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# in a certain deck of cards, each card has a postive integer

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in a certain deck of cards, each card has a postive integer [#permalink]  11 Jun 2007, 08:55
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in a certain deck of cards, each card has a postive integer written on it. In a multiplcation game, a child draws a card a multiplies the integer on the card by the next larger integer. if each possible product is between 15 and 200 , then the least and greatest intgers on the card could be

3 & 15
3 & 20
4 & 13
4 & 14
5 & 15
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Basically, they want the smallest and largest integers 'n' such that n(n+1) is between 15 and 200.

Smallest n would be 4, since 4*5 = 20.
n can't be 3 because 3*4 is less than 15.

Largest n would be 13, since 13*14 = 182.
n can't be 14 because 14*15 is more than 200.

Therefore answer is 4 & 13
Senior Manager
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I feel it is 4 and 13. By having 14, 14*15 = 210 which is greater than 200
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hsk wrote:

i was little consused with the next large integer. if the largest integer is not necessarily be a card, then it is 4 and 13. if the next large number has to be a card, it is 4 and 14.

seems it ios 4 and 13.
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