NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 21:39 It is currently 25 Apr 2024, 21:39
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The customs department has 3.2% of its inspected items opened...

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
Alessiod
Intern
Intern
Joined: 06 Jan 2017
Posts: 10
Own Kudos [?]: 11 [11]
Given Kudos: 19
Location: Italy
GMAT 1: 720 Q47 V41
GPA: 4
Send PM
Reviews Badge
The customs department has 3.2% of its inspected items opened... [#permalink] New post   22 Jul 2017, 11:57
1
Kudos
10
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

59% (02:40) correct 41% (02:53) wrong based on 135 sessions
Hide Show timer Statistics
The customs department has 3.2% of its inspected items opened and resealed before being released. It also has 20% of its opened items released but not resealed. What percentage of the items inspected are opened?

(A) 2.5%
(B) 3.0%
(C) 3.5%
(D) 4.0%
(E) 4.5%


Source: Optimus Prep


I got lost on this one... actually I barely understood the meaning of the question. Kudos for the best explanation :wink:
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22055 [7]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: The customs department has 3.2% of its inspected items opened... [#permalink] New post   26 Jul 2017, 16:43
3
Kudos
4
Bookmarks
Expert Reply
Alessiod wrote:
The customs department has 3.2% of its inspected items opened and resealed before being released. It also has 20% of its opened items released but not resealed. What percentage of the items inspected are opened?

(A) 2.5%
(B) 3.0%
(C) 3.5%
(D) 4.0%
(E) 4.5%


We can let 1000 = the number of inspected items and x = the number of opened items.

We are given that the number of inspected items opened and resealed is 3.2% or 32 items.

We are also given that 20% of the opened items, or 0.2x, are not resealed. Since the number of opened resealed items plus the number of opened unsealed items equals the total number of opened items, we have:

32 + 0.2x = x

32 = 0.8x

x = 32/0.8 = 320/8 = 40

Since there are 40 opened items out of 1000 inspected items, the percentage of inspected items that are opened is 40/1000 = 4/100 = 4%.

Answer: D
General Discussion
User avatar
S
Leo8
Manager
Manager
Joined: 23 May 2017
Posts: 192
Own Kudos [?]: 359 [4]
Given Kudos: 9
Concentration: Finance, Accounting
WE:Programming (Energy and Utilities)
Send PM
Re: The customs department has 3.2% of its inspected items opened... [#permalink] New post   22 Jul 2017, 15:05
4
Kudos
+D
Attachment:
FullSizeRender (15).jpg
FullSizeRender (15).jpg [ 71.63 KiB | Viewed 3997 times ]
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5206 [3]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
The customs department has 3.2% of its inspected items opened... [#permalink] New post   22 Jul 2017, 12:18
3
Kudos
Assume the total inspected items are 1000.
Since, 3.2% of the inspected items are opened and released(32 are opened and released)
Also, 20% of the items were opened but not released

Therefore, 80%(100-20) of opened items are not released.
80% of total opened items(which is x) is 32
\(x = \frac{32*100}{80} = 40\)

Therefore, the total number of opened items is 40,
which is \(\frac{40}{1000}*100\) or 4% of the items inspected(Option D)

Hope that helps!
User avatar
B
Devbek
Intern
Intern
Joined: 06 Feb 2016
Posts: 30
Own Kudos [?]: 32 [1]
Given Kudos: 26
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5
Send PM
Re: The customs department has 3.2% of its inspected items opened... [#permalink] New post   24 Jul 2017, 05:50
1
Bookmarks
Basically, 80% of opened items are resealed which is equal to 3.2% of total items. So:
80% of opened = 3.2% of the total items
4% of the total is opened.
User avatar
B
Alessiod
Intern
Intern
Joined: 06 Jan 2017
Posts: 10
Own Kudos [?]: 11 [0]
Given Kudos: 19
Location: Italy
GMAT 1: 720 Q47 V41
GPA: 4
Send PM
Reviews Badge
Re: The customs department has 3.2% of its inspected items opened... [#permalink] New post   27 Jul 2017, 01:37
ScottTargetTestPrep wrote:
Alessiod wrote:
The customs department has 3.2% of its inspected items opened and resealed before being released. It also has 20% of its opened items released but not resealed. What percentage of the items inspected are opened?

(A) 2.5%
(B) 3.0%
(C) 3.5%
(D) 4.0%
(E) 4.5%


We can let 1000 = the number of inspected items and x = the number of opened items.

We are given that the number of inspected items opened and resealed is 3.2% or 32 items.

We are also given that 20% of the opened items, or 0.2x, are not resealed. Since the number of opened resealed items plus the number of opened unsealed items equals the total number of opened items, we have:

32 + 0.2x = x

32 = 0.8x

x = 32/0.8 = 320/8 = 40

Since there are 40 opened items out of 1000 inspected items, the percentage of inspected items that are opened is 40/1000 = 4/100 = 4%.

Answer: D


Thank you Scott, extremely clear explanation. I was unable to understand the meaning of the data till now. Finally I got it :lol:
avatar
B
kdgupta
Intern
Intern
Joined: 02 Sep 2019
Posts: 6
Own Kudos [?]: 4 [0]
Given Kudos: 12
Send PM
Re: The customs department has 3.2% of its inspected items opened... [#permalink] New post   05 Sep 2019, 22:15
Consider - 3.2% as 80% of Materials Released after Opening …. Balance 20% Opened but not released
If 3.2% is 80% , then 100% is 3.2/80/100*100/100 = 4
avatar
B
kdgupta
Intern
Intern
Joined: 02 Sep 2019
Posts: 6
Own Kudos [?]: 4 [0]
Given Kudos: 12
Send PM
Re: The customs department has 3.2% of its inspected items opened... [#permalink] New post   05 Sep 2019, 22:15
Consider - 3.2% as 80% of Materials Released after Opening …. Balance 20% Opened but not released
If 3.2% is 80% , then 100% is 3.2/80/100*100/100 = 4
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32681
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: The customs department has 3.2% of its inspected items opened... [#permalink] New post   02 Sep 2023, 09:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: The customs department has 3.2% of its inspected items opened... [#permalink]
02 Sep 2023, 09:53
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions