turns of the wheel?

A. 1/9

B. 4/7

C. 4/9

D. 2/3

E. 8/9

Assign values
Let the barrel contain 9 units
One wheel turn: the barrel loses $$\frac{1}{3}$$ of its units
One turn, number lost: $$\frac{1}{3}$$* 9 = 3 lost
One turn, # remaining: (9-3)= 6 remain
Second turn, number lost: $$\frac{1}{3}$$*6= 2 lost
Second turn, # remaining: (6-2) = 4 remain

After these 2 turns, what fraction remains?
$$\frac{EndUnits}{OriginalUnits}=\frac{4}{9}$$

Algebraically
Let x = original number of units in the barrel
First turn, number lost: $$x*\frac{1}{3}=\frac{1}{3}x$$
First turn, number remaining:
$$(1x - \frac{1}{3}x)= \frac{2}{3}x$$

Second turn, number lost:
$$\frac{2}{3}x*\frac{1}{3}=\frac{2}{9}x$$
Second turn, number remaining: $$\frac{2}{3}x -\frac{2}{9}x=\frac{4}{9}x$$ =
Fraction that remains after 2 turns of the wheel

*Strictly defined, fraction that remains is
$$\frac{(\frac{4}{9})x}{x}=\frac{4}{9}x*\frac{1}{x}=\frac{4}{9}$$. No need for this step: x = 1 and we're working with fractions. It's for the meticulous folks.

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
One-third of a barrel's contents is emptied with each turn of the whee   [#permalink] 12 Jan 2018, 11:22
Display posts from previous: Sort by