Last visit was: 18 Nov 2025, 19:56

It is currently 18 Nov 2025, 19:56

Toolkit

Practice Tests

Data Insights Questions

Data Sufficiency (DS)

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

Request Expert Reply

Confirm Cancel

Nov 22
GMAT RC Masterclass
11:00 AM IST
-
01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment
Nov 23
Conquer Algebra on the GMAT Focus Edition
11:00 AM IST
-
01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Nov 25
Try OnDemand GMAT Masterclass
10:00 AM EST
-
11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.

Back to Forum

Create Topic

GMAT Club Olympics 2025 (Day 10): At a company with 36 employees, 23

1 2 3 4

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 18 Nov 2025

Posts: 105,355

Own Kudos:

778,086

[5]

Given Kudos: 99,964

Products:

Expert

Expert reply

Posts: 105,355

Kudos: 778,086

[5]

11 Jul 2025, 08:00

Kudos

Bookmarks

00:00

Start Timer

Pause Timer

Resume Timer

Show Answer

Hide

Show

History

Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

65% (01:33) correct

35% (01:34) wrong

based on 291 sessions

History

Date

Time

Result

Not Attempted Yet

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 Answer

Official Answer

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 18 Nov 2025

Posts: 105,355

Own Kudos:

778,086

[4]

Given Kudos: 99,964

Products:

Expert

Expert reply

Posts: 105,355

Kudos: 778,086

[4]

11 Jul 2025, 08:30

Kudos

Bookmarks

GMAT Club Official Explanation:

At a company with 36 employees, 23 are assigned to Project Alpha, and 18 are assigned to Project Beta. How many employees are assigned to both projects?

Total = A + B - Both + Neither
36 = 23 + 18 - Both + Neither

(1) Five employees are not assigned to either project.

This statement implies Neither = 5, so:

36 = 23 + 18 - Both + 5
Both = 10

Sufficient.

(2) Exactly 21 employees are assigned to only one of the two projects.

This statement implies:

(A - Both) + (B - Both) = 21

(23 - Both) + (18 - Both) = 21

Both = 10.

Sufficient.

Answer: D.

Archit3110

Major Poster

Joined: 18 Aug 2017

Last visit: 18 Nov 2025

Posts: 8,423

Own Kudos:

4,979

[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 Verified score

GMAT Focus 2: 645 Q83 V82 DI81 Verified score

GPA: 4

WE:Marketing (Energy)

GMAT Focus 2: 645 Q83 V82 DI81 Verified score

Posts: 8,423

Kudos: 4,979

[1]

11 Jul 2025, 08:34

Kudos

Bookmarks

At a company with 36 employees, 23 are assigned to Project Alpha, and 18 are assigned to Project Beta. How many employees are assigned to both projects?
solve using 2x2 matirx

------A----NA-----total
B------ ---- ------18
NB---- ---- ---------18
total--23---- 13----36

#1
Five employees are not assigned to either project.

------A----NA-----total
B------ 10 ---- 8 ------18
NB---- 13 ---- 5---------18
total--23---- 13----36

both projects 10 ; sufficient

#2

Exactly 21 employees are assigned to only one of the two projects.

------A----NA-----total
B------ 10 ---- 8 ------18
NB---- 13 ---- 5---------18
total--23---- 13----36
both projects 10 ; sufficient

IMO option D is correct

Bunuel

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

hakzarif

Joined: 31 May 2025

Last visit: 25 Oct 2025

Posts: 65

Own Kudos:

Given Kudos: 9

Products:

Posts: 65

Kudos: 29

11 Jul 2025, 08:34

Kudos

Bookmarks

There are 36 employees in total, with 23 assigned to Project Alpha and 18 to Project Beta.
Total= A + B - Both + None >>>>this relationship means that the number of employees assigned to neither project is always five less than the number assigned to both projects. Statement (1) tells us that 5 employees are assigned to neither project, which means the number assigned to both projects must be 10. Statement (2) tells us that 21 employees are assigned to only one project, which when combined with the totals for Alpha and Beta also leads to the conclusion that 10 employees are assigned to both projects. Because both statements independently allow us to determine the number of employees in both projects, each statement alone is sufficient to answer the question.

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 18 Nov 2025

Posts: 5,793

Own Kudos:

5,509

[1]

Given Kudos: 161

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,793

Kudos: 5,509

[1]

11 Jul 2025, 08:41

Kudos

Bookmarks

At a company with 36 employees, 23 are assigned to Project Alpha, and 18 are assigned to Project Beta.

How many employees are assigned to both projects?

	Alpha	~Alpha	Total
Beta	x = ?		18
~Beta			36-18=18
Total	23	36-23 = 13	36

(1) Five employees are not assigned to either project.

