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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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A) alone not sufficient. Because in that case, we dont know anyting about the amount of albums.
B) alone not sufficient. We dont know anything about the colors

taken together, we know, that we have to split up all the colors in 9 albums.
We have a capacity of 9*6 = 54 unique stamps without doubling of any kind. Taken together, we have 2 to much.
that means, we have to use a color at least two times.

therefore: 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.

Only got the information about the stamp color, but don't know the nos. of the album, insufficient.

(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.

Only got the information about the albums, but don't know the nos. of colors, insufficient.

But with combining both, we can say that 6*9 = 54 stamps can be placed without repetition, but then the next two will be of repetitive color. Hence, both are sufficient.
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D. Both together.

(1) There 56 stamps might be distributed onto 56 albums -> INSUFFICIENT
(2) There might be 56 different colors -> INSUFFICIENT

Together: Each album has 1 stamp of each color makes 9*6=54 total stamps
Since there's still 2 stamps left, they will in any case make a color repeat.

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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56 stamps into albums

(1)
If the number of albums is 56 and each stamp is in a distinct album, the answer is no.
If the number of albums is 2, the answer is yes.

INSUFFICIENT

(2)
If the number of colors is 56, the answer is no.
If the number of colors is 1, the answer is yes.

INSUFFICIENT

(1)+(2)
With 6 colors and 9 albums we can allocate, at most, 6*9 = 54 stamps without repeating color in any album.

There are 56>54, so there must be at least one album that contains two or more stamps of the same color.

SUFFICIENT

IMO 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.
Since number of albums and distribution of stamps are unknown
NOT SUFFICIENT

(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
Since colors of the stamps are unknown
NOT SUFFICIENT

(1) + (2)
(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.
Since there are 56 stamps and 9 albums, 9*6 = 54 stamps can be distributed such that each contains only 1 stamps of each colour, but remaining 2 stamps must be of the same colour in some of the albums.
There is at least 1 album that contains two or more stamps of the same color
SUFFICIENT

IMO C
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Bob has 56 stamps that he places into albums. We need to figure out if at least one album must have two or more stamps of the same color.

Statement (1): The stamps are in one of six colors (red, blue, green, yellow, orange, violet). But we have no information about how they’re placed into albums. It’s possible each album has just one stamp or stamps of different colors. So this alone doesn’t help.
→ Insufficient.

Statement (2): Bob uses 9 albums, each stamp in exactly one album. But we don’t know anything about the colors. Even if some albums have multiple stamps, without knowing the colors, we can’t guarantee any duplicates.
→ Insufficient.

Combining both statements:
There are 56 stamps in 9 albums. To avoid duplicates of any color, the maximum each album could have is 6 stamps (one of each color). That covers only 9 × 6 = 54 stamps. But we have 56 stamps, so at least one album must have 7 stamps. With only 6 colors, at least two stamps in that album must share the same color.

→ Together sufficient. Answer: C.
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Bob has 56 stamps and we want to check whether there is any album in which two or more stamps of same color can be placed.
to solve this we need to know different colored stamps are there and also how many albums are there

S1 = we have 6 different color for stamps. This statement is not sufficient as we can have as many as 100 albums or as minimum as 3 albums (question stem mentioned several albums and several means >2)

S2= this statement tells us that we have 9 albums, but we don't know how many different colored stamps are there, hence insufficient

S1+S2 = When we devide 6 color in 56 stamps we will have at least 10 stamps with same color
eg Red - 10
blue - 10
green- 9
yellow -9
orange- 9
violet -9

after dividing all the stamps equally in different envelops we will have at least 2 envelopes with 2 or more with stamps of same color
Hence sufficient
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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?

There are total of 56 stamps distributed in several albums. We need to determine whether one album has 2 stamps of same color

Statement 1
Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.

Each stamps of the 56 stamps is one of the six colors. But it isn't sure how many are of each color. Further no information on distribution in album is available.

So statement is insufficient.

(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.
Again stamps are placed in 9 albums but distribution is not clear. So it can be possible all albums are evenly distributed or one album can have max stamps, one can have min or one album can have specific no of stamps

It is not clear which album will have how many stamps. Further no information on the color of the stamps. So Statement is insufficient.

Combining both statements

Statement 1 & Statement doesn't provide information on how many stamps are of which color as well as how many stamps are there in ach album.

So combine statements are also insufficient

Answer should be E.
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There are totally 56 stamps of one or more colors placed into several albums

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.

If all the stamps are of same color and there are 56 albums, each album has only one stamp, then there can not be two or more stamps of same color

If there are less than 56 albums and all the stamps are of same color, at least one album will have two or more stamps of same color

Not Sufficient

Statement 2: Bob places the stamps into 9 albums, with each stamp placed in exactly one album.


If all the stamps are of different color, then there can not be two or more stamps of same color in any of the albums. No of colors of stamps is unknown

Not Sufficient

Statements Combined:

There are 6 colors & 9 albums. Here the worst case scenario will be the stamps are evenly distributed to colors & albums

Since there are 6 colors, each color will have at least 9 stamps in it and at least one color will have 10 stamps.

