Last visit was: 31 Aug 2026, 14:14

It is currently 31 Aug 2026, 14:14

Toolkit

Practice Tests

Quantitative Questions

Problem Solving (PS)

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

Aug 26
This Labor Day Save on GMAT™ Prep
10:00 AM EDT
-
11:59 PM EDT
Save up to $1,000 on select GMAT prep now. This Fall, achieve your most ambitious goals with millions of student success stories behind you.
Aug 27
BIG NEWS! We’ve been nominated, and we’d love your vote!
10:00 AM EDT
-
11:00 AM EDT
We’ve worked incredibly hard to build TTP into the best test prep experience possible, and it would mean a lot to us to win Newsweek’s 2026 Readers’ Choice Award for Best Test Prep. If TTP has helped you, we’d be incredibly grateful for your vote.
Aug 31
Serious score increases start here: OnDemand GMAT classes taught by Founder and Top GMAT Expert Scott Woodbury-Stewart
10:00 AM PDT
-
11:00 AM EDT
Top Scores Start with a Elite Online Prep Course. Enroll for 6 months of access to over 400 hours of GMAT video lessons AND 715+ Score Guarantee!
Sep 02
615 to 695 in 2 Months Despite a 70+ Hr Work Week
12:30 AM EDT
-
01:30 AM EDT
Thought your job leaves no time for GMAT prep? After multiple GMAT attempts and a demanding consulting job, Kshitij improved to 695 in under 2 months. Learn the mindset shifts, study strategy, and execution changes that made the breakthrough possible.
Sep 02
Free full-length test!
08:00 PM PDT
-
09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Sep 03
From ‘GMAT Is Not for Me’ to a 695— Beating Her Target by 50 Points
01:30 AM EDT
-
02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Sep 09
Masters' Spotlight Fair
07:00 AM PDT
-
10:00 AM PDT
Meet AdComs and explore top Master’s programs - MiM, MiF, MSc, MSBA and more. - Application Fee Waivers - Free 1-Week of GMAT Club Tests: - Master's Application Toolkit - Grand Prize Giveaway

Back to Forum

Create Topic

GMAT Club World Cup 2026 (Day 6): How many positive integers less than

1 2 3 4 5

Rishm

Joined: 05 May 2024

Last visit: 30 Aug 2026

Posts: 369

Own Kudos:

Given Kudos: 82

Location: India

Schools: Johnson '27 LBS '27 IESE '27

GPA: 10

WE:Consulting (Consulting)

Products:

Schools: Johnson '27 LBS '27 IESE '27

Posts: 369

Kudos: 77

13 Jul 2026, 12:22

Kudos

Bookmarks

E is the answer.

I basically saw what has 0 as reminder which is 44 and 88, now look for +1,+2,+3 numbers, you will see - 45,46,47,89,90,91 as numbers, adding 1,2,3 as well as they give the same reminder. Hence 12 is the correct answer here.

Shlok02

Joined: 08 Jan 2024

Last visit: 31 Aug 2026

Posts: 65

Own Kudos:

Given Kudos: 6

Products:

Posts: 65

Kudos: 41

13 Jul 2026, 12:23

Kudos

Bookmarks

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

Integer will have same remainders when divided by 4 and 11
on dividing by 4 we can get remainders - 0,1,2 and 3
we can say the same as the remainders when the number will be divided by 11

we take 4 cases
Case 1 - Remainder = 0
Here we can simply take Commom multiple of 4 and 11 before 100 and we get 44 and 88
Hence 2 Numbers

Case 2- Remainder = 1
We can denote the series as 4a + 1 and 11b + 1
4a + 1 = 11b + 1
4a = 11b
As this cannot be factorised we can say a = 11 and b = 4
We can conclude that every 11th term in 1st series (4a + 1) will be the same as every 4th term in 2nd series (11b + 1)
Based on this we get the integers 45 and 89 as the integers with remainders = 1 when dividing by 4 or 11
Hence 2 numbers

repeating the same steps for
Case 3 - remainder = 2
Common terms = 46 and 90

and Case 4 - remainder = 3
Common terms = 47 and 91

Hence Answer is (A) 8 terms

Coolguy22

Joined: 06 Jul 2024

Last visit: 31 Aug 2026

Posts: 5

Own Kudos:

[1]

Given Kudos: 15

Location: India

GMAT Focus 1: 675 Q86 V84 DI80 Verified score

Products:

GMAT Focus 1: 675 Q86 V84 DI80 Verified score

Posts: 5

Kudos: 7

[1]

