Last visit was: 05 Sep 2026, 03:37 It is currently 05 Sep 2026, 03:37
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   3   4   5   6   
605-655 (Medium)|   Overlapping Sets|         
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 05 Sep 2026
Posts: 113,150
Own Kudos:
839,230
 [11]
Given Kudos: 111,330
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,150
Kudos: 839,230
 [11]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:00
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

68% (01:55) correct 32% (01:51) wrong based on 520 sessions

History

Date
Time
Result
Not Attempted Yet
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 05 Sep 2026
Posts: 113,150
Own Kudos:
839,230
 [2]
Given Kudos: 111,330
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,150
Kudos: 839,230
 [2]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:30
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
­

GMAT Club Official Explanation:



A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.

This is insufficient, as we are given no information about how many boxes contain electronics.

(2) Four-fifths of the boxes in the shipment contain electronics.

If 80% (4/5) of the boxes were non-fragile and all of those contained electronics, then none of the fragile boxes would contain electronics (answer: NO). On the other hand, if 80% of the boxes were fragile and all of those contained electronics, then all fragile boxes would contain electronics (answer: YES). Not sufficient.

(1)+(2) Assume there are 15 boxes in total (LCM of 3 and 5).

From (1), we get that 10 fragile boxes and 5 non-fragile.
From (2), we get that 12 boxes contain electronics.

Even in the worst case where all 5 non-fragile boxes contain electronics, the remaining 7 electronics boxes must be among the 10 fragile boxes. So at least 7 out of 10 fragile boxes contain electronics, which is more than half.

Sufficient.

Answer: C.
General Discussion
User avatar
ishneetkaur28
User avatar
Joined: 03 Aug 2024
Last visit: 02 Jan 2026
Posts: 26
Own Kudos:
15
 [1]
Given Kudos: 29
Location: India
Concentration: Finance, General Management
Posts: 26
Kudos: 15
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:21
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statements 1 and 2 Alone are insufficient as they do not tell us about Fragile or Electronics together.

Let's try combining:

Take total items = 30
F=20 and NF=10
Electronics = 24

Even if we put all 10 NF in electronics, we still get 14 for F, which is more than half. Hence, C is the answer!
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
User avatar
simondahlfors
User avatar
Joined: 24 Jun 2025
Last visit: 23 Sep 2025
Posts: 48
Own Kudos:
48
 [1]
Posts: 48
Kudos: 48
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:24
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Information given:
- Shipment has two types of boxes: fragile and non-fragile
- Question: Did more than half of the fragile boxes contain electronics?

Question:
- Did more than half of the fragile boxes contain electronics?

Solution:
- Statement 1: Two-thirds of the boxes in the shipment are fragile
- 2/3 of all boxes are fragile, but we do not know anything about how many fragile boxes have electronics vs. not
- We can't answer whether more than half of the fragile boxes contain electronics
- Insufficient

- Statement 2: Four-fifths of the boxes contain electronics
- 4/5 of all boxes contain electronics, but we don't know how the electronics boxes are split, fragile or non-fragile
- Insufficient

- Statement 1 and 2 combined
- We can use numbers to test this scenario
- If we take total boxes = 15
- Statement 1 tells us 10 boxes are fragile, and 5 are non-fragile
- Statement 2 tells us 12 boxes contain electronics, and 3 do not contain electronics
- If we maximize the amount of non-fragile boxes with electronics (5), that still leaves 7 electronics for fragile boxes, which is more than half
- Therefore, combining the statements forces more than half of fragile boxes to contain electronics
- Sufficient

Answer: C, both statements together are sufficient, but neither alone is sufficient
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
User avatar
MaxFabianKirchner
User avatar
Joined: 02 Jun 2025
Last visit: 12 Jul 2025
Posts: 65
Own Kudos:
69
 [1]
Given Kudos: 122
Status:26' Applicant
Location: Denmark
Concentration: Finance, International Business
Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
GPA: 4.0
WE:Other (Student)
Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
Posts: 65
Kudos: 69
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The question asks whether the number of fragile boxes containing electronics is more than half the total number of fragile boxes. Let T be the total number of boxes, F be the number of fragile boxes, and F_E be the number of fragile boxes containing electronics. The question is whether F_E > (1/2)F. This is a Yes/No question that requires a definitive answer.

