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basketball cards

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basketball cards [#permalink] New post 09 Apr 2009, 08:50
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0% (00:00) correct 100% (01:29) wrong based on 3 sessions
A company produces basketball cards in equal numbers of regular packs of 16 and deluxe edition packs of 30. If, on a certain day, a company produces 241 cards, what is the smallest number of additional cards the company needs to produce in order to maintain its regular production practice?

Choices: 5,11,21,35,46
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Re: basketball cards [#permalink] New post 09 Apr 2009, 21:49
5 it is
trial and error
pick and plug data
jeevanchand wrote:
A company produces basketball cards in equal numbers of regular packs of 16 and deluxe edition packs of 30. If, on a certain day, a company produces 241 cards, what is the smallest number of additional cards the company needs to produce in order to maintain its regular production practice?

Choices: 5,11,21,35,46

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Re: basketball cards [#permalink] New post 09 Apr 2009, 23:45
16x+30x=241+m
m=?

when x=6, 46*6=276
276=241+m
m=35
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Re: basketball cards [#permalink] New post 10 Apr 2009, 00:11
Should be 35. OA?

Let num of packs = x
16x + 30 x = 241 + some additional cards
46x = 241 + some additional cards

Divide 241/46 => remainder is 11 cards
These 11 cards should constitute atleast 1 extra pack for both regular and deluxe editions.
hence additional cards needed = 30 + 16 - 11 = 35.
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Re: basketball cards [#permalink] New post 11 Aug 2011, 11:49
A quick approach is as follows.

Knock out E right away, since E is odd, and an odd cannot be a sum of two even numbers.

Now since since the total should be the sum of same multiple of 16 and 30, we know it can't be greater than 8
then make this quick table:
x 16 30 Total
5 80 150 230
6 96 180 276 = 241 + 35
Re: basketball cards   [#permalink] 11 Aug 2011, 11:49
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