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

1 2 3 4 5

Dipan0506

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08 Jul 2025, 09:34

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The first point is not sufficiently providing any information for the answer, however the second one helps in calculating the weighted avg mean, Hence both taken together gives an answer, hence point C is the answer.

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08 Jul 2025, 09:36

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S1
A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
These items will have to be divided equally per bag.
The number of bags could be 6 or 12
Since, both are more than 5, this is Insufficient

S2
Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.
We don't know what's the total number used for any of these items.
The items could be 24,36,48,60 or 12,18,24,30 making the bags to be 12 or 6
Insufficient

Combined as well, we see S2 is redundant as we have this info from S1 already. It is still insufficient

Answer E

Bunuel

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.

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08 Jul 2025, 09:36

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We want to find how many identical gift bags were packed, knowing there were more than 5 bags. Statement (1) alone gives the total items (24 magnets, 36 postcards, 48 bookmarks, 60 keychains) but says nothing about how many items per bag or their ratio, so it’s not sufficient. Statement (2) alone gives the ratio of items per bag (2:3:4:5) but without total quantities, we can’t find the number of bags, so it’s not sufficient. Together, from the ratio and totals, the number of bags equals the total divided by the items per bag for each type and must be the same. This leads to possible bag counts of 12 (if each bag has 2,3,4,5 items respectively) or 6 (if each bag has double those amounts), both greater than 5 and valid, so the number of bags is not uniquely determined. Therefore, even combined, the statements are not sufficient to find a unique number of gift bags.

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08 Jul 2025, 09:42

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Notes:
Magnets, Postcards, bookmarks, and keychains
Into identical gift bags
More than 5 bags are packed

Ask:
How many bags were packed?

1) 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains
we have lots of potential denominators here and we dont know how many of the items went into the bags. Not sufficient

2) 2magnets:3postcards:4bookmarks:5 keychains
we do not know how many of them are in there and there is no max.

Combined: This works! we know we packed 12 bags!

C Both 1 and 2 together!

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08 Jul 2025, 09:45

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First, the problem states that each bag contains the same number of each gift, and there are more than five bags in total.

Let's break down the conditions:

Condition 1:
(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
We start by finding the Greatest Common Factor (GCF):
GCF(24, 36, 48, 60) = 12
This means any factor of 12 can evenly divide these gifts:
1, 2, 3, 4, 6, 12
But the problem says there are more than five bags, so the possible options left are:
12 OR 6
However, we can't determine whether it's 6 or 12.
Not enough info here.

Condition 2:
(2) Each gift bag had magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.
We know the ratio but not the total number of each gift, so there are an infinite number of possibilities.
For example:
6 bags: 12:18:24:30 = 2:3:4:5
7 bags: 14:21:28:35 = 2:3:4:5
Not enough info here either.

Condition 1 + Condition 2:
6 bags: 12:18:24:30 = 2:3:4:5
12 bags: 24:36:48:60 = 2:3:4:5
Both fit Condition 1 and Condition 2, but we can't decide which is the final answer.
So, even with both conditions, we still don't have enough info.

The answer is E

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08 Jul 2025, 09:45

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Goal: Find the number of identical gift bags (N), given N>5.
Each bag has m magnets, p postcards, b bookmarks, k keychains.

Statement (1): Total items given (24 M, 36 P, 48 B, 60 K).

Since bags are identical, N must be a common divisor of all total item counts.

GCD(24, 36, 48, 60) = 12.

Possible values for N (divisors of 12) are 1, 2, 3, 4, 6, 12.

Given N>5, N could be 6 or 12.

Not Sufficient.

Statement (2): Ratio of items per bag is 2:3:4:5 (M:P:B:K).

This means m=2x,p=3x,b=4x,k=5x for some positive integer x.

This statement alone gives no information about the total number of items or bags.

Not Sufficient.

Combining (1) and (2):

From (1): N×m=24, N×p=36, etc.

From (2): Substitute ratios: N×(2x)=24⟹Nx=12. (All four equations simplify to Nx=12).

We know N must be 6 or 12 (from Statement 1 and N>5).

If N=6, then 6x=12⟹x=2. This is a valid integer.