Statement (1) alone is insufficient. It states that F = (2/3)T. This provides the total number of fragile boxes but gives no information about how many of them contain electronics. The number of fragile boxes with electronics, F_E, could be zero or it could be F, allowing for both "No" and "Yes" answers to the question.

Statement (2) alone is insufficient. It states that the total number of boxes with electronics is (4/5)T, but it provides no information about the number of fragile boxes, F. Without knowing F, the threshold for the question, (1/2)F, cannot be determined.

Combining both statements provides sufficient information. Let the total number of boxes, T, be 15 (a common multiple of the denominators 3 and 5). From statement (1), the number of fragile boxes is F = (2/3) * 15 = 10. From statement (2), the total number of boxes with electronics is E = (4/5) * 15 = 12. The question becomes: Is F_E > (1/2) * 10, or is F_E > 5? The minimum possible overlap between the fragile and electronics groups is given by the formula: Minimum Overlap = Group1 + Group2 - Total. In this case, the minimum value for F_E is 10 + 12 - 15 = 7. Since the minimum number of fragile boxes containing electronics is 7, the number must always be greater than 5. This provides a definitive "Yes" answer.

Because the statements together are sufficient to answer the question, but neither statement alone is sufficient, the correct answer is (C).
User avatar
Heix
User avatar
Joined: 21 Feb 2024
Last visit: 13 Jul 2026
Posts: 494
Own Kudos:
173
 [1]
Given Kudos: 63
Location: India
Concentration: Finance, Entrepreneurship
Schools: Ross MM "26 NUS Columbia '27
GMAT Focus 1: 485 Q76 V74 DI77
GPA: 3.4
WE:Accounting (Finance)
Products:
My Reviews
Schools: Ross MM "26 NUS Columbia '27
GMAT Focus 1: 485 Q76 V74 DI77
Posts: 494
Kudos: 173
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:34
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We have boxes that can be either fragile or non-fragile, and they either contain electronics or don't.
The question asks: Do more than half of the fragile boxes contain electronics?
Statement 1: Two-thirds of all boxes are fragile.
This only tells us how many fragile boxes there are, but nothing about electronics. Not enough information.
Statement 2: Four-fifths of all boxes contain electronics.
This only tells us how many boxes have electronics, but nothing about which ones are fragile. Not enough information.
Using both statements together:
Let's say we have 15 total boxes (a convenient number that works with our fractions):
* 10 boxes are fragile (2/3 of 15)
* 12 boxes contain electronics (4/5 of 15)
At most, 5 boxes are non-fragile (15 - 10). Even if ALL these non-fragile boxes contain electronics, that's only 5 boxes with electronics that aren't fragile.
This means at least 7 fragile boxes must contain electronics (12 total electronics boxes - 5 non-fragile boxes).
Since 7 out of 10 fragile boxes contain electronics, that's more than half.
Therefore, both statements together are sufficient to answer the question (answer C).
User avatar
k11work
User avatar
Joined: 12 Jan 2025
Last visit: 18 Nov 2025
Posts: 119
Own Kudos:
99
 [1]
Given Kudos: 84
Status:Complete
Affiliations: -
-: -
Products:
My Reviews
Posts: 119
Kudos: 99
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:37
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's take the Total number of boxes = 30
So Fragile (F) + Non-Fragile (NF) = 30

Now,
Statement 1 :
Two-thirds of the boxes in the shipment are fragile.
Thus, F = 2/3*30 = 20
So NF = 30-F = 10.

But since Statement 1 does not tell us anything about Electronics,
Therefore Not Sufficient.

Statement 2 :
Total Electronics (E) = 4/5*30 = 24
But if we look at statement 2 individually, we can't say about the number of Fragile boxes.
Therefore Not Sufficient.

Both Together,
We have F=20,
NF = 10,
E = 24
Now even if all of NF are Electronics boxes , we still have 24-10 =14 Electronics boxes.
Thus we will have at least 14 Fragile Electronics boxes.
And 14/24 >1/2
i.e. more than half of the fragile boxes will always contain electronics.

Thus, Answer is C.
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 05 Sep 2026
Posts: 8,811
Own Kudos:
5,333
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,811
Kudos: 5,333
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
solve using 2x2 matric

A department store received a shipment of two types of boxes on Monday: fragile and non-fragile.