	Alpha	~Alpha	Total
Beta	x = 23-13=18-8 = 10	13-5=8	18
~Beta	18-5=13	5	18
Total	23	13	36

10 employees are assigned to both projects

SUFFICIENT

(2) Exactly 21 employees are assigned to only one of the two projects.

	Alpha	~Alpha	Total
Beta	x = ?	y	18
~Beta	21-y	y-3	18
Total	23	13=2y-3	36

2y-3 = 13; y = 8

	Alpha	~Alpha	Total
Beta	x = 10	8	18
~Beta	13	5	18
Total	23	13	36

10 employees are assigned to both projects

SUFFICIENT

IMO D

Heix

Joined: 21 Feb 2024

Last visit: 18 Nov 2025

Posts: 361

Own Kudos:

153

[1]

Given Kudos: 63

Location: India

Concentration: Finance, Entrepreneurship

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

GPA: 3.4

WE:Accounting (Finance)

Products:

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

Posts: 361

Kudos: 153

[1]

11 Jul 2025, 08:46

Kudos

Bookmarks

Using our variables:
- A = employees assigned to Alpha only
-B = employees assigned to Beta only
- AB = employees assigned to both projects
- N= employees assigned to neither project
We know:
A + B+ AB+ N=36
A + AB = 23
B+ AB = 18
Statement (1): Five employees are not assigned to either project.
This tells us N= 5.
So: A + B+ AB =36-5=31
Now we have:
A + B+ AB=31
A + AB = 23
B+ AB = 18
Subtracting the second equation from the first:
B = 31-23 = 8
And now we can find AB:
B+ AB = 18
8+ AB= 18
AB = 10
Statement (1) is sufficient.
Statement (2): Exactly 21 employees are assigned to only one of the two projects.
This means A + B = 21.
From our original equations:
A+ AB = 23
B+ AB = 18
A+ B=21
Adding the first two equations:
A + AB+B+ AB= 23 + 18
A+B+ 2AB =41
Substituting A + B= 21:
21 + 2AB= 41
2AB = 20
AB = 10
Statement (2) is also sufficient.
Therefore, the answer is D: Each statement alone is sufficient.

Emkicheru

Joined: 12 Sep 2023

Last visit: 12 Sep 2025

Posts: 119

Own Kudos:

Given Kudos: 11

Location: Kenya

Schools: Anderson (UCLA) Sloan (MIT) Columbia '27

GMAT 1: 780 Q50 V48 Verified score

GRE 1: Q167 V164 Verified score

GPA: 3.7

Schools: Anderson (UCLA) Sloan (MIT) Columbia '27

GMAT 1: 780 Q50 V48 Verified score

GRE 1: Q167 V164 Verified score

Posts: 119

Kudos: 22

11 Jul 2025, 08:49

Kudos

Bookmarks

Bunuel

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

we have 36 employees 5 are not assigned to both ,therefore 23/31 are assigned to alpha, 18/31 are assigned beta therefore 23+18=41 are assigned to either but 21 are assigned to exactly one, implies 13 not assigned to beta for both or 8 not assigned to alpha ie 13+8=21. this proves that those not assigned are assigned to only one .therefore we subtract 21 from 41 implies 20 are assigned to both

Missinga

Joined: 20 Jan 2025

Last visit: 16 Nov 2025

Posts: 393

Own Kudos:

261

[1]

Given Kudos: 29

Posts: 393

Kudos: 261

[1]

11 Jul 2025, 08:56

Kudos

Bookmarks

At a company with 36 employees, 23 are assigned to Project Alpha, and 18 are assigned to Project Beta. How many employees are assigned to both projects?
..........B............NB............T
A....... X .........—-.......... 23
NA....——........—............13
T.......18...........18...............36
X=?

(1) Five employees are not assigned to either project.

..........B............NB............T
A....... X .........—-.......... 23
NA....——........(5)—............13
T.......18...........18...............36
X=23-13=10
Sufficient

(2) Exactly 21 employees are assigned to only one of the two projects.

..........B............NB............T
A....... X .........(23-x).......... 23
NA....(18-x)........—............13
T.......18...........18...............36

(23-x)+(18-x)=21
23+18-21=2x
2x=23+18-21=20
x=10
Sufficient

D

k11work

Joined: 12 Jan 2025

Last visit: 18 Nov 2025

Posts: 119

Own Kudos:

[1]

Given Kudos: 84

Status:Complete

Affiliations: -

-: -

Products:

Posts: 119

Kudos: 92

[1]

11 Jul 2025, 08:58

Kudos

Bookmarks

Total = 36
A = 23
B = 18
Both = ?

Statement 1 :
None = 5
Total = A+B - Both + None
Since we know all other values , we can calculate for Both.
Thus, SUFFICIENT

Statement 2 :
A+B-Both = 21
Since we know all other values , we can calculate for Both.
Thus, SUFFICIENT

Answer is D.

