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

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Bunuel

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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.

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Bunuel

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08 Jul 2025, 08:30

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GMAT Club Official Explanation:

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.

Clearly insufficient. We know the total, but nothing about how items were distributed.

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

Clearly insufficient. Without knowing total quantities, we cannot determine how many bags were packed.

(1)+(2) Combining the statements, we can check how many gift bags could have been packed by matching the total quantities to the given ratio. The following combinations are possible:

6 gift bags: 4 magnets, 6 postcards, 8 bookmarks, 10 keychains per bag
12 gift bags: 2 magnets, 3 postcards, 4 bookmarks, 5 keychains per bag

Since more than one value satisfies the conditions, we still cannot determine the exact number. Not sufficient.

Answer: E.

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08 Jul 2025, 08:10

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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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Clearly it can be seen in the ratio that there were a total of exactly 12 gifts bag by distributing them

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08 Jul 2025, 08:34

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Let's analyze each statement to determine if we can find the number of gift bags packed.
Statement (1): We know the total quantities of each item (24 magnets, 36 postcards, 48 bookmarks, and 60 keychains), but without knowing how these items were distributed among the gift bags, we cannot determine how many gift bags were packed. Statement (1) alone is insufficient
Statement (2) alone is insufficient.
Statement (2): We know the ratio of items in each gift bag (2:3:4,5 for magnets, postcards, bookmarks, and keychains respectively), but we don't know the total number of items.
Statements (1) and (2) together: Now we can determine how many gift bags were packed.
If each gift bag has items in the ratio 2:3:4:5, then each bag contains:
* 2x magnets
* 3x postcards
* 4x bookmarks
* 5x keychains
Where x is some multiplier that determines the actual quantities.
From statement (i), we know the total quantities:
* Total magnets: 24
* Total postcards: 36
* Total bookmarks: 48
* Total keychains: 60
If we have n gift bags, then:
* 2x×n= 24 → n= 24/(2x)
* 3xxn = 36 → n = 36/(3x)
* 4xxn 48 → n= 48/(4x)
* 5xx n= 60 → n= 60/(5x)
All these equations must give the same value of n. Let's solve:
* 24/(2x) = 12/x
* 36/(3x) = 12/x
* 48/(4x) = 12/x
* 60/(5x) = 12/x
Since all these equations equal 12/x, we have n = 12/x.
The simplest solution is x = 1, which gives n = 12 gift bags.
We need to check if this works with our original quantities:
* 12 bags x 2 magnets = 24 magnets
* 12 bags × 3 postcards = 36 postcards
* 12 bags × 4 bookmarks = 48 bookmarks
* 12 bags × 5 keychains = 60 keychains
Since n= 12 is greater than 5, it satisfies our condition that more than 5 gift bags were packed.
Therefore, the answer is 12 gift bags.
The correct answer is C) Both statements together are sufficient, but neither alone is sufficient.

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08 Jul 2025, 08:40

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Each statement alone is insufficient as Statement 1 does not tell about no. of items in each bag and Statement 2 has insufficient information on total item count

Combining both:
Total items: magnets = 24, postcards = 36, bookmarks = 48, keychains = 60
Ratio per bag: magnets : postcards : bookmarks : keychains = 2 : 3 : 4 : 5
More than 5 bags packed

Let:
Number of bags = n
Common factor = k
Items per bag = 2k, 3k, 4k, 5k
From totals:
24 = 2k * n → n = 24 / (2k) = 12 / k
36 = 3k * n → n = 36 / (3k) = 12 / k
48 = 4k * n → n = 48 / (4k) = 12 / k
60 = 5k * n → n = 60 / (5k) = 12 / k
All give:
n=12/k

Possible k (divisors of 12): 1, 2, 3, 4, 6, 12
Corresponding n = 12/k: 12, 6, 4, 3, 2, 1
Since n > 5, valid n = 12 or 6 --> Still cannot determine
Answer E.

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08 Jul 2025, 08:41

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The question asks for a unique value for the number of gift bags, given that the number is greater than 5 and the bags are identical. Since the bags must be identical, the number of bags must be a common divisor of the total quantity of each item.

Statement (1) provides the total quantities: 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains. The common divisors of 24, 36, 48, and 60 are 1, 2, 3, 4, 6, and 12. Applying the condition from the stem that more than 5 bags were packed, the possible number of bags is 6 or 12. Since two values are possible, Statement (1) is insufficient. Statement (2) provides only the ratio of items per bag and is therefore insufficient on its own to determine the total number of bags.

