How many sets containing 10 positive digits (integers from 1 : PS Archive
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# How many sets containing 10 positive digits (integers from 1

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How many sets containing 10 positive digits (integers from 1 [#permalink]

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07 Jul 2006, 23:11
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How many sets containing 10 positive digits (integers from 1 to 9) have a single mode of 9 and a mean of no more than 4.5?

(A) 3 (B) 4 (C) 5 (D) 6 (E) more than 6
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07 Jul 2006, 23:34
I don't know if I have understood the question or not.

What I understand is sets can contain only one value of 9 and 9 other value. Mean should not greater than 4.5.

If this is asked then I think E.

Set could be (9,Nine 1s), (9,2,Eight 1s), (9,2,3,Seven 1s) etc.....
So it will be more than 6.
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07 Jul 2006, 23:45
A set has a single mode of 9 only if 9 occurs more often than any other number. Some sets have several modes, others have no mode.
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08 Jul 2006, 00:11
I think anwsers by Kevin and ps_dahiya are contradictory.When 9 is the mode that means it occurs more than any other digit and at the same time the sum of ten digits should not be more than 45.
I think i have understood the question correctly and in the light of this i am unable to get any solution.
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08 Jul 2006, 00:28
kevincan wrote:
A set has a single mode of 9 only if 9 occurs more often than any other number. Some sets have several modes, others have no mode.

Then the answer is B = 4

If we take nines 2 times:
Then we have to take all other numbers only once and set will be 9912345678. Sum will exceed 45.

If we take nine three times:
Then we can take any number at a max of 2 times. To minimize the sum repeat the smallest numbers more. Sets are

9991122334 = 43.......................1
9991122335 = 44.......................2
9991122336 = 45.......................3
9991223344 = 46.. EXCEEDS 45.

If we take nine four times:
9999111222 = 45.......................4
9999111223 = 46.. EXCEEDS 45.

We can't take 9 five time or more because sum exceeds 45.
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08 Jul 2006, 05:17
Great approach, though you've overlooked 9991123344 9991122344 and 991122345
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08 Jul 2006, 19:42
kevincan wrote:
Great approach, though you've overlooked 9991123344 9991122344 and 991122345

Yes... thanks. Hope I don't miss on the G-Day .
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08 Jul 2006, 19:42
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