Apples and oranges

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Apples and oranges

by wahi00 » Tue Apr 15, 2008 9:03 am
This is DS question but I don't understand what they are asking for? Would somone please break it down for me.

A number of apples and oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one of each type of fruit. If there are 20 oranges to be distributed, what is the minimum number of apples needed so that every basket contains less than twice as many apples as oranges?

(1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket.

(2) If the number of oranges were halved, it would no longer be possible to place an orange in every basket.

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by AleksandrM » Tue Apr 15, 2008 9:18 am
I've only gotten this far:

You need to have less than twice as many apples in each basket as oranges. Since you cannot have a split fruit, you need whole fruits. For example, if you have 1 orange in each basket, then twice as many would be 2, but less than that would 1 and one half of an apple. So, you have to have 2 oranges in each basket, so that the number of apples will be 3 in each. But from this information, you need to construct an equation and then plug in the conditions listed in each statement and figure out if it is sufficient.

From statement one, it seems that if you plug in the values you know that the number of baskets is 10. If you have 20 oranges divided among the 10, you have 2 in each. If you half the number of baskets, then you divide 20 by 5 and get twice as many as before, which is 4.

From statement two, you know that there are MORE than 10 baskets, because you would still be able to place an orange into each basket if there were 10 baskets. If this is so, then the number of baskets in the first statement must be 20, and this means that we need to take both statements together.

If you put the two together, then there are 20 baskets and we must divide 20 oranges with an equal amount in each. Therefore, the only number of apples that you can have is zero in order for the condition of having less than twice the number of oranges to hold.

So both taken together would be sufficient.

I'll keep working on it, though.

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by AleksandrM » Wed Apr 16, 2008 10:02 am