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Maximimun & minimun problem

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by Taniuca » Sun Aug 22, 2010 6:42 am
Some help will be appreciatted!!!

It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?

35
105
180
210
420
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by Gurpinder » Sun Aug 22, 2010 7:10 am
Taniuca wrote:Some help will be appreciatted!!!

It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?

35
105
180
210
420
IMO 420.

We are told that no more than 7 children will be attending. But we CAN have less than 7 children.
So i guess we are just looking for a number from the answers that is divisible by every number including and below 7.

And 420 is divisible by 1,2,3,4,5,6,7, which means that it gives you an integer result. Therefore, if we have any number of children below or equal to 7, they will get equal cookies.

I hope that helps!
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by sdotcruz » Fri Aug 27, 2010 10:10 am
I agree with Gurpinder. I calculated 420 because:

From the problem children =< 7. so there can be 1,2,3,4,5,6, or 7 children.

looking at the prime factors there must be 2 two's, 1 three, 1 five and 1 7. Multiplying all 5 numbers together gives you 420. which is the smallest number divisible by 2*2*3*5*7.

The reason i did not count every prime factor of 1,2,3,4,5,6, and 7 is because the number of children attending will only be one of the possible 7 choices. The 5 prime numbers above can combine to make a number divisible by any of the possible number of children. ie. if 4 show up with have 2*2 in our number that will make the number divisible by 4, if 6 show up with have 2*3 in our number that will make the number divisible by 6 and so on.
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by diebeatsthegmat » Sun Aug 29, 2010 11:57 am
Taniuca wrote:Some help will be appreciatted!!!

It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?

35
105
180
210
420
the smallest number we must find must be able to divide 1,2,3,4,5,6,7
so eliminate A,B and C cos 180 /7 = non integer number
thus 210 and 420 left and 420 =2*210
select D
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by diebeatsthegmat » Sun Aug 29, 2010 11:58 am
diebeatsthegmat wrote:
Taniuca wrote:Some help will be appreciatted!!!

It is known that no more than 7 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?

35
105
180
210
420
the smallest number we must find must be able to divide 1,2,3,4,5,6,7
so eliminate A,B and C cos 180 /7 = non integer number
thus 210 and 420 left and 420 =2*210
select D
sorry, E is correct cos 210 cant devide 4 to get an integer . wrong
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