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01 May 2025, 06:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
63% (01:43) correct
37%
(01:45)
wrong
based on 95
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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.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
(1) The ratio of bananas to oranges in the basket is 4:5.
(2) There are more than 36 oranges in the basket.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
10 May 2025, 23:45
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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
General Discussion
01 May 2025, 08:05
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Ans- C
statement (1) is insufficient. statement (2) is in sufficient.
statement (1) tells that there are 4x bananas for every 5x orranges. statement (2) tells there are >36 oranges, (from 1 we know oranges are multiple of 5) there for no. of oranges could be 40,45,50 etc.
now from statement (1) we know there are 4x bananas for every 5x oranges, therefore for 40 oranges there will be 32 bananas and 8 apples. for 45 oranges there will be 36 bananas and -1 apple, which is not possible. therefore there are 8 apples.
therefore both statements are together sufficient but neither alone is sufficient.
statement (1) is insufficient. statement (2) is in sufficient.
statement (1) tells that there are 4x bananas for every 5x orranges. statement (2) tells there are >36 oranges, (from 1 we know oranges are multiple of 5) there for no. of oranges could be 40,45,50 etc.
now from statement (1) we know there are 4x bananas for every 5x oranges, therefore for 40 oranges there will be 32 bananas and 8 apples. for 45 oranges there will be 36 bananas and -1 apple, which is not possible. therefore there are 8 apples.
therefore both statements are together sufficient but neither alone is sufficient.
