percentage calculation

[lukaswelker]

Dear,

I'm almost able to resolve this one but I have a doubt with the result.

Here come the question,

At a certain factory, 10 percent of the staplers produced on Monday were defective and 2 percent of the non defective staplers were rejected by mistake. If 90 of the non defective staplers were rejected, what was the number of staplers produced that day?

4000 ; 4200 ; 4500 ; 4800 : 5000

At first I did the obvious mistake of considering that 90 staplers are equally to 2% of the researched amount.

After looking at it again, I realized my mistake and calculated the following.
90 represent (0.9*0.02 --> 0.018) 1.8% of the researched amount. This will imply that the final amount is closed to 5600. Which is a bit far of the 5000 given as the right answer.

Can anybody tell me if I'm doing something wrong? if yes, why ?

Many thanks
Lukas

[theCodeToGMAT]

Produced = X
Defective = 0.1*x
Non-Defective = 0.9 * x
Rejected = 0.02 * 0.9 * x

90 = 0.02 * 0.9 * x

90 * 100 * 10 / 18 = x

x = 5000

[GMATGuruNY]

At a certain factory, 10 percent of the staplers produced on Monday were defective and 2 percent of the non defective staplers were rejected by mistake. If 90 of the non defective staplers were rejected, what was the number of staplers produced that day?

4000 ; 4200 ; 4500 ; 4800 : 5000

An alternate approach is the PLUG IN THE ANSWERS, which represent the total number of staplers.
2% of the middle answer choice -- 4500 -- is equal to 90.
But the problem states that 2% of ONLY THE NONDEFECTIVE STAPLERS = 90.
Thus, the total number of staplers must be GREATER than 4500.
Eliminate A, B and C.

Between D and E, E seems easier to evaluate.

E: 5000
Defective = 10% of 5000 = 500.
Nondefective = 5000-500 = 4500.
Rejected nondefective = 2% of 4500 = 90.
Success!

The correct answer is E.

[ceilidh.erickson]

We can also solve this using an OVERLAPPING SETS matrix. (It's not strictly necessary in this problem, but it can be a helpful way of organizing information).


Then, fill in the given information. Call the total number of staplers X, and infer that 10% defective means 90% not defective:



Then, take 2% of the 90% that are not defective: 0.018x. We're told that that's equal to 90:



Whenever we have two expressions in the same box of the matrix, we can set them equal:
0.018x = 90
(18/1000)x = 90
x = 5,000

90 represent (0.9*0.02 --> 0.018) 1.8% of the researched amount. This will imply that the final amount is closed to 5600. Which is a bit far of the 5000 given as the right answer.

You were right - 90 does represent 1.8% of the total. I'm not sure how you got your estimated amount of 5600. Often the easiest way to deal with percents when you don't have a calculator is by turning them into fractions.

Turn 0.018 into 18/1000, and when you cross-multiply, it will be easy to divide 90 by 18, then multiply by 1,000.

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[Brent@GMATPrepNow]

Ceilidh's OVERLAPPING SETS matrix (aka "Double Matrix Method", aka "Group Grid") is a fast an easy way to organize information in overlapping sets questions. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of staplers, and the two characteristics are:
- defective or not defective
- rejected or not rejected

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

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- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
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Difficult Problem Solving questions
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Easy Data Sufficiency questions
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Medium Data Sufficiency questions
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Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
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Cheers,
Brent