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GMAT Club Olympics 2025 (Day 7): A museum gift shop packed a number of

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Rahilgaur

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09 Jul 2025, 03:27

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Bunuel

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More than 5 gift bags were packed.

1. A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains can be backed in 3 ways :-

a. 1 bag with 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains.
b. 6 bags with 4 magnets, 6 postcards, 8 bookmarks, and 10 keychains.
c. 12 bags with 2 magnets, 3 postcards, 4 bookmarks, and 5 keychains
It is given that more than 5 bags were packed hence, 1 will be discarded however we still have to possibilities - Insufficient

2. Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively. - We have no idea how many souvenirs were packed hence - Insufficient.

Combining 1 & 2 --> 14x = 168 --> x= 12
12 bags with 2 magnets, 3 postcards, 4 bookmarks, and 5 keychains - Both together are sufficient - C

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09 Jul 2025, 03:31

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Bunuel

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Gift bags = n
n > 5

Each bag has identical gifts

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
If I have to put each item in uniform numbers in each bag then I need
HCF (24, 36, 48, 60) = 12
Hence, 'n' can be 1, 2, 3, 4, 6, 12 bags
Now n> 5 hence n can only be 6 or 12

Insufficient

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.

magnets = 2n, postcards = 3n, bookmarks = 4n, and keychains = 5n

No limit to the number of bags that can be created with this
Insufficient

Combining 1 and 2 we get
If total magnets = 24 and
2n = 24 => n = 12

Hence the number of bags is 12

Option C

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09 Jul 2025, 03:51

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S1

Knowing the number of items packed (cumulatively) doesn't help. The grouping into bags could be in many different ways. Not sufficient.

S2

Knowing the ratio of the items in bags doesn't help either.

S1 and S2 together

Tempting, but still insufficient.

There could be 6 bags with 4,6,8,10 units of magnets, postcards, bookmarks, and keychains respectively.

There could be 12 bags with 2,3,4,5 units of magnets, postcards, bookmarks, and keychains respectively.

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09 Jul 2025, 03:58

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Each gift bag contains magnets, postcards, bookmarks, and keychains in the fixed ratio 2 : 3 : 4 : 5 — that means:

Every gift bag must have 2k, 3k, 4k, and 5k items for some constant value of k (same for all bags),

So if x bags were packed, total items = Magnets:2kx
Postcards:3kx
Bookmarks:4kx
Keychains:5kx

Let’s denote the total number of bags as x, and per-bag item counts as:

Magnets per bag:2k
Postcards per bag:3k
Bookmarks per bag:4k
Keychains per bag:5k

Then total items packed becomes:
Magnets per bag:2kx
Postcards per bag:3kx
Bookmarks per bag:4kx
Keychains per bag:5kx

From Statement(I):
Magnets = 24, Postcards = 36, Bookmarks = 48,Keychains = 60
So:
2kx=24 → kx=12
3kx=36 → kx=12
4kx=48 → kx=12
5kx=60 → kx=12

Number of bags x= 12/k
But since X and k must be positive integers, and we know x must be greater than 5, we need integer solutions of kx=12 such that x>5

Now, possible integer factor pairs of 12 and x>5
(k=1,x=12)
(k=2,x=6)

The combined data doesn't uniquely determine the number of bags.

Option (E)

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09 Jul 2025, 04:15

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We are given:
- m:p:b:k is identical between gift bags
- total bags > 5

Ask total bags = ?

(1) m:p:b:y = 24:36:48:60
can be divided into 6 or 12 gift bags (insufficient)

(2) m:p:b:y = 2:3:4:5
we know the ratio each bag has but the total can be any (insufficient)

(1)+(2)
m:p:b:y = 2:3:4:5 (12 bags) = 4:6:8:10 (6 bags)
still cannot be determined.

Answer: E

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(1)
24, 36, 48 and 60 are divisible by 12, 6, 4, 3, 2 and 1.
From them, 12 and 6 are the possible number of gift bags.

Statement (1) alone is insufficient.

(2)
The number of gift bags can be any number greater than 5.

Statement (2) alone is insufficient.

(1)+(2)
12 and 6 are still the possible numbers of gift bags.

Statement (1) and (2) together are insufficient

Answer E

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09 Jul 2025, 04:20

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Clearly, A & C is required to decide.

But one twist, we don't know whether constant n will be of 6 or 12, it may vary.

