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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] New post 25 Nov 2013, 11:49
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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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Re: At a certain factory, 10 percent of the staplers produced on [#permalink] New post 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.

Answer: E.

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

Start with C.

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] New post 15 Jan 2015, 09:24
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Re: At a certain factory, 10 percent of the staplers produced on [#permalink] New post 15 Jan 2015, 21:21
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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

Final Answer:
[Reveal] Spoiler:
E


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Re: At a certain factory, 10 percent of the staplers produced on [#permalink] New post 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

Answer = E
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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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