Last visit was: 21 Apr 2026, 05:51

It is currently 21 Apr 2026, 05:51

Toolkit

Practice Tests

Data Insights Questions

Two-part Analysis (TPA)

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

Apr 16
Sneak Peek: $200 Off GMAT Prep
12:00 PM EDT
-
11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 26
Score High on the GMAT with Target Test Prep
10:00 AM EDT
-
11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 27
Try OnDemand GMAT Masterclass
11:00 AM EDT
-
12:00 PM EDT
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
Apr 28
Join - GMAT Day!
08:00 AM PDT
-
11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.

Back to Forum

Create Topic

GMAT Club Olympics 2025 (Day 7): At a summer camp, a class of students

1 2 3 4

MinhChau789

Joined: 18 Aug 2023

Last visit: 12 Apr 2026

Posts: 132

Own Kudos:

140

[1]

Given Kudos: 2

Posts: 132

Kudos: 140

[1]

09 Jul 2025, 04:38

Kudos

Bookmarks

From the info, N must be in the form of:
(1) N = 4+ 5a . So N = 9, 14, 19, 24, 29, 34,...
(2) N = 4 + 6b . So N = 10, 16, 22, 28, 34,...
(3) N = 7c + r (where r <7)

From (1) & (2), we know that N can be 34. So N must be in form of 30a + 34. From the options, only "Groups of 7" = 4, and remaining students = 6 can satisfy.

LastHero

Joined: 15 Dec 2024

Last visit: 12 Dec 2025

Posts: 134

Own Kudos:

147

[1]

Given Kudos: 1

Posts: 134

Kudos: 147

[1]

09 Jul 2025, 04:43

Kudos

Bookmarks

math session: (students-4) is a multiple of 5
biology session: (students-4) is a multiple of 6

(students-4) can be 30, 60, 90, 120 and so on
students can be 34, 64, 94, 124 and so on

Check the numbers in the answers:
students=7*(Groups of 7) + (Remaining students)
34=7*(Groups of 7) + (Remaining students)
34 = 7*4 + 6

The right answers:
Groups of 7=4
Remaining students=6

sanjitscorps18

Joined: 26 Jan 2019

Last visit: 03 Mar 2026

Posts: 723

Own Kudos:

740

[1]

Given Kudos: 130

Location: India

Schools: IMD'26

Products:

Schools: IMD'26

Posts: 723

Kudos: 740

[1]

09 Jul 2025, 04:53

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

At a summer camp, a class of students participates in three different sessions: math, biology, and history.

• For the math session, the students are divided so that one group has 4 students and all other groups have 5 students each.
• For the biology session, they are divided so that one group has 4 students and all other groups have 6 students each.
• For the history session, the same students are divided so that one group has fewer than 7 students and all other groups have 7 students each.

Select for Groups of 7 the number of groups that have 7 students each in the history session, and select for Remaining students the number of students in the remaining history group, that would be jointly consistent with the given information. Make only two selections, one in each column.

Let total student be T

For Maths
T = 4 + 5a

For Biology
T = 4 + 6b

For History
T < 7 + 7c

Now
4 + 5a = 4 + 6b
=> 5a = 6b
=> 5a and 6b could be 30. 60, 90, 120 .......

Hence T = 34, 64, 94, 124 ........

Let's take T = 34 = 7c + k ---- [c is groups of 7 and k is remaining students]
=> c = 4 and k = 6
this combination is available in the answer choices

Let's try T = 64 = 7c + k
=> c = 9 and k = 1

Let's try T = 94 = 7c + k
=> c = 13 and k = 3

Hence

Groups of 7 = 4
Remaining student = 6

andreagonzalez2k

Joined: 15 Feb 2021

Last visit: 26 Jul 2025

Posts: 308

Own Kudos:

503

[1]

Given Kudos: 14

Posts: 308

Kudos: 503

[1]

09 Jul 2025, 04:58

Kudos

Bookmarks

math = 4 + 5a = total -> total-4 must be a multiple of 5
biology = 4 + 6b = total -> total-4 must be a multiple of 6
history = c + 7d = total, with c<7

if total-4 must be a multiple of 5 and 6, total can be: 34, 64, 94...

if c+7d=34, c=6 and d=4, that are in the options

Groups of 7 = 4 and Remaining students = 6

ODST117

Joined: 15 Aug 2024

Last visit: 27 Jan 2026

Posts: 173

Own Kudos:

[1]

Given Kudos: 149

Posts: 173

Kudos: 88

[1]

09 Jul 2025, 05:11

Kudos

Bookmarks

Total number of students in the math session -> $4+5x_1$ ($x_1$ is the number of groups with $5$ students in them)
Total number of students in the biology session -> $4+6x_2$ ($x_2$ is the number of groups with $6$ students in them)

The total number of students doesn't change per session, therefore, students in the math session = students in the biology session

$4+5x_1=4+6x_2$

$5x_1=6x_2$

The minimum value of LHS and RHS where they are equal is $30$, when $x_1=6$ and $x_2=5$

The total number of students $= 30+4 = 34$

The history session had groups with $7$ students each and one group with less than $7$ students.
The max number of groups of $7$ students that can be made with $34$ students is $4$ (because $7*4 = 28$. If we said 5 groups, that would mean $7*5=35$ students total, which is more than what we have)
If $28$ students are in $4$ groups of $7$, that leaves $6$ students in the group which has less than $7$ students.

Tanish9102

Joined: 30 Jun 2025

Last visit: 20 Nov 2025

Posts: 59

Own Kudos:

[1]

Posts: 59

Kudos: 49

[1]

09 Jul 2025, 05:48

Kudos

Bookmarks

Correct Answer: Group of 7 students= 4 and Remaining students= 6
For this question check by option method,
Let’s check with options and try to find total students:
2*7= 14
4*7= 28
6*7= 42
8*7= 56
10*7= 70

Now by random take group= 4 and use remaining= 6
Now total= 7*4+6= 28+6= 34

• For the math session, the students are divided so that one group has 4 students and all other groups have 5 students each.
If we divide 5 students each so here we have 6 groups and 4 are the remaining students. Hence we got this correct.

• For the biology session, they are divided so that one group has 4 students and all other groups have 6 students each.
Similarly if we divide 6 students each so here we have 5 groups and 4 are the remaining students. Hence we got this also correct.

• For the history session, the same students are divided so that one group has fewer than 7 students and all other groups have 7 students each.
Lastly if we divide 7 students each so here we have 4 groups and 6 are the remaining students as this less than 7. Hence we got this also correct.

jkkamau

Joined: 25 May 2020

Last visit: 21 Apr 2026

Posts: 226

Own Kudos:

190

[1]

Given Kudos: 142

Location: Kenya

Schools: Haas '25

GMAT 1: 730 Q50 V46 Verified score

GPA: 3.5

Products:

Schools: Haas '25

GMAT 1: 730 Q50 V46 Verified score

Posts: 226

Kudos: 190

[1]

09 Jul 2025, 05:52

Kudos

Bookmarks

Based on the Math and Biology groups whose numbers are given with 4 being constant we need to find the LCM of 5 and 6 to find a number that would easily fit the groupings without a remainder.
The LCM of 5 and 6 is 30 meaning those distributed in groups of 5 and 6 could be 30 or multiples of 30 meaning total students are either 34, 64, 94......
Testing those values with the history class distribution the only available answer from the choices is
4 Groups of 7
6 Remaining students meaning the total students are 34

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

twinkle2311

Joined: 05 Nov 2021

Last visit: 14 Apr 2026

Posts: 150

Own Kudos:

178

[1]

Given Kudos: 21

Location: India

Concentration: Finance, Real Estate

Schools: ISB '26 Wharton '26

GPA: 9.041

Products:

Schools: ISB '26 Wharton '26

Posts: 150

Kudos: 178

[1]

09 Jul 2025, 05:58

Kudos

Bookmarks

Total no. of students = N
For maths, 1 group has 4 , remaining have 5
-> N – 4 is a multiple of 5.
For biology, 1 group has 4, remaining have 6
-> N – 4 is also a multiple of 6.

LCM (5, 6) = 30
-> N – 4 = 30
-> N = 34

For history, we can split 34 students into groups of 7, which will give us 4 full groups and 6 remaining students

Answer :
Groups of 7: 4
Remaining students: 6

Edwin555

Joined: 10 Aug 2023

Last visit: 16 Apr 2026

Posts: 88

Own Kudos:

[1]

Given Kudos: 17

Location: India

Posts: 88

Kudos: 54

[1]

09 Jul 2025, 05:59

Kudos

Bookmarks

Let math, biology, and history be represented by m, b, h.
m has 1 team with 4 members, rest is split into teams of 5 members each
b has 1 team with 4 members, rest is split into teams of 6 members each
n has 1 team with < 7 members, rest is split into teams of 7 members each

From first two statements, taking LCM of 5 & 6 we have 30+4, say 34 students in total.
Considering the last statement 7*4 = 28 and the rest in 1 team which has 6 members which is < 7.
That is a total of 34 students and all the conditions are satisfied and the values are consistent.

Correct answers are,
Groups of 7 : 4
Remaining students : 6

Sketchitesh

Joined: 29 Nov 2024

Last visit: 09 Feb 2026

Posts: 141

Own Kudos:

110

[1]

Given Kudos: 19

Concentration: Operations, Finance

Schools: INSEAD Jan '26 Kellogg Yale

GPA: 7.2

WE:Operations (Other)

Products:

Schools: INSEAD Jan '26 Kellogg Yale

Posts: 141

Kudos: 110

[1]

09 Jul 2025, 06:09

Kudos

Bookmarks

From the math session, N = 4 + 5x (where x is the number of groups with 5 students) => N will end in either 4 or 9 since 5X will end in (0,5)
From the biology session, N = 4 + 6y (where y is the number of groups with 6 students) => N will be even
=> N will end in "4"
This also gives that (N-4) is multiple of 30 LCM of (5,6)
From the history session, N = 7G + R we know that R<7 so R can be 2,4,6

Try options, start with B, G=4 ,

If R = 2, N = 7(4) + 2 = 28 + 2 = 30 (Ends in 0, not 4)
If R = 4, N = 7(4) + 4 = 28 + 4 = 32 (Ends in 2, not 4)
If R = 6, N = 7(4) + 6 = 28 + 6 = 34 (ends with 4 and (n-4) is multiple of 30.

So answer is 4 and 6.

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

UfuomaOh

McCombs School Moderator

Joined: 14 Sep 2023

Last visit: 07 Mar 2026

Posts: 83

Own Kudos:

[1]

Given Kudos: 14

Posts: 83

Kudos: 50

[1]

09 Jul 2025, 06:51

Kudos

Bookmarks

Total number of students in

Maths = 5k+4

Biology= 6m+4

The plausible number for the total number of students is a multiple of 5 and 6
which is 30. Thus N=34

if 34 is divided into groups of 7 students. How many groups would we have

34/7= 4 R6

So we would have 4 groups of 7 Students with the remaining 6 put into the last group

harshnaicker

Joined: 13 May 2024

Last visit: 04 Jan 2026

Posts: 91

Own Kudos:

[1]

Given Kudos: 35

Posts: 91

Kudos: 60

[1]

09 Jul 2025, 06:57

Kudos

Bookmarks

Let M = 4*1 + 5n
B = 4 + 6m
H = 7p + (<7)

We need to find the split of H i.e. History session
M = B
5n = 6m
Presume n = 6 and m=5 and total = 34

We can see that:
7*4+6 = 34

Groups of 7: 4
Remaining students: 6

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

Mardee

Joined: 22 Nov 2022

Last visit: 02 Feb 2026

Posts: 225

Own Kudos:

191

[1]

Given Kudos: 20

Posts: 225

Kudos: 191

[1]

09 Jul 2025, 07:07

Kudos

Bookmarks

Three different sessions: math, biology, and history.

Let T be the total number of students

For the math session, the students are divided so that one group has 4 students and all other groups have 5 students each.

=> T = 5a + 4 (a>=1)

For the biology session, they are divided so that one group has 4 students and all other groups have 6 students each.

=> T = 6b + 4 (b>=1)

For the history session, the same students are divided so that one group has fewer than 7 students and all other groups have 7 students each.

