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04 Jul 2025, 08:00
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Difficulty:
55%
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Question Stats:
65% (01:43) correct
35%
(01:55)
wrong
based on 457
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Bob is organizing his stamp collection by placing all 56 of his stamps into several albums. Is there at least one album that contains two or more stamps of the same color?
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
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04 Jul 2025, 08:30
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Bob is organizing his stamp collection by placing all 56 of his stamps into several albums. Is there at least one album that contains two or more stamps of the same color?
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
If there are 56 albums, we could place one stamp in each, and the answer would be NO. But if there are only 2 albums, one of them could contain two red stamps, giving a YES answer. Not sufficient.
(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
If all 56 stamps are of different colors, no album will contain two of the same color. But if the stamps are only of two colors, then at least one album must contain two of the same color. Not sufficient.
(1)+(2) We can distribute 6 different color stamps (1 red, 1 blue, 1 green, 1 yellow, 1 orange, and 1 violet) to album 1, album 2, and so on until album 9. This covers 6 * 9 = 54 stamps. Each of the remaining 2 stamps must go into an album that already has a stamp of the same color. So in any case, at least one album will contain two or more stamps of the same color. Sufficient.
Answer: C.
GMAT Club Official Explanation:
Bob is organizing his stamp collection by placing all 56 of his stamps into several albums. Is there at least one album that contains two or more stamps of the same color?
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
If there are 56 albums, we could place one stamp in each, and the answer would be NO. But if there are only 2 albums, one of them could contain two red stamps, giving a YES answer. Not sufficient.
(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
If all 56 stamps are of different colors, no album will contain two of the same color. But if the stamps are only of two colors, then at least one album must contain two of the same color. Not sufficient.
(1)+(2) We can distribute 6 different color stamps (1 red, 1 blue, 1 green, 1 yellow, 1 orange, and 1 violet) to album 1, album 2, and so on until album 9. This covers 6 * 9 = 54 stamps. Each of the remaining 2 stamps must go into an album that already has a stamp of the same color. So in any case, at least one album will contain two or more stamps of the same color. Sufficient.
Answer: C.
General Discussion
04 Jul 2025, 08:20
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Information given:
- Bob has 56 stamps
- He places them into several albums
Question:
- Is there at least one album that contains two or more stamps of the same color?
Solution:
- Statement 1: Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
- We know there are 6 colors, but know nothing about how the albums are arranged.
- For example, if each album has just 1 stamp, there are no albums that contain 2+ stamps of the same color
- Insufficient
- Statement 2: Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
- 56 stamps into 9 albums means each album will have around 6 stamps on average
- However, we don't know how many colors there are
- For example, each stamp could have a different color
- Insufficient
- Statements 1 and 2
- We now know, 6 colors, 56 stamps, 9 albums
- To avoid repeats, each album could hold at most 6 different colors, so 6 stamps per album
- 9 albums * 6 stamps max = 54 stamps
- But Bob has 56 stamps, so at least 2 stamps must share a color in the same album
- Therefore, it must be true that at least one album has two or more stamps of the same color
- Sufficient
Answer: C, both statement together are sufficient, but neither alone is sufficient
- Bob has 56 stamps
- He places them into several albums
Question:
- Is there at least one album that contains two or more stamps of the same color?
Solution:
- Statement 1: Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
- We know there are 6 colors, but know nothing about how the albums are arranged.
- For example, if each album has just 1 stamp, there are no albums that contain 2+ stamps of the same color
- Insufficient
- Statement 2: Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
- 56 stamps into 9 albums means each album will have around 6 stamps on average
- However, we don't know how many colors there are
- For example, each stamp could have a different color
- Insufficient
- Statements 1 and 2
- We now know, 6 colors, 56 stamps, 9 albums
- To avoid repeats, each album could hold at most 6 different colors, so 6 stamps per album
- 9 albums * 6 stamps max = 54 stamps
- But Bob has 56 stamps, so at least 2 stamps must share a color in the same album
- Therefore, it must be true that at least one album has two or more stamps of the same color
- Sufficient
Answer: C, both statement together are sufficient, but neither alone is sufficient
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