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Each of the products produced yesterday was checked by x or [#permalink]

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15 May 2013, 00:31

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70% (01:51) correct
30% (02:39) wrong based on 208 sessions

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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?

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".

Re: Each of the products produced yesterday was checked by x or [#permalink]

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15 May 2013, 02:59

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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 [ 4.43 KiB | Viewed 2537 times ]

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Re: Each of the products produced yesterday was checked by x or [#permalink]

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28 Jul 2014, 02:38

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Each of the products produced yesterday was checked by x or [#permalink]

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09 Aug 2014, 01:54

SrinathVangala wrote:

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

Hi, I am not aware of allegation. can you please explain about this or point me to some useful but short source.

Re: Each of the products produced yesterday was checked by x or [#permalink]

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16 Dec 2015, 01:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Each of the products produced yesterday was checked by x or [#permalink]

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14 Jun 2017, 12:01

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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

0.5X + 0.8Y = 0.75 ( X + Y ) => 0.05 Y = 0.25 X => Y / X = 5 / 1