anairamitch1804 wrote:
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.
Please help with this DS problem.
We know the following:
1) We must distribute the 20 oranges equally across all baskets
2) At least 1 orange and 1 apple in each basket (Note: Even if you have 1 apple per basket, it satisfies the constraint that number of apples must be less than twice the number of oranges per basket)
3) No of apples must be less than twice the number of oranges in each basket.
If we have to distribute 20 oranges equally, we would end up with the following as the probable number of baskets: n = 1, 2, 4, 5, 10, 20
So if know the number of baskets, we can arrive at the minimum number of apples to be divided between the baskets.
From 1) If the number of baskets have to be halved, possible number of baskets must be even, => n= 2, 4, 10 or 20. But we won't know the total number of apples since we don't know the exact number of baskets. Hence this statement is NOT SUFFICIENT.
From 2) If number of oranges is halved, we won't have sufficient oranges to place in all baskets.
Remember, we have 20/2 = 10 oranges now and n could be 1,2,4,5,10 or 20.
If 10 oranges are not enough to distribute to all the baskets, then n (number of baskets) MUST be 20.
If n = 20, total number of apples = 20x1 = 20.
Hence this statement is SUFFICIENT.
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36% (02:30) correct 