If N=12, then 12x=12⟹x=1. This is also a valid integer.

Since both N=6 and N=12 are consistent with all given information, we cannot uniquely determine N.

Conclusion: Both statements together are not sufficient.
Answer: E

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08 Jul 2025, 09:52

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>5 gift bags were packed

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

HCF is 12.
We can have either 12 bags with 2 magnets, 3 postcards, 4 bookmarks & 5 keychains each (basically in the ratio 2:3:4:5)
OR
We can have 6 bags with 4 magnets, 6 postcards, 8 bookmarks & 10 keychains each (basically in the ratio 2:3:4:5)
Not Sufficient
(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.
We dont have any numbers here, not sufficient

Combining also we can have either 6 or 12 bags, Not Sufficient.

Ans E

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08 Jul 2025, 10:09

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They packed the items so that each bag had magnets, postcards, bookmarks, and keychains in the ratio 2 : 3 : 4 : 5, and in total there were 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains. If each bag holds 2 k magnets, 3 k postcards, 4 k bookmarks, and 5 k keychains, then multiplying by the number of bags n gives n*(2 k)=24, n*(3 k)=36, n*(4 k)=48, and n*(5 k)=60. In each case those equations simplify to n k = 12. Since n and k must be whole numbers, the possible pairs are (n,k) = (12,1), (6,2), (4,3), (3,4), (2,6), or (1,12). Because we know there are more than five bags, n could be 6 or 12. Both of these satisfy all the information, so even using both statements together we cannot tell exactly whether they packed 6 bags or 12 bags. Therefore, the data are still insufficient to determine a unique number of bags. E.

Bunuel

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08 Jul 2025, 10:33

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Bunuel

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The first two statements independently are not sufficient as in each statement one or other information is missing. For example, in the first statement we are not told anything about the distribution in each bag and hence we can have any number of bags.

In the second statement, we are not told about the number of items and again depending on the same we can have any number of bags.

Combined, we can conclude that if we put one set of each items ie, 2 magnets, 3 postcards, 4 bookmarks and 6 keychains in each bag, we can have 12 bags. However, we can also have an multiple of these items, for example each bag can contain 4 magnets, 6 postcards, 8 bookmarks and 12 keychains. In that case, we can have 6 bags. As the number is not fixed, the statements combined is not sufficient.

Option E

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08 Jul 2025, 10:41

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Statement 1 insufficient:
24:36:48:60 can be 6 and 12 bags

Statement 2 insufficient as we only have the ratio, and any number of items can fit that ratio, for example:
12:18:24:30 will deduce to 2:3:4:5 i.e. 6 bags, similarly
13:21:28:35 will be 7 bags

Therefore, combining the 2 statements will give us 12 bags.

Ans-C

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08 Jul 2025, 10:45

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Let n be the total number of gift bags. We know that n > 5 and each gift bag is identical which means that each bag contains magnets (m), postcards (p), bookmarks (b), and keychains (k) in the same ratio.

To find n, we must know the total number of each item and the ratio in each bag.

(1) Total $= 24+36+48+60 =168$
Ratio $= 24:36:48:60 = 2:3:4:5 $
=> Each bag contains m, p, b, k in the ratio of $2:3:4:5$

If the ratio $= 2:3:4:5$ then total gift bags $=$ $\frac{168}{(2+3+4+5)}$ $= 12$

If the ratio $= 4:6:8:10$ then total gift bags $= 6$

Not sufficient. Options A and D are out.

(2) m:p:b:k $= 2:3:4:5$

We don't know the total number of each item.

Not sufficient. Option C is out.

(1) and (2)
Total $= 168$; Ratio $= 2:3:4:5$
n $= 12$

Sufficient. The answer is C.

Bunuel

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08 Jul 2025, 10:53

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Let's say there are "x" number of bags. We know that x>5

Statement 1:

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

This tells us that there are a total of 168 items that are to be put in "x" boxes. Insufficient.

Statement 2:

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

This tells us 2 things.
First, that each bag contains the same ratio of these items, and secondly, the ratio of these items in each bag.

Let's say that there are 14m items per bag

Magnets = 2m
Postcards = 3m
Bookmarks = 4m
Keychains = 5m

Insufficient.

