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

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Intern
Joined: 06 Jan 2017
Posts: 10
Location: Italy
GMAT 1: 720 Q47 V41
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The customs department has 3.2% of its inspected items opened...  [#permalink]

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22 Jul 2017, 11:57
4
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:45) correct 42% (02:32) wrong based on 77 sessions

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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
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The customs department has 3.2% of its inspected items opened...  [#permalink]

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22 Jul 2017, 12:18
3
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!
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Re: The customs department has 3.2% of its inspected items opened...  [#permalink]

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22 Jul 2017, 15:05
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+D
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Re: The customs department has 3.2% of its inspected items opened...  [#permalink]

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24 Jul 2017, 05:50
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.
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Re: The customs department has 3.2% of its inspected items opened...  [#permalink]

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26 Jul 2017, 16:43
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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%.

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Intern
Joined: 06 Jan 2017
Posts: 10
Location: Italy
GMAT 1: 720 Q47 V41
GPA: 4
Re: The customs department has 3.2% of its inspected items opened...  [#permalink]

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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%.

Thank you Scott, extremely clear explanation. I was unable to understand the meaning of the data till now. Finally I got it
Re: The customs department has 3.2% of its inspected items opened...   [#permalink] 27 Jul 2017, 01:37
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