Combining the statements, we test the two possibilities from Statement (1) against the ratio from Statement (2). If 6 bags were packed, the items per bag would be 4 magnets, 6 postcards, 8 bookmarks, and 10 keychains. This creates a ratio of 4:6:8:10, which simplifies to 2:3:4:5, satisfying Statement (2). If 12 bags were packed, the items per bag would be 2 magnets, 3 postcards, 4 bookmarks, and 5 keychains. This creates a ratio of 2:3:4:5, also satisfying Statement (2). As both 6 and 12 are valid numbers of bags that satisfy all conditions, a unique answer cannot be determined.

Therefore, the statements together are insufficient. The correct answer is (E).

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08 Jul 2025, 08:44

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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.

This question was provided by GMAT Club
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Number of bags > 5

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

All of these could be packed in the x number of bags. We don't know what the value of x is.

Statement 1 is not sufficient.

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

Knowing the ratio doesn't help. Let's assume we have infinite suppliers, we can have infinite bags, or if we have limited supplies, we can have limited amount of bags.

The statement is not sufficient.

Combined

Let's take one of the item - magnets

If we put 2 magnets in each bag, we can create 12 bags. This may look sufficient, but this is a ratio. We can also put 4 magnets in one bag. In that case, the number of bags will be 6.

The statements combined are not sufficient.

Option E

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08 Jul 2025, 08:44

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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.
24M+36P+48B+60K = 6(4M+6P+8B+10K) = 12(2M+3P+4B+5K)
Total number of gift bags could be 6 or 12
Insufficient

(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
We don’t have total number of gift bags or gifts
Insufficient

(1)&(2)
12(2M+3P+4B+5K)
GIFT Bags=12
Sufficient

C

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08 Jul 2025, 08:46

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Option 1 there are 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains.

Suppose if there are 6 bags,then each bag would have 4 magnets,6 postcards,8 bookmarks and 10 keychains
But then suppose if there was 12 bags then each bag there would be 2 magnets,3 post,4 bookmarks,5 keychains
It could be 6 or 12 bags.
Hence not suffiecint

Option 2 gives is the ratio.But this itself is not sufficient,

If we take both,then its sufficient.Because when we do 24/2=12, 36/3=12 [divide by ratio]
It gives us 12 bags

Hence C is the answer.

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.

This question was provided by GMAT Club
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08 Jul 2025, 08:50

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Each Alone is anyone not sufficient as we would need the bifurcation possible in each bag.

when both together we have the below possibilities to divide 24,36,48,60 in ratio 2:3:4:5 --> 2x,3x,4x,5x
if x =1 then we have 12 bags
if x=2 then we have 6 bags
both are greater than 5 and hence we do not have a single answer.

E. Not sufficient

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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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08 Jul 2025, 08:52

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Given that,

>4 types of souvenir items: magnets, postcards, bookmarks, and keychains
>identical gift bags, which mean each bag must equal number and ratio of these souvenir items
>more than 5 gift bags were packed

Target Question --> how many gift bags were packed?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
For each bag to be identical, each bag should has souvenirs in the same ratio, in other words the souvenirs will be distributed in a common multiples.
Possible common multiple of all the items are 1,2,3,4,6 and 12. Possible number of bags are 1,2,3,4,6 and 12. Provided that number of bags are greater than 5, number of bags can either be 6 or 12. Hence Insufficient.

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.
Since there is no limit on number of souvenirs, there could be any number of bags. Also notice that ratio is already implied from statement 1, Hence it's a tautological statement. Insufficient.

Since statement 1 and 2 provides similar information.

Correct Answer is E.

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08 Jul 2025, 08:58

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gifts items
magnets, postcards, bookmarks, and keychains into identical gift bags for visitors.
we know gift bags more than 5 were packed

#1
A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
gift bags con be 6 or 12
insufficient
#2

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

it can be any count >5 ; insufficient
from 1 &2
we know that gift bags must be 12
as 24:36:48:60 all have 12 as common factor which makes ratio 2:3:4:5

OPTION C is correct

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.

This question was provided by GMAT Club
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08 Jul 2025, 09:00

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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?

