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01 May 2025, 01:02
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A vendor has a box containing 30 bottles of juice. Each bottle is either 100 percent apple juice, 100 percent grape juice, or a mixture of apple and grape juices. How many bottles contain both apple and grape juices?
(1) Of the 30 bottles, 12 are 100 percent grape juice.
(2) Of the 30 bottles, 26 contain some grape juice and 18 contain some apple juice.
(1) Of the 30 bottles, 12 are 100 percent grape juice.
(2) Of the 30 bottles, 26 contain some grape juice and 18 contain some apple juice.
01 May 2025, 01:02
Kudos
Bookmarks
Official Solution:
A vendor has a box containing 30 bottles of juice. Each bottle is either 100 percent apple juice, 100 percent grape juice, or a mixture of apple and grape juices. How many bottles contain both apple and grape juices?
We have:
Total = Only apple + Only grape + Both
30 = Only apple + Only grape + Both
(1) Of the 30 bottles, 12 are 100 percent grape juice.
This implies that Only grape = 12, but we have no information about the number of Only apple or Both. Not sufficient.
(2) Of the 30 bottles, 26 contain some grape juice and 18 contain some apple juice.
• If 26 bottles contain grape juice, then 4 do not. These 4 must be Only apple.
• If 18 bottles contain apple juice, then 12 do not. These 12 must be Only grape.
Thus:
30 = 4 + 12 + Both
Both = 14
Sufficient.
Answer: B
A vendor has a box containing 30 bottles of juice. Each bottle is either 100 percent apple juice, 100 percent grape juice, or a mixture of apple and grape juices. How many bottles contain both apple and grape juices?
We have:
Total = Only apple + Only grape + Both
30 = Only apple + Only grape + Both
(1) Of the 30 bottles, 12 are 100 percent grape juice.
This implies that Only grape = 12, but we have no information about the number of Only apple or Both. Not sufficient.
(2) Of the 30 bottles, 26 contain some grape juice and 18 contain some apple juice.
• If 26 bottles contain grape juice, then 4 do not. These 4 must be Only apple.
• If 18 bottles contain apple juice, then 12 do not. These 12 must be Only grape.
Thus:
30 = 4 + 12 + Both
Both = 14
Sufficient.
Answer: B