----- F----NF-----total
E----- a ----- -------
NE----- ----- -------
Total--- x ---- ------
determine value of a wrt to x for target Did more than half of the fragile boxes contain electronics?

#1
Two-thirds of the boxes in the shipment are fragile.
----- F----NF-----total
E----- ----- -------
NE----- ----- -------
Total--- 2x/3 ----x/3 ------x

insufficient as no info about Electronics

#2

Four-fifths of the boxes in the shipment contain electronics.


----- F----NF-----total
E----- ----- ------- 4x/5
NE----- ----- ------- x/5
Total--- ---- ------ x

insufficient as fragile info not known
from 1 &2

----- F----NF-----total
E----- ----- ------- 12
NE----- ----- ------- 3
Total--- 10 ---- 5 ------ 15

if we maximize value of Electronics in fragile we get
----- F----NF-----total
E----- 7----- 5 ------- 12
NE----- 3----- 0 ------- 3
Total--- 10 ---- 5 ------ 15

true to target

if we minimize value of electronics in fragile we get

----- F----NF-----total
E----- 10-----2 ------- 12
NE----- 0----- 3 ------- 3
Total--- 10 ---- 5 ------ 15

true to target

OPTION C is correct
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
User avatar
Mohak01
User avatar
Joined: 05 Sep 2020
Last visit: 01 Apr 2026
Posts: 104
Own Kudos:
65
 [1]
Given Kudos: 70
Location: India
Schools: ISB '26 NUS '26 (A) IIMA '26 (WL) EPGP '26 (D)
GMAT Focus 1: 695 Q83 V87 DI83
GPA: 8
Schools: ISB '26 NUS '26 (A) IIMA '26 (WL) EPGP '26 (D)
GMAT Focus 1: 695 Q83 V87 DI83
Posts: 104
Kudos: 65
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
First lets be clear on the exact information provided,
--> only 2 boxes - fragile and non-fragile
---> Electronics are present in some boxes, electronics may be both fragile or non-fragile

Target Question : Did more than half of the fragile boxes contain electronics

(1) Two-thirds of the boxes in the shipment are fragile.
This states that 66.67 % of boxes are fragile. We still don't know the share of electronics inside these boxes. Insufficient

(2) Four-fifths of the boxes in the shipment contain electronics.
This states that 80% of the boxes have electronics. Here we don't know share of fragile and non-fragile boxes. Let say if non-fragile boxes are 10%, then there could be any possibility for electronics present inside these boxes. Insufficient

Considering option 1 and 2 together,

66.67% boxes are fragile and 80% boxes contains electronics.

Lets find try to find out the least probability of electronics in fragile shipment.
For this, maximize the electronics present in non-fragile boxes which would be 33.33%. Hence remaining electronics = 80-33.33 = 46.67% will be definitely in non-fragile box and 46.67% is more than half of 66.67% fragile boxes. If this condition satisfies for minimum possible share of electronics in fragile boxes, the same will hold true for any other combination.


Hence correct answer is C.
User avatar
Dav2000
User avatar
Joined: 21 Sep 2023
Last visit: 03 Jan 2026
Posts: 75
Own Kudos:
46
Given Kudos: 69
Location: India
Schools: Full Time MBA '26 (A)
GPA: 8.6
Schools: Full Time MBA '26 (A)
Posts: 75
Kudos: 46
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
Given: two categories of boxes: fragile and non-fragile

asked: How many fragile contain electronics

Statement 1: 2/3 of total = Fragile.
No mention of electronics. So not sufficient.

Statement 2: 4/5 of total = electronics
No detail about Fragile boxes. So not sufficient.

Combined Statements 1 and 2:
Total number of Fragile and electronics are separately mentioned with no detail of both or neither. So the formula Total = Fragile + Electronics - Both + neither cannot be applied so Option E Answer
User avatar
RDM42
User avatar
Joined: 20 Jan 2025
Last visit: 24 Aug 2026
Posts: 464
Own Kudos:
328
 [1]
Given Kudos: 29
Posts: 464
Kudos: 328
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
F=2/3 , no information about electronics
Not sufficient

(2) Four-fifths of the boxes in the shipment contain electronics.
E=4/5, no information about fragile boxes
Insufficient

