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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]

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Updated on: 25 Nov 2013, 13:04
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Difficulty:

25% (medium)

Question Stats:

75% (01:45) correct 25% (01:39) wrong based on 489 sessions

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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

Originally posted by gmatfighter12 on 25 Nov 2013, 12:49.
Last edited by Bunuel on 25 Nov 2013, 13:04, edited 1 time in total.
Edited the question.
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Posts: 58332
Re: At a certain factory, 10 percent of the staplers produced on  [#permalink]

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25 Nov 2013, 13:12
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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]

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25 Nov 2013, 21:23
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]

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15 Jan 2015, 22:21
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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

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

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21 Jan 2015, 21:18
2
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]

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20 Mar 2017, 02:32
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

let the no of staplers produces be x
non defective stapler = 0.9x
no of non defective stapler rejected= 0.02*0.9x = 90

therefore x = 5000

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

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11 Sep 2018, 19:19
Of the people who go this question correct, the average time to solve it was only 49 seconds. I try to read the question and pay close attention to detail, and the first time seeing this question, it took me close to 1 minute and 30 seconds, even though I have no issues with it mathematically. Is there some special speed reading technique or something that people use to solve word problems like this (which involve multiple steps) in under a minute?
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Re: At a certain factory, 10 percent of the staplers produced on  [#permalink]

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02 Oct 2018, 20:45
How do you know if the 90 rejected are rejected by mistake? I initially think that 90 rejected are either correctly rejected or by mistake.

Can anyone explain? Byjus EMPOWERgmatRichC
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Re: At a certain factory, 10 percent of the staplers produced on  [#permalink]

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02 Oct 2018, 21:18
Hi anguyengt,

Based on the descriptions "defective" and "nondefective", the implication is that the 'defective' staplers are the ones that SHOULD be rejected. If you do not think that that is an obvious interpretation, then that's fine - but which of the 5 answers did you come up with using your interpretation?

GMAT questions tend to be written so that 'interpretational bias' won't happen on Test Day - but if you find that 'your way' of interpreting the prompt doesn't lead to any of the answers, then you know that something was incorrect about that interpretation and you need to go back and consider how you thought through the prompt.

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

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24 Oct 2018, 11:12
Let the number of staplers produced = x
No. of staplers defective = 10% of x = 0.1x
No. Non-defective staplers: (x - 0.1x) = 0.9x
No. of non- defective staplers rejected by mistake = 2% of 0.9x
Actual number of non-defective staplers rejected by mistake = 90
$$\frac{2}{100} * 0.9x = 90$$

$$x = \frac{90 * 100}{0.9 * 2}$$

x = 5000
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Re: At a certain factory, 10 percent of the staplers produced on  [#permalink]

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13 Oct 2019, 07:31
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

0.02*non defective = 90
non defective = 4500
so 4500/.9 = 5000
IMO E
Re: At a certain factory, 10 percent of the staplers produced on   [#permalink] 13 Oct 2019, 07:31
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