Both statements together:

From one we have, 168 total items
From two we have, 14m items per bag

If we divide them, we get, x = number of bags = 168/14m = 12/m

Now since, x>5, we know, that 12/m > 5, or we can say that 12/5 > m

This gives us that, m<2.4
Since, m needs to be an integer, m can only be 1 or 2

If m=1, x=12 (since this is >5 this works)
If m=2, x=6 (this is also >5 so it works)

We have two different answers that satisfy this criterion, so insufficient.

Answer E.

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08 Jul 2025, 11:01

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How many gift bags were packed? (>5)

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

Case 1-> 12 bags of 2 magnets, 3 PC, 4 BM, and 5 K possible
Case 2-> 6 bags of 4 magnets, 6 PC, 8 BM, 10 K possible

Not sufficient.

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

The ratio of items in each bag cannot determine the number of gift bags. Not sufficient.

(3) 1+2
Both case 1 and case 2 are in the ratio 2:3:4:5. Therefore, not sufficient (E)

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08 Jul 2025, 11:05

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1) =>As >5 gift bags, it can be 6 or 12
2)=> Does not give total value of any item to get required answer.
1 and 2 together gives the solution. Hence, C.

Bunuel

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08 Jul 2025, 11:09

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Statement 1 :
Not enough as we do not know how the distribution is made.

Statement 2 :
Not enough as we do not know how the total count.

Both together :
24 magnets, 36 postcards, 48 bookmarks, and 60 keychains = 2:3:4:5
However , lets say all bags have 2,3,4,5 items respectively ; then we need 12 bags.
But its also possible say 5 bags have 2,3,4,5 items then we are still left with 14,21,28,35 respectively. These can now go in just 1 bag or more bags, we do not know.

Therefore both NOT SUFFICIENT.
Ans is E.

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08 Jul 2025, 11:38

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First, be careful about the word "identical" in the question; this means that the ratios of items are the same in each bag. Second, the number of bags that are more than 5. We assign b to the number of bags.

Statement 1:
All the numbers are multiples of 12, so we can write the ratio as 2:3:4:5. To consider all of the souvenir, we can write the ratio as 2ab:3ab:4ab:5ab, where b is the number of bags, and 2a,3a,4a,5a, are the number of each different suvenier in one bag. So, we know $a*b=12$
But from the question, we know that b is greater than 5. So b can be only 6 or 12. But we don't know which one.
So, Statement A is not sufficient.

Statement 2:
This statement does not give any information about the total number of each souvenir or the number of each in one bag. There could be infinite possibilities.
So, Statement 2 is not sufficient.

Both statements together:
If we consider both statements together, the second statement does not add any new information to the first one. So, the number of bags could still be 6 or 12.

So, both statements together are not sufficient.
The answer is E.

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08 Jul 2025, 11:38

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Given condition,
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 = ?

Let N be gift bags and N > 5 were packed

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
M = 24, P = 36, B = 48, K = 60
N must be a common divisor of 24, 36, 48, and 60.
GCD = 12
The divisors of 12 are: 1, 2, 3, 4, 6, 12.
Both 6 and 12 satify N>5 condition.
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 means that for each gift bag, if it contains 2x magnets, it contains 3x postcards, 4x bookmarks, and 5x keychains, for some positive integer x.
Since we are told each gift bag contained magnets, postcards, bookmarks, and keychains, x must be at least 1.
This statement gives us the ratio of items within each bag, but it doesn't tell us the total number of any item or the total number of bags.
If x=1, each bag has (2 magnets, 3 postcards, 4 bookmarks, 5 keychains). We don't know how many bags there are.
Statement (2) alone is NOT sufficient.

From Satement (1) and Statement(2), we can express N×x:
N×2x=24⟹Nx=12
N×3x=36⟹Nx=12
N×4x=48⟹Nx=12
N×5x=60⟹Nx=12

All equations consistently give Nx=12.

We know from statement (1) that N must be a divisor of 12, and N>5.
So, N can be 6 or 12.