(1)&(2) together
Let, total number of boxes=15
Fragile boxes=2/3 *15=10............. Non Fragile boxes=5
Electronic = 4/5 *15=12............... Box that doesn’t contain electronic =3

Even if all 5 non fragile boxes contain electronic items. We have still 12-5=7 electronic item left that have to be put in fragile boxes and number of remaining electronic item is more than halftge number of fragile boxes.
Sufficient

C
User avatar
Emkicheru
User avatar
Joined: 12 Sep 2023
Last visit: 12 Sep 2025
Posts: 119
Own Kudos:
22
Given Kudos: 11
Location: Kenya
Schools: Anderson (UCLA) Sloan (MIT) Columbia '27
GMAT 1: 780 Q50 V48
GRE 1: Q167 V164
GPA: 3.7
Schools: Anderson (UCLA) Sloan (MIT) Columbia '27
GMAT 1: 780 Q50 V48
GRE 1: Q167 V164
Posts: 119
Kudos: 22
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
2/3 is fragile ,4/5 is electronic therefore 2/3*4/5=8/15 hence it's more than half
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 01 Jul 2026
Posts: 1,382
Own Kudos:
928
 [1]
Given Kudos: 243
Posts: 1,382
Kudos: 928
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let total be x
Fragile all be F
Non Fragile all be N
Fragile Electronics be FE
Fragile No Electronics be FN
Non-fragile Electronics be NE
Non-fragile No Electronics be NN

F = FE+FN
E = FE+NE

Is FE> 0.5*F?

S1
F = FE+FN = 2x/3
We do not know the split of FE and FN
Insufficient

S2
E = FE+NE = 4x/5
We do not know the split of FE and NE
Insufficient

Combined,
Not F = x-2x/3 = x/3
Not E = x-4x/5 = x/5

FN max can be x/5, which means FE min can be 2x/3 - x/5 = 7x/15
FE/F = 7x/15 / 2x/3 = 7/10 = 0.7, which is more than 0.5
Sufficient

Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
User avatar
praneethkarempudi
User avatar
Joined: 23 Jul 2018
Last visit: 31 Oct 2025
Posts: 35
Own Kudos:
18
Given Kudos: 9
Location: India
Schools: ISB '26 IIMA '26 IIM
GMAT 1: 690 Q50 V34
GPA: 85%
Products:
My Reviews
Schools: ISB '26 IIMA '26 IIM
GMAT 1: 690 Q50 V34
Posts: 35
Kudos: 18
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 08:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total

FNFTotal
E24
NE66
total 2010

To minimize the Electronics and Fragile count, we need to maximize the NE fragile count --> Making it 6
in that case E/F = 14/20
and this can only go up but won't come down.

both statements needed to answer

Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
User avatar
Cana1766
User avatar
Joined: 26 May 2024
Last visit: 17 May 2026
Posts: 85
Own Kudos:
80
Given Kudos: 12
Posts: 85
Kudos: 80
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 09:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
At first C might look like the answer, but E is the answer.

Each option by itself is not sufficient.
When we take both, we get fragile=2/3 of total=10/15 of total boxes
electronics=4/5 of total=12/15 of total boxes
If you take the total boxes as 15,it might look sufficient to answer that half of the fragile boxes contain electronics. Because this will always be yes in the worst-case scenario.But if the total boxes are 60,100. Then things change. Then it's not sufficient to answer Did more than half of the fragile boxes contain electronics?.Because there will be cases where we can find fewer than half fragile boxes containing electronics.

Hence the answer is E.
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
User avatar
chasing725
User avatar
Joined: 22 Jun 2025
Last visit: 16 Aug 2026
Posts: 241
Own Kudos:
235
 [1]
Given Kudos: 6
Location: United States (OR)
Schools: Stanford
Schools: Stanford
Posts: 241
Kudos: 235
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 09:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more

Total number of box should be multiple of 3 and 5.

Assume number of boxes = 15

1) We don't know the number of boxes containing electronics. Hence, the statement alone is not sufficient.

2) We don't know the number of boxes that are fragile. Hence the statement alone is not sufficient.

Combined

Number of fragile boxes = 2/3 * 15 = 10
Number of non fragile box = 5

Number of boxes that contain electronics = 4/5*15 = 12

Now if all of the 5 boxes that are non fragile contain electronics, 7 of 10 fragile boxes must have electronics. Hence, we have a "Yes" for the question asked.

