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# One-fifth of the batteries produced by an upstart factory are defectiv

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Math Expert
Joined: 02 Sep 2009
Posts: 50652
One-fifth of the batteries produced by an upstart factory are defectiv  [#permalink]

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26 Nov 2014, 06:56
1
7
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:55) correct 35% (02:47) wrong based on 204 sessions

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Tough and Tricky questions: Overlapping Sets.

One-fifth of the batteries produced by an upstart factory are defective and one-quarter of all batteries produced are rejected by the quality control technician. If one-tenth of the nondefective batteries are rejected by mistake, and if all the batteries not rejected are sold, then what percent of the batteries sold by the factory are defective?

A) 4%
B) 5%
C) 6%
D) 8%
E) 12%

Kudos for a correct solution.

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Re: One-fifth of the batteries produced by an upstart factory are defectiv  [#permalink]

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26 Nov 2014, 23:39
4
1

Using matrix method; refer diagram below

Attachment:

def.png [ 4.5 KiB | Viewed 3344 times ]

1. Say total number of batteries = 100

2. 20% are detective = 20

3. Total non-defective = 100-20 = 80

4. 25% are rejected = 25

5. Total not rejected = 100-25 = 75

6. One-tenth of the non-defective batteries are rejected by mistake $$= \frac{1}{10} * 80 = 8$$

7. Batteries with defect rejected = 25-8 = 17

8. Batteries with defect NOT rejected = 20-17 = 3

Fraction of defective batteries sold $$= \frac{3}{75} = \frac{1}{25}$$

Percentage$$= \frac{1}{25} * 100 = 4%$$
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Re: One-fifth of the batteries produced by an upstart factory are defectiv  [#permalink]

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26 Nov 2014, 09:33
Whoo... this one's a doozy. Here's how I broke it down with all percentages representing percentages of the whole 100% of the products made. We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective.
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Re: One-fifth of the batteries produced by an upstart factory are defectiv  [#permalink]

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26 Nov 2014, 20:55
Lets assume 100 Batteries are manufactured.
1/5(100) = 20 are defective.
1/4(100) = 25 are rejected
1/10(100-20) = 8 Rejected by mistake.
75 Non rejected and sold.
So out of 25 batteries, 8 are rejected by mistake => 25-8 =17.
20 were defective and 17 are already rejected, but 3 leaked to non-rejected lot.
(3/75)*100 = 4%

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Re: One-fifth of the batteries produced by an upstart factory are defectiv  [#permalink]

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21 Mar 2016, 13:12
took the total number as 200 and solved it in a matrix fashion .that way i found it easy
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Re: One-fifth of the batteries produced by an upstart factory are defectiv  [#permalink]

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22 Nov 2017, 11:24
Bunuel wrote:

Tough and Tricky questions: Overlapping Sets.

One-fifth of the batteries produced by an upstart factory are defective and one-quarter of all batteries produced are rejected by the quality control technician. If one-tenth of the nondefective batteries are rejected by mistake, and if all the batteries not rejected are sold, then what percent of the batteries sold by the factory are defective?

A) 4%
B) 5%
C) 6%
D) 8%
E) 12%

We can let the total number of batteries produced = 100.

Thus, 1/5(100) = 20 batteries are defective and thus 80 batteries are not defective.

Also, 1/4(100) = 25 are rejected and thus 75 batteries are not rejected and are sold.

1/10(80) = 8 non-defective batteries are rejected by mistake and thus 72 non-defective batteries are sold. However, since there are a total of 75 batteries sold, among them, thus must be 75 - 72 = 3 defective batteries. Therefore, the percent of the batteries sold that are defective is:

3/75 = 1/25 = 4%

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Re: One-fifth of the batteries produced by an upstart factory are defectiv &nbs [#permalink] 22 Nov 2017, 11:24
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