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26 Nov 2014, 07:56
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
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Question Stats:
65% (02:55) correct
35%
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wrong
based on 428
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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.
27 Nov 2014, 00:39
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Answer = A = 4%
Using matrix method; refer diagram below
def.png [ 4.5 KiB | Viewed 11542 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\(= \frac{1}{25} * 100 = 4%\)
Using matrix method; refer diagram below
Attachment:
def.png [ 4.5 KiB | Viewed 11542 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\(= \frac{1}{25} * 100 = 4%\)
General Discussion
intheend14
GMAT 1: 740 Q49 V41
Posts: 125
26 Nov 2014, 10:33
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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.
A
A