Gift bags > 5
The number of gift bags = ?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
Let the number of gift bags be n
24 = 2^3*3
36 = 2^2*3^2
48 = 2^4*3
60 = 2^2*3*5
HCF(24,36,48,60) = 2^2*3 = 12
Possible number of gift bags is any factor of 12 = {1,2,3,4,6,12}
Since number of gift bags > 5
The number of gift bags = 6 or 12
NOT SUFFICIENT

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.
Let the magnets, postcards, bookmarks, and keychains in each gift bag be 2k, 3k, 4k & 5k respectively
Since the total items available are unknown
NOT SUFFICIENT

(1) + (2)
(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.
Let the magnets, postcards, bookmarks, and keychains in each gift bag be 2k, 3k, 4k & 5k respectively
Let the number of gift bag be n.
kn = 24/2 = 12
Case 1: k = 2; n = 6 > 5
Case 2: k = 1; n = 12 > 5
NOT SUFFICIENT

IMO E

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08 Jul 2025, 09:05

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08 Jul 2025, 09:09

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1. Consider 6 bags each with 4M,6P,8B,10K
Consider 12 bags each with 2M,3P,4B,5K...NOT SUFFICIENT

2. Each bag contains M: P: B: K as 2:3:4:5..but no. of bags cannot be concluded.. NOT SUFFICIENT

Together,

Consider 6 bags each with 4M,6P,8B,10K..ratio= 2:3:4:5
Consider 12 bags each with 2M,3P,4B,5K...ratio= 2:3:4:5...NOT SUFFICIENT

Ans E

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08 Jul 2025, 09:10

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We know that Gift bags > 5 we need N ?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed. =>
Now if we find GCD for this it is 12. So there can be 12 bags but GCD is greatest no of bags possible the factors of GCD will also be factor of all this numbers so if possible bags are 1, 2, 3, 4, 6, 12 no for N >5 possible are 6 and 12. so
Not Sufficient

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively. =>
So total will be => Here we know only the ratio in each bag but we don't know bag in it there may be 2 bags maybe 3 maybe 6, maybe 12 so Not Sufficient

Now lets Combine 1 and 2 =>
2k * N = 24, k * N = 12
3k * N. = 36, K * N = 12
So we get N = 12/k

can 12/k > 5
yes if k =1, N =12 which is greater than 5
yes if k = 2, N = 6 which is greater than 5
Still two values for N
This is also Not Sufficient

Hence Ans E

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08 Jul 2025, 09:16

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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.

This question was provided by GMAT Club
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asked: How many gift bags were packed?

Statement 1: Total number of items packed are given but we donot know how many were packed in each specific gift bag. So not sufficient.

Statement 2: we are given ratio but not the exact quantity for each bag. So not sufficient.

Combined Statements 1 and 2: we are given the total number of item and the ratio from which we can figure out how many gift bags were packed. So sufficient Answer Option C

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08 Jul 2025, 09:23

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Number of bags>5 (given)
(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
-24M+36P+48B+60k>5?
6(4M+6P+8B+10K)>5 OK
12(2M+3P+4B+5K) >5 OK
Insufficient
(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.
-we do not know the number of bags here
Insufficient
Combining 1+2:
both 6(4M+6P+8B+10K) and 12(2M+3P+4B+5K)
are in the ratio 2:3:4:5
Insufficient
IMO:E

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08 Jul 2025, 09:25

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1 - Statement (1) alone is insufficient - We don't know how many of these souvenir items go in a single bag.
2 - Statement (2) alone is insufficient - We know how many of each type in a single bag, but don't know the actual no. of souvenir items.

[b]Combine (1) and (2):
From (1):[/b]

Magnets = 24
Postcards = 36
Bookmarks = 48
Keychains = 60

From (2):

The ratio of contents per bag is 2:3:4:5.

Let’s find how many complete 2:3:4:5 sets fit into each total:
Let’s say each bag has:

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

So total items:

2x * (number of bags) = 24 -> (total x) * bags = 24/2 = 12
3x * bags = 36 -> 12
4x * bags = 48 -> 12
5x * bags = 60 -> 12

So in all cases, number of bags = 12 and x = 1
So from both statements, we get a unique solution: 12 bags
Also satisfies the condition: more than 5 bags.
-> Statements together are sufficient

(C)

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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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APram

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Schools: ISB '26 HEC INSEAD Jan '26

GMAT Focus 1: 605 Q86 V78 DI76 Verified score

Posts: 708

Kudos: 280

08 Jul 2025, 09:28

Kudos

Bookmarks

Number of identical bags > 5
How many bags were packed?

Statement 1:
(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.
Number of bags required = GCD {24,36,48,60}
= 12
maximum bags can be 12 or factors of 12 ie 1,2,3,4,6,12
Since we are told number of bags > 5
so we are left with either 6 or 12

We need more info

Statement 2:
Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.
With just ratio we cannot determine the exact number of bags and hence insufficient

Combining 1 & 2
total of ratios = 2+3+4+5 = 14
total of gifts = 24+36+48+60 = 168
=> number of gift bags required = 168/14 = 12

Since we have unique value hence sufficient
C is correct

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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more