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GMAT Club Olympics 2025 (Day 5): Bob is organizing his stamp

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05 Jul 2025, 06:09

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(1) Tells us there are 6 colors, but nothing about how stamps are arranged in albums → Not sufficient
(2) Tells us stamps are placed in 9 albums, but nothing about stamp colors → Not sufficient
Together:
56 stamps, 6 colors → avg ~9.3 stamps/color
9 albums → avg ~6.2 stamps/album
But without knowing how colors are distributed across albums, it's possible that all stamps in an album are of different colors.
So, even combined, we can’t be sure any album has two stamps of the same color. (E)

Bunuel

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.

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05 Jul 2025, 06:57

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(1) What if Bob has 56 albums? Each stamp has a separate album. So, it could also be that no album has >=2 stamps of the same color.
(2) What if Bob has stamps of 56 colors? Then, again, possible that no album contains >=2 stamps.

(1) and (2) -> Even if we try to ensure that no color repeats in an album - that I think will look like 8 albums of 6 stamps each and 9th album has 8 stamps. While it is still possible that the 8 albums (containing 6) have stamps of the 6 different colors, the album with 8 stamps will definitely contain 2 stamps of the same color, for 2 colors. Whatever the distribution, I think we can see that there is at least one album that has >=2 stamps of same color.

Option C

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05 Jul 2025, 06:58

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Statement 1: Definitely NOT SUFFICIENT.
Statement 2: We don't know anything about the distribution of the stamps nor their respective colors.

Combining: Still not sufficient. Option E.

Bunuel

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05 Jul 2025, 07:17

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There are $56$ total stamps. Is there at least one album that contains two or more stamps of the same color?

Statement 1 -> Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
This tells us nothing about how the albums are grouped. Not sufficient.

Statement 2 -> Bob places the stamps into $9$ albums, with each stamp placed in exactly one album.
This statement does not give us any color data. There could be $56$ different colors distributed in $9$ albums. Not sufficient.

1+2 -> We know there are $56$ stamps, $6$ different colours of stamps and $9$ albums. The maximum number of stamps we can put in an album without repeating a color is $6$.
$56$ divided by $9$ gives us $6$ with a remainder of $2$. These two cards have to go in one of the $9$ albums and no matter the color distribution of the cards, there will be atleast one album with $7$ or more stamps containing duplicate color stamps.

Answer - C

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05 Jul 2025, 07:30

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Bob is organizing his stamp collection by placing all 56 of his stamps into several albums

Given the
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
There are only 6 possible stamp colors.
But we don’t know how the 56 stamps are placed into albums i.e, maybe all of one color are in different albums, maybe the same color appears across albums
Statement is not sufficient

(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
This gives us the number of albums. But we have no idea about the colors of the stamps.
So, we can't determine whether an album has 2 or more stamps of the same color
Statement is not sufficient

Combining statement (1) and (2),
Let’s assume a scenario where Bob tries to avoid putting same-colored stamps in same albums

We know that max number of colors = 6
Number of albums = 9
Number of stamps = 56

Avergae number of stamps per album = 56/9 = 6.22
So atleast 1 album contains 7 stamps

If there are only 6 colors then, an album with 7 stamps must have 2 of same color.

C. Both statements together are sufficient, but neither alone is

RedYellow

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05 Jul 2025, 07:32

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To be sure that you are able to organize 56 stamps with "c" different colors in "a" albums without repeating a color in any album there must be at most c*a stamps

(1)
6a>56

true if a>=10
false if a<10

Insufficient

(2)
9c>56

true if c>=7
false if a<7

Insufficient

(1) and (2)
6*9=54 is less than 56

The answer is yes.

Sufficient

Correct answer is C

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05 Jul 2025, 07:37

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(1)
The answer depends on the number of albums too.

Statement (1) alone is insufficient.

(2)
The answer depends on the number of colors too.

Statement (2) alone is insufficient.

(1)+(2)
6 colors and 9 albums guarantee that it is possible to place 6*9=54 stamps without repeating color in any album. As they are 56 stamps, it is impossible to do it without repeating in at least one album.

Statement (1) and (2) together are sufficient

Answer C

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05 Jul 2025, 07:57

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1) we don’t know the number of albums and hence not how stamps are distributed ns
2) we don’t know the number of colors ns
Combined

We know the number and color of stamps
Suff

And C

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05 Jul 2025, 10:36

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Bob has 56 stamps, sorted into albums. Is there at least one album with two or more stamps of the same color?
(1) Each stamp is exactly one of six colors.
→ The 56 stamps are colored from 6 colors.
Can Bob arrange them into albums so that no album has two of the same color?
If he places ≤ 6 stamps in any album, each of different color, he can avoid repeats.
But there’s no constraint given on how many albums he uses.
So with just (1), we don't know if he used many albums (e.g. 56 albums with 1 stamp each, guaranteeing no repeated color in any album) or few albums with >6 stamps.
✅ (1) alone is insufficient.
[hr]
(2) Bob places the stamps into 9 albums.
→ 56 stamps in 9 albums.
What’s the worst-case distribution? Even if he spreads them as evenly as possible:
569≈6.22\frac{56}{9} \approx 6.22956≈6.22
He must have at least one album with at least 7 stamps (by the pigeonhole principle).
If an album has ≥ 7 stamps but only 6 possible colors, at least two stamps must be the same color in that album.
✅ (2) alone is sufficient.

Bunuel

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05 Jul 2025, 13:38

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Question goal: Find weather at least an album will contain 2 or more stamps of the same color
Question data: number of stamps = 56 | every stamp will go on an album
Question mindest: As it asks if there is at least one album, we should work with extreme allowed scenarios (e.g 56 albums or only 1 or 2 colors) on the alternatives, making tests easier

I- there are six colors: There may be 56 different albums, allowing no stamps from same color to be together or a single album, making stamps from same color together -> Not Suf

II- Number of albums = 9, each stamp goes in a slingle album: If there are 56 different colors, no 2 stamps from same color together. If there are 2 colors, there will be stamps from same color together -> Not Suf

Together: 56 stamps of 6 colors across 9 albums: 56/9 = 6 (stamps per album) + 2 (remainder). As there are 6 colors, we can put 1 stamp from each color on each of 9 albums, but there will still be 2 stamps that need allocation. Whatever album they go, there will be another stamp from same color -> SUF (C)

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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.

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05 Jul 2025, 23:06

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Total Number of Stamps = 56
Let A represent Album with s representing number of stamps in it, then
A(0s)+A(1s)+A(2s)+.....+A(xs) = 56

We need
Atleast one album that contains two or more stamps of the same color, that is
56-A(0s)-A(1s) = ?

I. Total number of stamps colors = 6 INSUFFICIENT
II. 9 albums had exatly 1 stamp INSUFFICIENT

C SUFFICIENT

56- (9*54) = 2

Bunuel

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06 Nov 2025, 05:24

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What is the significance of the phrase from St2 - "with each stamp placed in exactly one album"??

That kinda made me confused for a while.

Is that ruling out the possibility of splitting the stamp into multiple albums?

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06 Nov 2025, 07:04

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glagad

It rules out any possibility of one stamp being split across multiple albums or counted twice. In other words, no stamp is shared between albums; every stamp belongs to a single, distinct album. The line is just there to make the distribution rule explicit, not to introduce any new condition.