Now we use the relationship Nx=12 with these possible values of N:

If N=6:
6x=12⟹x=2.
This is a valid integer value for x.
If N=6 and x=2, then each bag contains: 4 magnets, 6 postcards, 8 bookmarks, 10 keychains.
Total items: 6×4=24 magnets, 6×6=36 postcards, 6×8=48 bookmarks, 6×10=60 keychains. This is consistent with Statement (1).

If N=12:
12x=12⟹x=1.
This is also a valid integer value for x.
If N=12 and x=1, then each bag contains: 2 magnets, 3 postcards, 4 bookmarks, 5 keychains.
Total items: 12×2=24 magnets, 12×3=36 postcards, 12×4=48 bookmarks, 12×5=60 keychains. This is consistent with Statement (1).

Both N=6 and N=12 are possible values that satisfy all conditions from both statements and the initial condition (N>5).
Since there are still two possible values for N, even when combining both statements, the information is not sufficient to determine the exact number of gift bags.

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08 Jul 2025, 11:42

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Bunuel

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A museum gift shop packs a number of souvenirs items into identical gift bags for visitors. The souvenir items are : Magnets M, Postcards PC, Bookmarks BM, and Keychains KC.

Given that the gift bags are MORE than 5. Thus, Number of Gift bags = ?

Statement 1:

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

M =24, PC = 36 , BM =48 and KC = 60.

24 = 6*4
36 = 6*6
48 = 6*8
60 = 6*10

So, the number of bags can be 6.

24 = 12*2
36 = 12*3
48 = 12*4
60 = 12*5

So, the number of bags can be 12.

Since, we don’t get a concrete answer for number of bags, which can be 6 or 12. Hence, Insufficient.

Statement 2:

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

The ratio of M: PC : BM : KC = 2 : 3 : 4 : 5 = 2x : 3x : 4x : 5x

x can take any value and hence Insufficient.

Lets combine statements 1 and 2, we get

Only 12 gift bag matches statement 2.

ratio of M: PC : BM : KC = 2 : 3 : 4 : 5. Which can be explained by

24 = 12*2
36 = 12*3
48 = 12*4
60 = 12*5

So, the number of bags can be 12.

Hence, Sufficient.

option C

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08 Jul 2025, 12:24

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We have magnets, postcards, bookmarks, keychains as M,P,B and K.
And Let N be the number of bags.

Statement (1): A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
N should be HCF of 24,36,48 and 60. There are two possibility (6 and 12)
Thus, We can't determine the exact N.
Insufficient.

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

If there were x units per bag, then each bag has:

2x magnets,
3x postcards,
4x bookmarks,
5x keychains.

Across all N bags, total items:

magnets: 2x * N=24
postcards: 3x * N=36
bookmarks: 4x * N=48
keychains: 5x * N=60

Each equation must give the same xN Let’s check:

2xN=24 => xN=12
3xN=36 => xN=12
4xN=48 => xN=12
5xN=60 => xN=12

So xN=12 Since N>5, N must be a divisor of 12 greater than 5.
But from xN=12

If N=6, then x=2.
If N=12, then x=1.

We get two possible solutions again.
Insufficient.

E)Neither 1 nor 2 alone are sufficient.

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08 Jul 2025, 13:06

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Let M = magnets, P = postcards, B = bookmarks, and K = keychains.

Bags are identical.
#bags > 5
#bags = ?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
M = 24, P = 36, B = 48, and K = 60

Let's find the prime factorization:

M = 2^3*3
P = 2^2*3^2
B = 2^4*3
K = 2^3*3*5

Common factors: GCF (M,P,B,K) = 2^2*3 = 12. So, the factors are: 1, 2, 3, 4, 6, and 12.

Due to our restriction, #bags > 5, we are left with 2 possible values: 6 and 12. Since we cannot define one specific value the statement 1 alone is not sufficient. Eliminate answer choices A and D.

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

Is it sufficient? No, it's not. We can have infinitely valid choices for the items amount (and therefore we can not determine a specific value for the bags amount). Eliminate answer choice B.

Statements (1) and (2)

With the two statements together we can have:

06 bags: 4*6 : 6*6 : 8*6 : 10*6
or
12 bags: 2*12 : 3*12 : 4*12 : 5*12

Since we cannot define one specific value:

Answer = E we cannot define one specific value with Statements (1) and (2) together

1 2 3 4 5

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