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A number of apples and oranges are to be distributed evenly

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A number of apples and oranges are to be distributed evenly

by Anaira Mitch » Thu Jan 12, 2017 10:25 am
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.
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Jan 12, 2017 11:24 am
Anaira Mitch 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.
Since it is possible for each basket to contain 1 apple each, the minimum number of apples is equal to the total number of baskets:
If there is 1 basket, then at least 1 apple is needed.
If there are 2 baskets, then at least 2 apples are needed.
If there are 3 baskets, then at least 3 apples are needed.

Question stem, rephrased:
What is the total number of baskets?

Since every basket must contain the same number of oranges -- and there are a total of 20 oranges -- the total number of baskets must be a factor of 20:
1, 2, 4, 5, 10, 20.

Statement 1:
Case 1: 2 baskets, each with 10 oranges
Here, if the total number of baskets is halved to 1, then the 1 remaining basket will contain 20 oranges, satisfying the constraint that the number of oranges per basket doubles.

Case 2: 4 baskets, each with 5 oranges
Here, if the total number of baskets is halved to 2, then the 2 remaining baskets will each contain 10 oranges, satisfying the constraint that the number of oranges per basket doubles.

Since the total number of baskets can be different values, INSUFFICIENT.

Statement 2:
In other words, the total number of baskets is too great to allow for an even distribution of 10 oranges.
Of the factors of 20, only the greatest -- 20 itself -- is too large to allow for an even distribution of 10 oranges.
Thus, the total number of baskets = 20.
SUFFICIENT.

The correct answer is B.
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by [email protected] » Thu Jan 12, 2017 2:49 pm
Hi Anaira Mitch,

GMAT questions are always specifically worded (because they're built around patterns that help to define what the correct answer is). Thus, when a question places limitations on variables, you should pay careful attention to those limitations.

Here, we're told that apples and oranges are supposed to be EVENLY distributed among an unknown number of baskets and that each basket must hold at least one of each fruit. The 20 oranges that we're given must be EVENLY distributed, so the number of baskets is limited to the following options:

Number of Baskets = 1, 2, 4, 5, 10 or 20

The question also tells us that each basket must hold a number of apples that is LESS than TWICE the number of oranges. This is just a wordy way of saying that there has to be LESS than 40 total apples. However, the question asks us for the MINIMUM number of apples. Given the fact that apples are also supposed to be EVENLY distributed, we really just need to know the number of baskets (since each basket must contain at least one apple) to determine the minimum number of apples needed.

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

IF we had....
2 baskets with 10 oranges each
halving that would give us...
1 basket with 20 oranges and the answer to the question would be 1 apple.

4 baskets with 5 oranges each
halving that would give us...
2 baskets with 10 oranges and the answer to the question would be 2 apples.
Fact 1 is INSUFFICIENT

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

Since we have 20 oranges, the ONLY situation in which 10 oranges wouldn't put at least 1 orange in each basket is if there were 20 baskets. Thus, there would have to be 20 apples.
Fact 2 is SUFFICIENT

Final Answer: B

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by Matt@VeritasPrep » Wed Jan 18, 2017 6:22 pm
Anaira Mitch 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.
One last approach:

To solve this, we'd first like to know how many oranges there are. Since we can divide the 20 oranges among the baskets evenly (= the same number of oranges in each basket), we know that the number of baskets must be a factor of 20.

S1 tells us that the number of oranges is even: we can cut that number in half and still have an integer. So we could have 2, 4, 10, or 20 oranges; NOT SUFFICIENT.

S2 tells us that the number of oranges > 10. That forces the number to be 20. Since the number of baskets must be a factor of this that's also > 10, we've got 20 baskets. We need at least one apple per basket, so the minimum is exactly one per basket, or 20; SUFFICIENT.

It's conceptually valuable to notice all the other consequences of the stem, but under time constraints we don't necessarily need to.
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