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

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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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:

GMAT assassins aren't born, they're made,
Rich

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.

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

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

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?

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

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.

GMAT assassins aren't born, they're made,
Rich

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

0.02*non defective = 90
non defective = 4500
so 4500/.9 = 5000
IMO E

This was pretty simple. But I Kind of thought that the 10% includes the erroneously detected 2% and went into an inception spiral

90 non defective staples = 2% of the non defective staplers
4500 = 100% of non defective staples

4,500 = 90% total staplers
5,000 = 100% total staplers

Answer is E.
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If 2 % is 90, then 100 % is 90*50 = 4,500

Now 4,500 is 90%, So 5000 is 100 %

Let 1000 be the no. of staplers
100 are defective (10% of 1000)
900 are nondefective
2% of 900=18

\(18/1000\)=\(90/x\)
x=5000

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

Let the number of staplers produced on monday = x

number of defective = 10% of x

number of non-defective = 90% of x

Now we are given that, 2 percent of the non-defective staplers were rejected by mistake.

so 2/100 of 90% of x = 90

x = 5000

Hope it hels!