And there are 9 albums, each album will have one stamp of each color and there will be remaining 2 stamps must be placed in one of the albums. By this way, at least one album will contain two or more stamps of the same color.

Sufficient

Answer: C
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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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Total stamps = 56
Albums = x
Colors = y

(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
We have Colors as red, blue, green, yellow, orange, or violet
Hence y = 6

But we don't know the number of albums. It could be 56 albums and despite 6 colors, all stamps may be in different albums and make the statement false

Alternatively, there could be just 1 album, and all colors would have to be in that 1 album, and that will make the statement true

Insufficient

(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.

We have 9 Albums
Hence x = 6

But we don't know the number of colors. It could be 56 colors and despite 9 albums, all colors may be in different albums and make the statement false

Alternatively, there could be just 1 color album, and all albums would have just one color and that will make the statement true

Insufficient

Together 1 and 2 we get
x = 6
y = 9
Total stamps = 56

If we are to place the stamps in the 9 albums without keeping more than 1 color in one album, we can get a total of 9 * 6 = 54 stamps
However, when adding the last two stamps we would have to add a similar color stamp into both the albums.

IMHO Option C
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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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From statement 1 we can deduce 2 possiblities- 1 is if he wants to place seperate color into seperate album then it would be 56/6. We cannot deduce anything conclusive but if we combine this data with 2 then we get to know that there would be 2 stamps which have to be either placed with same color or with different colors. Now we can determine based on total number of stamps and the 2 statement so both staments are required to answer.
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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Bob has 56 stamps, We are to determine whether there is atleast one album in which two or more stamps are of the same color.

Statement 1:
This means all 56 stamps are colored using 6 colors. We don't have any information about the number of albums, or how many stamps per album.
Insufficient.

Statement 2:
56 stamps are placed in 9 albums. So avg number of stamps per album = 56/7 = approx 6.22
No information about colors.
Insufficient

Both 1 & 2,
By logic, If any album has more than stamps and there are only 6 possible colors, then there is a possibility that at least one color must be repeated.
Therefore, At least one album contains two or more stamps of the same color.

C) Both together are sufficient.
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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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TO solve this question we will need to know the possible colors of the stamps and how they will be arranged in the album:

Let us look at each Statement:

Statement 1:
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.

Now we know that we have 6 different colors of stamps, we do not know how many stamps are in one album. It is also possible to have 56 albums with different stamp colours.

Statement 1 is not sufficient

Statement 2:
(2) Bob places the stamps into 9 albums, with each stamp placed in exactly one album.

The statement tells us how many stamps are in an album, but its also possible that there are 9 different colors of stamps. So we cannnot confirm if there is at least one album that contains two or more stamps of the same color.

Statement 2 is not sufficient


If we take both statements together, we can solve the problem with 9 stamps in each albums with only 6 colors, it is possible to have 2 or more in the same album.

So the answer is (C) both statement together are sufficient.
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Total 56 stamps
Total 9 Albums
Total 6 colours.
Each color is placed in each box, so three boxes will repeat the colours.One album may have 2 or more stamps of same colour.
Coming to the solution- Both statements together are supportive of the conclusion, but alone they are not sufficient. Hence Point C.
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Statement 1 provides us with the information about the total quantity of different colors, which alone is clearly insufficient because it doesn't tell us anything about the number of albums or how many stamps we will place in an album. Statement 2 tells us that there are a total of 9 albums which tells us that there are on average a bit more than 6 stamps per album (56 / 9 = 6.2). Because we don't know anything about the colors using statement 2 alone we can't sufficiently determinate a definitive answer choice, thus this statement is insufficient. Looking at the statements together we know that there are 6 colorcodes and that there is at least one album that contains more than 6 stamps to make the average greater than 6, e.g. a possible combination could be stamps per album: 6, 6, 6, 6, 6, 6, 6, 6, 6, 8. Due to the fact that there are 6 different colors and we have at least one album with more than 6 stamps, we can conclude that this album has to have two or more stamps of the same color. Answer C.

Regards,
Lucas
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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56 stamps, does any album have two or more stamps of the same color?
(1) Each stamp is exactly one of 6 colors. Not sufficient: There could be 56 albums
(2) There are only 9 albums, and each stamp is only in one album. Not sufficient. There could be 56 different colors and each album could contain different colours.

(1) + (2) There are 6 colours, and 9 albums. We just need to see the possibility of just one album containing two stamps of the same colours.

There could be 1 stamp each in 8 albums and 48 stamps in the 9th album. There could be 48 stamps of the same colour and the rest 8 stamps could be of the remaining 5 colours. So in this case, there is not one album that contains atleast two stamps of the same colour.

There could be 6 stamps each in 7 albums and 7 stamps in the remaining 2 albums, there could be 9 stamps each of 4 colours and 10 stamps of 2 colours each. This would allow an album to contain two or more stamps of the same colour.

So these statements are not sufficient.
Option 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.


 


This question was provided by GMAT Club
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