Option C
User avatar
BeachStudy
User avatar
Joined: 30 Jun 2025
Last visit: 18 Aug 2025
Posts: 61
Own Kudos:
37
Given Kudos: 4
Posts: 61
Kudos: 37
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 09:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What we know:

Two shipments. Two types of boxes in each shipment
Types: Fragile, not fragile.

Ask:

Did more than half the fragile boxes contain electronics?

1) 2/3 the boxes in the shipment are fragile - We do not know if fragile means it has electronics. so this alone is not sufficient

2) 4/5 of the boxes in the shipment contain electronics. - Alone this is not sufficient as we do not know how many of those electronics are in fragile labeled boxes.

Combined)
we know that 2/3 or 10/15 of the boxes are fragile
we know that 4/5 or 12/15 of the boxes contain Electronic.
I am going to double that one more time to work with even numbers. 20/30 fragile. 24/30 electronics.
in a worst case 100% of the not electronics (N/E) are in fragile boxes. That would put 6 N/E inside the 20/30 fragile boxes. leaving us 14/30. That means that there is a scenario where the less than half the fragile boxes contain electronics and a scenario where more than half them do. Not sufficient.

Answer: E - Not sufficient alone or combined.
User avatar
iamchinu97
User avatar
Joined: 14 Dec 2020
Last visit: 26 Jun 2026
Posts: 136
Own Kudos:
154
 [1]
Given Kudos: 35
Products:
My Reviews
Posts: 136
Kudos: 154
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 09:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Okay lets solve using the Table method we need to find if Fragile electronics > 0.5 Fragile
lets assume total items = 300

F = fragile
NF = non fragile
E = elctronics
NE = non-elctronics

(1) Two-thirds of the boxes in the shipment are fragile. =>
F = 2/3 * 300 = 100 that means NF= 1/3*300 = 100. but this does not give us any info about amount of electronic items in the F and NF. so Not Sufficient
(2) Four-fifths of the boxes in the shipment contain electronics. =>
E = 4/5 * 300 = 240 that mean NE = 60. but this does not give us info about Fragile items and Electronics in them so Not Suffcient

Combine 1 and 2 =>

ENFTotal
Fpq200
NFrs100
Total24060300

Now we need to find if p > 0.5 * 200
is p > 100
Now if we see p = 240 - r and r can never be greater than 100 when r(max)=100 so p(min) = 140 which is always > 0.5 * 200 = 100, so this is Suffcient

Hence Ans C: Both together sufficient.
User avatar
AviNFC
User avatar
Joined: 31 May 2023
Last visit: 09 Aug 2026
Posts: 365
Own Kudos:
421
 [1]
Given Kudos: 5
Posts: 365
Kudos: 421
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 09:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total 90
1. Fragile=60.. Electronix box can be more or less than 30...NOT SUFFICIENT
2. Total electronix=72..fragile Electronix can be ascertained as fragile is not known..NOT SUFFICIENT

Together.. If all the 30 non-fragile are electronix box, then the remaining 42 has be to fragile electronix. so >50%

Ans C
User avatar
vnandan2001
User avatar
Joined: 22 Apr 2025
Last visit: 11 Mar 2026
Posts: 25
Own Kudos:
20
 [1]
Given Kudos: 11
Posts: 25
Kudos: 20
 [1]
GMAT Club Olympics 2025 (Day 6): A department store received 07 Jul 2025, 09:14
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(1) - No mention of no. of boxes containing electronics. Not sufficient
(2) - we don’t know how many are fragile or whether the electronics are in fragile or non-fragile boxes - Not sufficient.

Combine (1) and (2):
Let’s assume total boxes = 15
From (1):

Fragile = (2/3) * 15 = 10
Non-fragile = 5

Electronics boxes = (4/5) * 15 = 12
Non-Electronics boxes = 3

Let’s suppose worst case: all 3 Non-Electronics are inside Fragile Boxes
Even then, we would have 10 - 3 = 7(more than half) Fragile Boxes that contain Electronics

Sufficient.

(C)
Bunuel
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?

(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.


 


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

 

Show more
 1   2   3   4   5   6   
Moderators:
Bunuel
Math Expert
113150 posts
FrozenDragon
DI Forum Moderator
409 posts