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05 Jul 2025, 01:00
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Total stamps = 56. Is there at least 1 album that has 2 or more stamps of same color?
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
=> Don't know how the stamps are distributed among the albums
=> Insufficient.
(2) Bob places the 56 stamps into 9 albums, with each stamp placed in exactly one album.
56/9 = 6 remainder 2
=> At least 1 box has 7 stamps
=> Still don't know how the stamps of colors are arranged
=> Insufficient.
(1) + (2) => 56 stamps into 9 albums + at least 1 album has 7 stamps, meanwhile there are only 6 colors => there must be at least 2 same colors in 7-stamp box.
=> Sufficient
Answer: C
(1) Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet.
=> Don't know how the stamps are distributed among the albums
=> Insufficient.
(2) Bob places the 56 stamps into 9 albums, with each stamp placed in exactly one album.
56/9 = 6 remainder 2
=> At least 1 box has 7 stamps
=> Still don't know how the stamps of colors are arranged
=> Insufficient.
(1) + (2) => 56 stamps into 9 albums + at least 1 album has 7 stamps, meanwhile there are only 6 colors => there must be at least 2 same colors in 7-stamp box.
=> Sufficient
Answer: C
Rahul_Sharma23
GMAT Focus 1: 695 Q87 V83 DI83 
Posts: 116
05 Jul 2025, 01:13
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Statement 1: How many albums are there is needed
Statement 2: Stamp colours are needed
Taking both statement together
We have 9 albums and 6 different clours
Suppose,
R = 9 stamps
B = 9 stamps
G = 9 stamps
Y = 9 stamps
O = 9 stamps
V = 11 stamps
and if we try to put same colour stamps in 9 different album so that no album have same two colours, there will be at least 1 album which will contain more than one violet colour stamps. No matter what permutation combination we try there will be at least one colour out of those six colours having number of stamps more than the number of albums. Both statement together sufficient
Statement 2: Stamp colours are needed
Taking both statement together
We have 9 albums and 6 different clours
Suppose,
R = 9 stamps
B = 9 stamps
G = 9 stamps
Y = 9 stamps
O = 9 stamps
V = 11 stamps
and if we try to put same colour stamps in 9 different album so that no album have same two colours, there will be at least 1 album which will contain more than one violet colour stamps. No matter what permutation combination we try there will be at least one colour out of those six colours having number of stamps more than the number of albums. Both statement together sufficient
Bunuel
05 Jul 2025, 01:45
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Option C is the correct answer.
Before diving into solving the question lets understand the question first. The question starts with telling us that "Bob is organizing his stamp collection by placing all 56 of his stamps into several albums" and then asks us "is their any album which is containing two or more stamps of the same color". Here in order to answer the question we need to find the how many type of color stamps are available and in how many albums are there in which Bob will organize them.
Lets check the available statements and see if we can get our answer from them or not.
Statement 1: "Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet". So this statement tells us that their are a total of six colors of stamp available to Bob. But this statement does not give us any information about the number of album in which Bob needs to arrange those stamps. Lets suppose if he is arrange the stamps into 56 albums then we can say that no album will contain two or more stamp of a single color however if we say that he has only 3 albums then we can say that atlest one of them contain two or more stamp of a single color because from the total number of stamps which is '56' and type colors which is '6 colors' we can say that on average each color have atlest 9 of stamps in it.
So as we are unable to get any confirmed answer from this statement. We can say it is Not Sufficient.
Statement 2: "Bob places the stamps into 9 albums, with each stamp placed in exactly one album". This statement also only tells us about the total of albums and that each stamp is placed in exactly one album only from here we can tell that on average 7 out of 9 albums contain 6 stamps each and rest 2 will contain 7-7 each. But it does not tell us anything about the number of color in stamps like whether there are only 3 types of color stamps, 4 type of color stamps or 10 type of color stamps and so on.
This statement is also unable to give a any confirmed answer to us. We can say it also is Not Sufficient.
As we have checked that both the statements alone are Not Sufficient to answer the question. Lets try by Combing both of them.
So from the first statement we know that their are 6 types of colors in stamps when we also concluded that "On average each color have atlest 9 of stamps in it" and from the second we came to know that Bob is organizing the stamps into 9 albums with each stamp to be placed in exactly one album only.
Now lets check whether "there at least one album that contains two or more stamps of the same color or not".
=>Total number of stamps that Bob can place in 9 album without repeating any color will be: 9*6 = 54 however Bob have a total of 56 stamps which would mean that remaining 2 stamps will be organized in any one or two of the 9 albums which will result in atleast one album containing two or more stamps of a single color.
From this we can conclude that with the help of Combination we can answer this question which mean Option C is the correct answer.
Before diving into solving the question lets understand the question first. The question starts with telling us that "Bob is organizing his stamp collection by placing all 56 of his stamps into several albums" and then asks us "is their any album which is containing two or more stamps of the same color". Here in order to answer the question we need to find the how many type of color stamps are available and in how many albums are there in which Bob will organize them.
Lets check the available statements and see if we can get our answer from them or not.
Statement 1: "Each stamp in the collection is exactly one of the following six colors: red, blue, green, yellow, orange, or violet". So this statement tells us that their are a total of six colors of stamp available to Bob. But this statement does not give us any information about the number of album in which Bob needs to arrange those stamps. Lets suppose if he is arrange the stamps into 56 albums then we can say that no album will contain two or more stamp of a single color however if we say that he has only 3 albums then we can say that atlest one of them contain two or more stamp of a single color because from the total number of stamps which is '56' and type colors which is '6 colors' we can say that on average each color have atlest 9 of stamps in it.
So as we are unable to get any confirmed answer from this statement. We can say it is Not Sufficient.
Statement 2: "Bob places the stamps into 9 albums, with each stamp placed in exactly one album". This statement also only tells us about the total of albums and that each stamp is placed in exactly one album only from here we can tell that on average 7 out of 9 albums contain 6 stamps each and rest 2 will contain 7-7 each. But it does not tell us anything about the number of color in stamps like whether there are only 3 types of color stamps, 4 type of color stamps or 10 type of color stamps and so on.
This statement is also unable to give a any confirmed answer to us. We can say it also is Not Sufficient.
As we have checked that both the statements alone are Not Sufficient to answer the question. Lets try by Combing both of them.
So from the first statement we know that their are 6 types of colors in stamps when we also concluded that "On average each color have atlest 9 of stamps in it" and from the second we came to know that Bob is organizing the stamps into 9 albums with each stamp to be placed in exactly one album only.
Now lets check whether "there at least one album that contains two or more stamps of the same color or not".
=>Total number of stamps that Bob can place in 9 album without repeating any color will be: 9*6 = 54 however Bob have a total of 56 stamps which would mean that remaining 2 stamps will be organized in any one or two of the 9 albums which will result in atleast one album containing two or more stamps of a single color.
From this we can conclude that with the help of Combination we can answer this question which mean Option C is the correct answer.
Bunuel
