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defect problem kindly help

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defect problem kindly help [#permalink]  15 Nov 2010, 08:59
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Question Stats:

11% (00:00) correct 88% (01:26) wrong based on 0 sessions
The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

not able to understand what question is asking for? kindly help me to solve this one.

cheers,
Sonia saini
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Re: defect problem kindly help [#permalink]  15 Nov 2010, 09:16
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SoniaSaini wrote:
The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

not able to understand what question is asking for? kindly help me to solve this one.

cheers,
Sonia saini

Basically we have a set with 6 terms: {4, 6, 7, 9, 10, x}. The question asks if x is either 3, 7, or 12 then for which values of x the mean of the set equals to the median (note that mean=\frac{4+6+7+9+10+x}{6}=\frac{36+x}{6} and the median will be the average of two middle terms, so it depends on the value of x).

If x=3 then mean=\frac{36+3}{6}=6.5 and median=\frac{6+7}{2}=6.5, so mean={median};

If x=7 then mean=\frac{36+7}{6}=\frac{43}{6} and median=\frac{7+7}{2}=7, so mean\neq{median};

If x=12 then mean=\frac{36+12}{6}=8 and median=\frac{7+9}{2}=8, so mean={median}.

Answer: D (I and III only).
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Re: defect problem kindly help [#permalink]  16 Nov 2010, 07:40
Hey Bunuel,
you're really an awesome person.

thank you very much.
Re: defect problem kindly help   [#permalink] 16 Nov 2010, 07:40
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