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23 Mar 2022, 01:30
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95%
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Question Stats:
41% (02:51) correct
59%
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wrong
based on 128
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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.
Are You Up For the Challenge: 700 Level Questions
Similar question to practice: https://gmatclub.com/forum/a-number-of- ... 99963.html
(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.
Are You Up For the Challenge: 700 Level Questions
Similar question to practice: https://gmatclub.com/forum/a-number-of- ... 99963.html
23 Mar 2022, 14:30
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Bunuel
Breaking Down the Info:
Less than twice as many apples = "<2A". "As" is the equal sign here, so we have O < 2A, and we want to minimize A. Note the O here is the number of oranges per basket, so we simply need to know that value in order to find A. We can set the number of baskets as B to have \(\frac{20}{B} = O\).
Statement 1 Alone:
20 is already a multiple of the number of baskets, so naturally, this is true. This only tells us the number of baskets is an even number.
Statement 2 Alone:
According to the wording, we cannot even place a single orange in every basket. The only possible scenario for this is B = 20, as the 2nd largest factor of 20 is just 10. Then O = 1 and we can calculate A next. Sufficient.
Answer: B
03 Mar 2023, 18:52
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Each basket must contain at least one of each type of fruit. We also must ensure that every basket contains less than twice as many apples as oranges. Therefore, the minimum number of apples that we need is equal to the number of baskets, since we can simply place one apple per basket (even if we had only 1 apple and 1 orange per basket, we would not be violating any conditions). If we are to divide the 20 oranges evenly, we know we will have 1, 2, 4, 5, 10, or 20 baskets (the factors of 20). But because we don't know the exact number of baskets, we do not know how many apples we need. Thus, the question can be rephrased as: "How many baskets are there?"
Statement 1 - INSUFFICIENT: This tells us only that the number of baskets is even (halving an odd number of baskets would result in half of a basket). Since we have 20 oranges that must be distributed evenly among an even number of baskets, we know we have 2, 4, 10, or 20 baskets. But because we still do not
know exactly how many baskets we have, we cannot know how many apples we will need.
Statement 2 - SUFFICIENT: This tells us that 10 oranges (half of the original 20) would not be enough to place an orange in every basket. So we must have more than 10 baskets. Since we know the number of baskets is 1, 2, 4, 5, 10, or 20, we know that we must have 20 baskets. Therefore, we know how many apples we will need.
The correct answer is B.
Statement 1 - INSUFFICIENT: This tells us only that the number of baskets is even (halving an odd number of baskets would result in half of a basket). Since we have 20 oranges that must be distributed evenly among an even number of baskets, we know we have 2, 4, 10, or 20 baskets. But because we still do not
know exactly how many baskets we have, we cannot know how many apples we will need.
Statement 2 - SUFFICIENT: This tells us that 10 oranges (half of the original 20) would not be enough to place an orange in every basket. So we must have more than 10 baskets. Since we know the number of baskets is 1, 2, 4, 5, 10, or 20, we know that we must have 20 baskets. Therefore, we know how many apples we will need.
The correct answer is B.
