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Each of the products produced yesterday was checked by x or

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Each of the products produced yesterday was checked by x or [#permalink] New post 14 May 2013, 23:31
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69% (02:47) correct 30% (02:02) wrong based on 46 sessions
Each of the products produced yesterday was checked by x or y. 0.5% of the products checked by x are defective and 0.8% of the products checked by y are defective. If the total defective rate of all the products checked by x and y is 0.75%, what fraction of the products was checked by y?

A. 3/5
B. 5/6
C. 7/11
D. 4/5
E. 5/8
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Re: Each of the products produced yesterday was checked by x or [#permalink] New post 14 May 2013, 23:47
Expert's post
navigator123 wrote:
Each of the products produced yesterday was checked by x or y. 0.5% of the products checked by x are defective and 0.8% of the products checked by y are defective. If the total defective rate of all the products checked by x and y is 0.75%, what fraction of the products was checked by y?

A. 3/5
B. 5/6
C. 7/11
D. 4/5
E. 5/8


The easiest way to do these types of questions is to look at the difference between x and y on a number line. x is at 0.5 and y is at 0.8, and together the average is 0.75. This means that every product checked by x brings down the average by 0.25 and every product checked by y brings up the average by 0.05. To balance these two out, y needs to check 5 products for every time x checks 1 product. Hence 1/6 of total checked by x and 5/6 of total checked by y.

Algebra works too but the number line strategy gets you the correct answer quickly. If you practice doing that, this is a 1-minute question, from starting to read to clicking "next".

Hope this helps!
-Ron
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Re: Each of the products produced yesterday was checked by x or [#permalink] New post 15 May 2013, 00:08
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You can use alligation to solve this.
Ratio X=0.75-0.5=0.25

Ratio Y=0.8-0.75=0.05
Now the ratio y/x is:
\frac{Y}{X}=\frac{0.25}{0.05} or \frac{5}{1}

So for 6 products there were 5 Y and 1 X. 5/6 is the answer
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Re: Each of the products produced yesterday was checked by x or [#permalink] New post 15 May 2013, 01:59
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navigator123 wrote:
Each of the products produced yesterday was checked by x or y. 0.5% of the products checked by x are defective and 0.8% of the products checked by y are defective. If the total defective rate of all the products checked by x and y is 0.75%, what fraction of the products was checked by y?

A. 3/5
B. 5/6
C. 7/11
D. 4/5
E. 5/8



This is a allegation problem.

We can use a shortcut.

See the attachment for the shortcut.Its a simple one


So X/Y = 0.05/0.25 = 1/5

Therefore the fraction of products checked by Y = 5/6
Attachments

File comment: The shortcut
untitled.JPG
untitled.JPG [ 4.43 KiB | Viewed 667 times ]


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Re: Each of the products produced yesterday was checked by x or   [#permalink] 15 May 2013, 01:59
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