Cana1766

Joined: 26 May 2024

Last visit: 15 Nov 2025

Posts: 85

Own Kudos:

[1]

Given Kudos: 11

Posts: 85

Kudos: 79

[1]

11 Jul 2025, 09:06

Kudos

Bookmarks

From first option,five employees are not assigned to any project
36=23+18-(people in both projects)+people not assigned any project
36=41-(people in both projects)+5
36=46-(people in both projects)
(people in both projects)=0

Hence first option is sufficient

from second option, 21 employees with only one of the two projects where x is people in both projects
41−2x=21
x=10

Hence second option is sufficent

Hence answer is D.

Bunuel

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

D3N0

Joined: 21 Jan 2015

Last visit: 12 Nov 2025

Posts: 587

Own Kudos:

572

[1]

Given Kudos: 132

Location: India

Concentration: Operations, Technology

Schools: Smeal'21 (WD) Arizona State'21 (A$) Simon '21 (WD)

GMAT 1: 620 Q48 V28 Verified score

GMAT 2: 690 Q49 V35 Verified score

WE:Operations (Retail: E-commerce)

Products:

Schools: Smeal'21 (WD) Arizona State'21 (A$) Simon '21 (WD)

GMAT 2: 690 Q49 V35 Verified score

Posts: 587

Kudos: 572

[1]

11 Jul 2025, 09:06

Kudos

Bookmarks

Ans: D

At a company with 36 employees (T), 23 are assigned to Project Alpha (A) , and 18 are assigned to Project Beta (B). How many employees are assigned to both projects (C)?

(1) Five employees are not assigned to either project.
N = 5
We know from Venn diagram rules
Total = A + B - C + N
36 = 23 + 18 - C + 5
C = 0

(2) Exactly 21 employees are assigned to only one of the two projects.

A + B - C = 21
23 + 18 - C = 21
C = 20

Decimal

Joined: 20 Jul 2022

Last visit: 03 Oct 2025

Posts: 9

Own Kudos:

[1]

Given Kudos: 16

Posts: 9

Kudos: 9

[1]

11 Jul 2025, 09:12

Kudos

Bookmarks

Given :
Total Employee = 36
Employees in Project Alpha = 23
Employees in Project Beta = 18

Not Given : Employees not involved in any of the projects

Asked : Number of employees assigned to both the projects.

Statement 1

Five employees are not assigned to either project.

=> Number of employees who are not part of any project =5
=> Number of employees distributed to both the projects is 36 - 5 = 31
=> No of employees who are part of both the projects = 23 + 18 - 31 = 10.

Hence, Statement 1 is sufficient.
Eliminate option B, C & E.

Statement 2

Exactly 21 employees are assigned to only one of the two projects.

=> 21 employees are involved in one of the two projects only.
Therefore, number of employees in both the projects
=> Employees (Project Alpha + Project Beta) = Employees (in any one project) + 2 * Employees (in both projects)
=> 23 + 18 = 21 + 2 * Employees (in both projects)
=> 41 = 21 + 2 * Employees (in both projects)
=> Employees (in both projects) = (41 - 21) / 2 =10

Hence, Statement 2 is sufficient.

Therefore, since statements 1 & 2 are both sufficient,
Option D is the answer

Bunuel

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

Dav2000

Joined: 21 Sep 2023

Last visit: 14 Sep 2025

Posts: 75

Own Kudos:

[1]

Given Kudos: 69

Posts: 75

Kudos: 44

[1]

11 Jul 2025, 09:19

Kudos

Bookmarks

Bunuel

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

Given: Number of employees assigned to Project Alpha = 23 and project Beta = 18 and total = 36

asked: Value of Both(employees in both the projects)?

Statement 1: Using Total = A + B - Both + neither, we can figure out the value of Both since we are given neither = 5. So sufficient

Statement 2: Using A + B - 2*Both = A only + B only, we can figure out the value of Both since we are given A only + B only = 21. So sufficient
Hence the answer is Option D.

SaanjK26

Joined: 08 Oct 2022

Last visit: 18 Nov 2025

Posts: 77

Own Kudos:

[1]

Given Kudos: 69

Location: India

Posts: 77

Kudos: 63

[1]

11 Jul 2025, 09:20

Kudos

Bookmarks

Statement 1: Sufficient.
Five employees are not assigned to either project,
Employees assigned to atleast one project= 36-5=31.
Number of employees on both projects: 31=23+18-x = 10.
So sufficient.

Statement 2: Sufficient.
Employees in alpha only: 23-x
Employees in beta only:18-x
So (23-x)+(18-x)=21
x= 10
So sufficient.

