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A fruit vendor has a total of 80 apples, oranges, and bananas in a basket. How many apples are there?
(1) The ratio of bananas to oranges in the basket is 4:5.
(2) There are more than 36 oranges in the basket.
(1) The ratio of bananas to oranges in the basket is 4:5.
(2) There are more than 36 oranges in the basket.
01 May 2025, 06:41
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Official Solution:
A fruit vendor has a total of 80 apples, oranges, and bananas in a basket. How many apples are there?
(1) The ratio of bananas to oranges in the basket is 4:5.
This implies that the number of bananas and oranges must be multiples of 4 and 5, respectively. However, multiple combinations are possible. For example, bananas = 4, oranges = 5, apples = 71; or bananas = 8, oranges = 10, apples = 62. Not sufficient.
(2) There are more than 36 oranges in the basket.
Clearly not sufficient.
(1)+(2) We have that the number of oranges is a multiple of 5 greater than 36, so the number of oranges can be 40, 45, and so on. If the number of oranges is 40, the number of bananas becomes 32, and the number of apples is 80 - 40 - 32 = 8. If the number of oranges is 45, the number of bananas becomes 36, which would make the total of just these two fruits 81, exceeding the total number of fruits in the basket. This makes this case and all other cases with 45 or more oranges invalid. Thus, the only possible case is 40 oranges, 32 bananas, and 8 apples. Sufficient.
Answer: C
A fruit vendor has a total of 80 apples, oranges, and bananas in a basket. How many apples are there?
(1) The ratio of bananas to oranges in the basket is 4:5.
This implies that the number of bananas and oranges must be multiples of 4 and 5, respectively. However, multiple combinations are possible. For example, bananas = 4, oranges = 5, apples = 71; or bananas = 8, oranges = 10, apples = 62. Not sufficient.
(2) There are more than 36 oranges in the basket.
Clearly not sufficient.
(1)+(2) We have that the number of oranges is a multiple of 5 greater than 36, so the number of oranges can be 40, 45, and so on. If the number of oranges is 40, the number of bananas becomes 32, and the number of apples is 80 - 40 - 32 = 8. If the number of oranges is 45, the number of bananas becomes 36, which would make the total of just these two fruits 81, exceeding the total number of fruits in the basket. This makes this case and all other cases with 45 or more oranges invalid. Thus, the only possible case is 40 oranges, 32 bananas, and 8 apples. Sufficient.
Answer: C