E

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(1)
All the numbers are multiples of 12. But they are also mutiples of 6, that is greater than 5 too. So there are two options.

Insufficient

(2)
It does not contribute anything to calculating the number of bags.

Insufficient

(1) and (2)
st (2) is included in st (1), so there are still two possibilities, 6 or 12.

Insufficient

Correct answer is E

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09 Jul 2025, 04:42

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(1)
A common divisor of all the items that is greater than 5 can be 6 or 12.

Bags can be 6 if each bag has 4 magnets, 6 postcards, 8 bookmarks and 10 keychains
Bags can be 12 if each bag has 2 magnets, 3 postcards, 4 bookmarks and 5 keychains

Two possible answers

Statement is insufficient

(2)
Bags can be 6 if each bag has 4 magnets, 6 postcards, 8 bookmarks and 10 keychains
Bags can be 12 if each bag has 2 magnets, 3 postcards, 4 bookmarks and 5 keychains

Infinite possible answers

Statement is insufficient

(1)+(2)
Bags can be 6 if each bag has 4 magnets, 6 postcards, 8 bookmarks and 10 keychains
Bags can be 12 if each bag has 2 magnets, 3 postcards, 4 bookmarks and 5 keychains

Two possible answers

Both statements are insufficient

The right answer is E

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09 Jul 2025, 04:45

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A museum gift shop packed a number of souvenir items: magnets, postcards, bookmarks, and keychains into identical gift bags for visitors. If more than 5 gift bags were packed, how many gift bags were packed?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.

There are four souvenir items packed into identical gift bags. Are the gift bags more than 5. To answer this we need to know the total number of each souvenir item and how they are arranged into the gift bags.

Statement 1 : Tells us the total of each of the souvenir items but it doesnt tell us how they were arranged into the bag. Statement 1 is insufficient.

Statement 2: It gives us the ratio of each of the souvenir items but not the total of each of these souvenir items. Thus statement 2 is insufficient.

Together both statements are sufficient as they contain the information of the total and the ratio of each item in each bag. The common divisor when the ratios are applied to the total is 12. Thus we know there are 12 identical gift bags.

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09 Jul 2025, 04:57

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(1)
gcd of 24, 36, 48 and 60 is 12.

The number of gift bags can be 12 or any divisor of 12.

Divisors of 12: 1, 2, 3, 4, 6, 12

As gift bags>=5, then gift bags can be 6 or 12.

INSUFFICIENT

(2)
No enough information to calculate gift bags

INSUFFICIENT

(1)+(2)
Only with (1) we already knew that ratio was 2:3:4:5, so (2) doesn't add any information.

INSUFFICIENT

IMO E

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09 Jul 2025, 05:21

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Given, Number of gift-bags, n>5

Statement 1,
A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 key-chains were packed.
This does not tell us how many of each gift was in a bag and so this would not give us an answer.

Statement 2,
Each gift bag contained magnets, postcards, bookmarks, and key-chains in the ratio 2:3:4:5, respectively.
While this does provide a ratio 2:3:4:5, since we do not have the number of gifts and gifts in each bag this does not give us an answer.

Taking Statements 1 & 2 together,
Taken together, there could be 2, 3, 4, 5 of magnets, postcards, bookmarks, and key-chains in each bag in which case the number of bags is 12 but if it is 4, 6, 8, 10 of the items in each bag, we would have a total of 6 bags. So this still does not give us the answer.

Correct option is option E.

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09 Jul 2025, 05:42

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Identical bags, more than 5 bags are packed.
no of bags packed ?

(1) A total 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed
So common divisor of (24,36,48,60) are 1,2,3,4,6,12
Since no is greater than 5, no of bags packed can 6 or 12
Insufficient

(2) ratio 2:3:4:5. We dont know the total quantity so it can be 2,3,4,5 or 4,6,8,10 or in that manner Insufficient

Together,
2:3:4:5 for (24,36,48,60) can be 12 bags each having 2:3:4:5 items
or 6 bags each having 4:6:8:10 items Insufficient

E is the answer

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09 Jul 2025, 05:43

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Let n = no. of bags ( >5 )

Statement 1 : A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed
Since all items are split evenly, n must divide each total. GCD (24, 36, 48, 60) = 12
Possible values of n (>5) are the divisors of 12 : 6, 12
Insufficient

Statement 2 : Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively
This statement only gives relative count of items in each bag and says nothing about how many bags are there.
Insufficient

Both statements :
Based upon the ratio and total values : 2x * n = 24 -> xn = 12
n can be still be either 6 or 12
Insufficient

Answer: E

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09 Jul 2025, 05:51

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C. Since, we know they were in same ratio, 2:3:4:5, always and quantities to provided in 1st statement. No. of gift packs can be calculated, which will come out to be 12.