Answer: Option (D) . Each statement alone is sufficient,

AviNFC

Joined: 31 May 2023

Last visit: 13 Nov 2025

Posts: 216

Own Kudos:

288

[1]

Given Kudos: 5

Posts: 216

Kudos: 288

[1]

11 Jul 2025, 09:21

Kudos

Bookmarks

36=23+18-both+neither

1. neither=5..SUFFICIENT
2. 23-Both+18-both=21...SUFFICIENT

Ans D

Jarvis07

Joined: 06 Sep 2017

Last visit: 18 Nov 2025

Posts: 295

Own Kudos:

236

Given Kudos: 160

GMAT 1: 750 Q50 V41 Verified score

Posts: 295

Kudos: 236

11 Jul 2025, 09:22

Kudos

Bookmarks

If 5 people aren’t on either project, then the remaining 31 must belong to Alpha, Beta, or both. Since Alpha and Beta together account for 41 project‐slots (23+18), the only way to fill exactly 31 slots among employees is for ten of those slots to be double‐counted. meaning 10 people must be on both projects. That gives a unique answer from statement (1) alone.

Similarly, if exactly 21 employees work on just one of the two projects, then the remaining slots (forty‐one total minus those twenty‐one single‐project assignments) must come from people counted twice. That again forces ten people to hold two assignments. So statement (2) by itself also fixes the overlap.

Because each statement independently yields a single, consistent count of employees on both projects, the correct choice is that each one alone is sufficient, hence D!

Bunuel

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

iamchinu97

Joined: 14 Dec 2020

Last visit: 18 Nov 2025

Posts: 132

Own Kudos:

139

Given Kudos: 34

Products:

Posts: 132

Kudos: 139

11 Jul 2025, 09:28

Kudos

Bookmarks

At a company with 36 employees, 23 are assigned to Project Alpha, and 18 are assigned to Project Beta. How many employees are assigned to both projects?

(1) Five employees are not assigned to either project. =>
So We know XUY = 36
X= 23
Y= 18
SO XUY = X + Y - Both
36 = 23+18 - Both
so Both = 10, hence Sufficient

(2) Exactly 21 employees are assigned to only one of the two projects. =>
X only + Y only = 21

X + Y - 2* Both = 21
23 + 18 -2*Both = 21
20 = 2 * Both
So Both = 10
Hence Sufficient

Hence Ans D

Dipan0506

Joined: 24 May 2021

Last visit: 17 Nov 2025

Posts: 72

Own Kudos:

Given Kudos: 3

Products:

Posts: 72

Kudos: 14

11 Jul 2025, 09:32

Kudos

Bookmarks

Out of 36 employees, 5 have not been assigned to any project, whereas 31 has been assigned. Out of 31, 21 is there for one project, we can conclude of employees with both assignments.

ManifestDreamMBA

Joined: 17 Sep 2024

Last visit: 18 Nov 2025

Posts: 1,282

Own Kudos:

784

Given Kudos: 236

Products:

Posts: 1,282

Kudos: 784

11 Jul 2025, 09:34

Kudos

Bookmarks

T= A+B-b+n, where b = both and n=none/no assignment
36=23+18-b+n
b-n=5

b=?

S1
n=5
b-5=5
b=10
Sufficient

S2
23-b+18-b=21
20=2b
b=10
Sufficient

Answer D

Bunuel

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

bart08241192

Joined: 03 Dec 2024

Last visit: 17 Nov 2025

Posts: 75

Own Kudos:

Given Kudos: 13

Posts: 75

Kudos: 64

11 Jul 2025, 09:40

Kudos

Bookmarks

A = Number of people in Project Alpha = 23
B = Number of people in Project Beta = 18
x = Number of people in both projects
N = Number of people in neither project

Total company size is 36. Using the "addition principle":
Number in at least one project + N = 36
And "in at least one" = |A ∪ B| = |A| + |B| – |A∩B| = 23 + 18 – x = 41 – x

Translation:

All 36 = 41 - X + N

Condition One:
By providing N,
we can calculate
36 = 41 - X + 5
X = 10
The condition is sufficient.

Condition Two:
A - X + B - X = 21
41 - 2X = 21
X = 10
This condition is also sufficient.

1 2 3 4

Moderators:

Bunuel

Math Expert

105355 posts

kingbucky

496 posts

Prep Toolkit

Announcements

Master in Management, Finance, Business Analytics and more Master’s Programs!

Solving 705+ Level MSR Questions with Data Synthesis Skils

Tuesday, Nov 18, 2025
10:30am NY / 3:30pm London / 9pm Mumbai

Live Profile Evaluation Chat Session with ARINGO

Wednesday, November 19, 2025
09:00 am PDT | 10:30 pm IST
Location: GMAT Club Chat

Top GMAT Focus Debriefs

GMAT Club Olympics 2025 (Day 10): At a company with 36 employees, 23

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

GMAT Club Olympics 2025 (Day 10): At a company with 36 employees, 23

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards