Each of 30 parents chose one of five days from Monday

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Each of 30 parents chose one of five days from Monday [#permalink]

14 Mar 2011, 16:31

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284. Each of 30 parents chose one of five days from Monday through Friday to attend parent-teacher conferences. Was at least one of the five days chosen by more than 10 parents?
(1) 15 parents chosen Monday or Tuesday.
(2) Each of the five days was chosen by at least 5 parents.

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Re: 30 parents [#permalink]

14 Mar 2011, 17:49

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_ _ _ _ _
M T W T F

a. 15 parents chose M/T.. its possible that 8 chose M and 7 chose T ---> insufficient

b. each day was chosen by atleast 5 --> 5*5 = 25, the rest 5 can be assigned to any one of the days making the number = 10. but it cannot be more than 10. -->sufficient

ans b

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Re: 30 parents [#permalink]

14 Mar 2011, 17:50

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banksy wrote:

Each of 30 parents chose one of five days from Monday through Friday to attend parent-teacher conferences. Was at least one of the five days chosen by more than 10 parents?

(1) 15 parents chosen Monday or Tuesday --> we can have YES answer, (for example: 14-1-5-5-5) as well as NO answer, (for example: 10-5-5-5-5). Not sufficient.

(2) Each of the five days was chosen by at least 5 parents --> even if we distribute parents: 5-5-5-5-10, we still won't have any day which was chosen by more than 10 parents (minimizing # of parents who chose each of 4 days to maximize # of parents who chose the fifth day). Sufficient.

Answer: B.
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Re: 30 parents [#permalink] 14 Mar 2011, 17:50

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Each of 30 parents chose one of five days from Monday

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Each of 30 parents chose one of five days from Monday

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