Bunuel

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09 Jul 2025, 06:05

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Given -> Number of gift bags ($n$) $> 5$. Gift bags are packed with magnets, postcards, bookmarks, and keychains.
To determine -> Number of gift bags ($n$)$=$?

Statement 1 -> A total of $24$ magnets, $36$ postcards, $48$ bookmarks, and $60$ keychains were packed.
We don't know how these souvenir items were distributed in the bags. Could be $1$ bag for each item, or every item evenly distributed between $10$ bags. Not sufficient.

Statement 2 -> Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio $2:3:4:5$, respectively.
This distribution ratio does not tell us how many items of each souvenir exist. Impossible to find the number of bags. Not sufficient.

1+2 -> If the distribution of items in the bag is in the ratio magnets:postcards:bookmarks:keychains = $2:3:4:5$, then totals of each type of souvenir per bag are $2k, 3k, 4k $ and $5k$.
Souvenir totals can be represented as:
Magnets -> $n*2k = 24$
Postcards -> $n*3k = 36$
Bookmarks -> $n*4k = 48$
Keychains -> $n*5k=60$

Simplifying each gives us $n=\frac{12}{k}$.
To get $n>5$, $k$ can be $1$ or $2$. That will give us two different values for the number of gift bags.
Therefore, both statements together are not sufficient.

Answer - E

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09 Jul 2025, 06:36

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Given:

We have 4 souvenir items
And we know gift bags are more than 5
The gift bags are packed with same ratio of items (Identical gift bags)

Question:

How many gift bags?

Lets analyse the statement:

S1:A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

We are sure ratio of items in each bag is identical.

So in order to see how many bags we will have to see Min ratio and then will sum up the values to see number of bags

ANother way can be by directly finding HCF.

I will go with HCF approach,

24,36,48,60
All are factors of 12 so max bags with all items are 12.

So we know 12 bags are packed.

Hence this is sufficient alone.

S2: Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.

Here we just know the ratio and not number of items,

We can say minimum bags packed are sum of ratio of the items, But cant definitely say how many bags in absolute terms. All we can say is either 12 or multiple of 12 are number of bags packed.

So this is not sufficient.

Statement 2 Not Sufficient

Answer A

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09 Jul 2025, 06:38

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M, P, B and K
bags > 5. How many bags were packed ?

Statement 1:
m=24 p=36 b=48 k=60
Don't know configuration of the bags.
Not sufficient.

Statement 2:
Ratio is given. But we don't know quantity of each.
Not sufficient

Combining:
If each bag had 2 magnets, there would be 12 bags.
If each bag had 4 magnets, there would be 6 bags.
Multiple possibilities, hence NOT SUFFICIENT.

Answer is E.

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09 Jul 2025, 06:54

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Souvenir items: magnets, postcards, bookmarks, and keychains
All of these are put into identical gift bags for visitors which means each bag will have same and equal number of items for those items
One of the constraint is that more than 5 gift bags were packed
But we need to find out how many are packed in total

Given statements,

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

We start of by computing the GCD of all the 4 numbers 24,36,48,60 which is 12
But, the possible common divisors for the above 4 numbers is 1,2,3,4,6,12 which is also the possible number of bags

But we know that, more than 5 gift bags were packed
=> Possible number of bags = 6 or 12

Statement (1) alone is NOT sufficient

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.

This tells us the ratio of items in each bag, which means that there could be 2:3:4:5 items in one bag, or 4:6:8:10 in each bag similarly to the prev statement

Statement (2) alone is NOT sufficient

Combining statemnent (1) and (2),
We know that,
24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed
magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5

Let the items in each bag be, 2x, 3x,4x and 5x
Let the number of bags = n

=> 2x * number of bags = 24
=> 2x* n = 24
=> x*n = 12

Similarly we get for other items too, xn = 12
Now we know that,
n = 6 or 12 as it should be greater than 5
=> x = 2 or 1 which is valid

Since two possibilities again possibile, both statemenbts combined not sufficient

E. Statements (1) and (2) together are not sufficient.