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A foreman for an injection-molding firm

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by manhhiep2509 » Sun Sep 21, 2014 7:21 am
A foreman for an injection-molding firm admits that
on 10% of his shifts, he forgets to shut off the injection
machine on his line. This causes the machine
to overheat, increasing the probability from 2%
to 20% that a defective molding will be produced
during the early morning run. What proportion of
moldings from the early morning run is defective?

A. 0.012
B. 0.027
C. 0.014
D. 0.038
E. 0.010

Answer: D
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by [email protected] » Sun Sep 21, 2014 10:52 am
Hi manhiep2509,

This question isn't quite worded the way that the Official GMAT would word it, and the math concept that it's based on isn't too common on the GMAT, but here's how you can solve it.

On any given day, we won't know if the foreman shut off the line or not, so we have to account for two situations:
1) Forgot to shut off the line (10% of the time) --> leads to a 20% chance of defects in the morning
2) DID NOT forget to shut off the line (the other 90% of the time) --> normal 2% chance of defects in the morning

1st option: (.1)(.2) = .02
2nd option: (.9)(.02) = .018
Total = .02 + .018 = .038

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
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by Brent@GMATPrepNow » Sun Sep 21, 2014 11:06 am
manhhiep2509 wrote:A foreman for an injection-molding firm admits that on 10% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability from 2% to 20% that a defective molding will be produced during the early morning run. What proportion of moldings from the early morning run is defective?

A. 0.012
B. 0.027
C. 0.014
D. 0.038
E. 0.010

Answer: D
As Rich noted, this question isn't GMAT-quality.
Plus, as it stands, the correct answer is actually F. Cannot be determined, because we have no idea hom many moldings were produced during the early morning run.
For example, if only 2 moldings were produced, then there could be only 3 correct answers: 0/2, 1/2 or 2/2, in which case none of the answer choices match.

That said, the (poorly-worded) INTENT of the question is to determine the EXPECTED proportion of defects. In that case Rich's solution is perfect.


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Matt@VeritasPrep » Mon Sep 22, 2014 9:10 am
This question is pretty easily fixed by changing "proportion" to "expected proportion" and by stipulating that the foreman is present during every early morning run in which moldings are made. Over time, we'd expect 3.8% of the moldings to be defective: 2% of the 90% made on mindful days plus 20% of the 10% made on forgetful days.
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