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# At a certain factory, 10 percent of the staplers produced on

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At a certain factory, 10 percent of the staplers produced on [#permalink]  25 Nov 2013, 11:49
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73% (01:55) correct 28% (00:46) wrong based on 119 sessions
At a certain factory, 10 percent of the staplers produced on Monday were defective and 2 percent of the nondefective staplers were rejected by mistake. If 90 of the nondefective staplers were rejected, what was the number of staplers produced that day

A. 4,000
B. 4,200
C. 4,500
D. 4,800
E. 5,000
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Nov 2013, 12:04, edited 1 time in total.
Edited the question.
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Kudos [?]: 42162 [3] , given: 5957

Re: At a certain factory, 10 percent of the staplers produced on [#permalink]  25 Nov 2013, 12:12
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gmatfighter12 wrote:
At a certain factory, 10 percent of the staplers produced on Monday were defective and 2 percent of the nondefective staplers were rejected by mistake. If 90 of the nondefective staplers were rejected, what was the number of staplers produced that day

A. 4,000
B. 4,200
C. 4,500
D. 4,800
E. 5,000

Given that:
2 percent of the nondefective staplers were rejected.
90 of the nondefective staplers were rejected.

Thus 0.02*{nondefective} = 90 --> {nondefective} = 4,500.

We also know that nondefective staplers were 90% of all staplers, thus 0.9*{total} = 4,500 --> {total} = 5,000.

Hope it's clear.
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Re: At a certain factory, 10 percent of the staplers produced on [#permalink]  25 Nov 2013, 20:23
Expert's post
You can also plug in answer choices to solve this one quickly.

Since 90 is 2% of 4500, we know this answer choice is equal to the number of non-defective staplers.

Since we know that 90% of all of the staplers are non-defective, 4500/.9, or 4500*(100/90), will give you the correct result: 5000.
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Re: At a certain factory, 10 percent of the staplers produced on [#permalink]  15 Jan 2015, 09:24
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Re: At a certain factory, 10 percent of the staplers produced on [#permalink]  15 Jan 2015, 21:21
Expert's post
Hi All,

This question is all about percents and ratios, so you can use a variety of "math approaches" to solve it (including TESTing THE ANSWERS).

Here's an approach that focuses on the ratios.

We're told that 10% of staplers in a factory are defective.

X = Total staplers
.1X = defective staplers
.9X = normal staplers

Next, we're told that 2% of the normal staplers were rejected by mistake and that this = 90 staplers...

.9X(.02) = 90
.018X = 90
18X = 90,000
X = 5,000

[Reveal] Spoiler:
E

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Re: At a certain factory, 10 percent of the staplers produced on [#permalink]  21 Jan 2015, 20:18
Defective ..................... Non defective ................... Total

$$\frac{10x}{100}$$ ........................... $$\frac{90x}{100}$$ ........................ x (Say total staplers = x)

Given that 2% of the non defective rejected = 90

$$\frac{90x}{100} * \frac{2}{100} = 90$$

x = 5000

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Re: At a certain factory, 10 percent of the staplers produced on   [#permalink] 21 Jan 2015, 20:18
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