=> T = 7c + d (d < 7 and c>=1)

Now we have 2 equations,
T = 5a + 4
T = 6b + 4

=> T ≡4 mod 5 and T ≡4 mod 6
=> T - 4 must be divided by LCM(5,6) = 30
Thus,
T = 30k + 4 for an integer k

From equation 3, and above condition we need to find k where T when divided by 7 gives remainder (d) < 7
Lets try k = 1.
T = 30*1 + 4 = 34
34 divided by 7 gives a remainder 6

=> Groups of 7 = 4 and remainder students = 6
If we were to tally this with the other equations,
For Maths ; 5a + 4 = 34 => a = 6
For Biology; 6b + 4 = 34 => b = 5
Both are integers and satisfy above a and b constraint so its valid

Groups of 7 = 4
Remaining students = 6

adityaprateek15

Joined: 26 May 2023

Last visit: 21 Apr 2026

Posts: 346

Own Kudos:

170

[1]

Given Kudos: 323

Location: India

Schools: Ross '26 Tepper '26 McCombs '26

GPA: 2.7

Products:

Schools: Ross '26 Tepper '26 McCombs '26

Posts: 346

Kudos: 170

[1]

09 Jul 2025, 07:18

Kudos

Bookmarks

Gievn:
Math = 5x+4 (x = no. of groups with 4 people)
Biology = 6y+4 (y = no. of groups with 6 people)
History: 7z + (>7) (z = no. of groups with 7 people)
Determine the total students in the summer camp
Consider math and biology: Total student has to be LCM(5,6) + 4
Possible values: 4,34,64...
Now, the same total should be written in the form 7z+ >7
If total = 34, 7*4+6
Matches the criteria and also there in the options. Test the next value
If total = 64, 7*9 + 1
Both 9 and 1 are not available in Option choices.
Answer 4 and 6

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

eshika23

Joined: 01 Aug 2024

Last visit: 21 Jan 2026

Posts: 71

Own Kudos:

[1]

Given Kudos: 65

Posts: 71

Kudos: 34

[1]

09 Jul 2025, 07:25

Kudos

Bookmarks

Given:
All students divided
For maths groups of 5 students with one group of 4 (this means no. of group is multiple of 5 and remainder is 4)
For Biology, Groups of 6 students with one group of 4 (No. of groups is multiple of 6 with remainder 4)
History, (7 students per group and remainder is unknown)

So we need to first see how many students are there in class.

So if we say 6 groups of 5, 5groups of 6 is created then 34 is total number of students in class.

So no. of students when divided by 34/7, 4 total groups with remainder 6 students.

and this answer is available as well.

Answer: 4 groups of 7 students and 6 students in one group (remainder).

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

jnxci

Joined: 29 Nov 2018

Last visit: 28 Mar 2026

Posts: 39

Own Kudos:

[1]

Given Kudos: 338

Posts: 39

Kudos: 18

[1]

09 Jul 2025, 07:39

Kudos

Bookmarks

Math: 4 + 5M | Bio: 4 + 6B | History: <7 + 7H
- From math & bio, we have the ratio M:B = 6:5 and we can plug back in to find the common total number of students: 34, 64, 94..
- To satisfy the history class w/ the above total, we only have H (groups of 7) = 4 & its remaining students = 6

muuss

Joined: 10 Aug 2024

Last visit: 18 Apr 2026

Posts: 108

Own Kudos:

Given Kudos: 38

GMAT Focus 1: 615 Q84 V81 DI76 Verified score

Posts: 108

Kudos: 83

09 Jul 2025, 07:48

Kudos

Bookmarks

Maths:5x+4
biology:6y+4
history:7z+a (a<7)
Let the total number of students be N.
So,
4+5x=4+6y
=>5x=6y
=>x/y=6/5
y should be a multiple of 5
N=4+6×5=34
For history it can be 4*7+6 (since we know a is less than 7)
Groups of 7: 4
Remaining students: 6

shriwasakshat

Joined: 08 Aug 2024

Last visit: 21 Apr 2026

Posts: 84

Own Kudos:

[1]

Given Kudos: 107

Products:

Posts: 84

Kudos: 62

[1]

09 Jul 2025, 07:54

Kudos

Bookmarks

Maths = 4 + 5x
Biology = 4 + 6y

As students are same in both subjects we can equate both equation

x/y = 6/5, Taking x = 6 and y = 5 give the total students = 30 + 4 = 34. Which satisfy the given constraints according to given options.

34/7 = 4 groups of 7 plus 6 students in History.

Groups of 7 = 4 and Remaining students = 6