13 Jul 2026, 12:27

Kudos

Bookmarks

Let K and Q be intergers,

according to question 4K + x = 11Q + x

K/Q=11/4

Let Q = 4, it implies K=11 This 44,45,46,47
Let Q = 8, it implies K =22 This 88,87,98,90
Let Q = 0, it implies K = 0 This 0,1,2,3 (cant be 0 as the question says +ve integers)

total number of cases = 4+4+3 = 11

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

Sajal193

Joined: 06 Jan 2025

Last visit: 30 Aug 2026

Posts: 15

Own Kudos:

Given Kudos: 5

Products:

Posts: 15

Kudos: 2

13 Jul 2026, 12:41

Kudos

Bookmarks

1,2,3,44,45,46,47,88,89,90,91. Total 11 nimbers

AviNFC

Joined: 31 May 2023

Last visit: 09 Aug 2026

Posts: 365

Own Kudos:

421

[1]

Given Kudos: 5

Posts: 365

Kudos: 421

[1]

13 Jul 2026, 13:03

Kudos

Bookmarks

LCM(4,11)=44
n=44k+r
r can be 0,1,2,3
k=0, r=1,2,3..n=1,2,3
k=1, r=0,1,2,3...n=44,45,46,47
k=2, r=0,1,2,3...n=88,89,90,91

total 11 nos.

Ans D

chasing725

Joined: 22 Jun 2025

Last visit: 16 Aug 2026

Posts: 241

Own Kudos:

235

[1]

Given Kudos: 6

Location: United States (OR)

Schools: Stanford

Posts: 241

Kudos: 235

[1]

13 Jul 2026, 13:04

Kudos

Bookmarks

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

n = 4x + r
n = 11y + r

n = 44z + r

r can be 0, 1, 2, or 3

When r = 0 ; n = 44, 88
r = 1 ; n = 1, 45, 89
r = 2 ; n = 2, 46, 90
r = 3 ; n = 3, 47 , 91

Number of integers = 9 + 2 = 11

Option D

Maesha

Joined: 11 Jun 2026

Last visit: 31 Jul 2026

Posts: 29

Own Kudos:

[1]

Given Kudos: 4

Concentration: Leadership, Economics

Schools: HBS '26 (S)

Posts: 29

Kudos: 25

[1]

13 Jul 2026, 13:15

Kudos

Bookmarks

lets suppose, number of total integer = x
and each time the remainder = y

so, x ( mod 4) = y
x( mod 11) =y

LCM of 4 and 11 is 4, so , x(mod44)=y
if modulo is 4 remainder must be one of 0/1/2/3

so , suppose , x==44a+y where a = 0,1,2,3,4,.............

if a = 0 , x= 0+ ( 0,1,2,3)=(0,1,2,3)
if a = 1 , x= 44 +(0,1,2,3) =( 44,45 ,46 47)
if a = 2 , x= 88+(0,1,2,3)=(88,89,90,91)
if a =3 , x=132+(0,1,2,3)= not valid because , x must be greater than 0 and less than 100

so, possible value = 1,2 ,3 ,44 ,45,46,47,88,89,90,91

total possible value is 11 .

ShreyaMittal1609

Joined: 05 Nov 2025

Last visit: 31 Aug 2026

Posts: 82

Own Kudos:

Given Kudos: 208

GMAT Focus 1: 545 Q77 V77 DI77 Verified score

Products:

GMAT Focus 1: 545 Q77 V77 DI77 Verified score

Posts: 82

Kudos: 45

13 Jul 2026, 13:23

Kudos

Bookmarks

My ans is C) 10

remainder when n is divided by 4 can be 0,1,2,3.

when remainder for both are same-
for n<4, remainder=n. Positive Integers = 1,2,3 will give remainders=integers upon division by both 4 and 11
1)0= 44,11
2)1= 45,89
3)2= 47,79
4)3= 91

Total count= 10. There can be a more efficient way for sure.

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

SmileAndSolve

Joined: 25 Aug 2024

Last visit: 31 Aug 2026

Posts: 80

Own Kudos:

[1]

Given Kudos: 327

Location: India

Concentration: Strategy, Entrepreneurship

GPA: 4

Products:

Posts: 80

Kudos: 52

[1]

13 Jul 2026, 13:45

Kudos

Bookmarks

Answer:

Attachments

WhatsApp Image 2026-07-14 at 2.13.54 AM.jpeg [ 127.48 KiB | Viewed 105 times ]

FlushLoop

Joined: 05 Jul 2026

Last visit: 06 Aug 2026

Posts: 62

Own Kudos:

[1]

Posts: 62

Kudos: 57

[1]

13 Jul 2026, 14:22

Kudos

Bookmarks

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

When we divide a number by 4 the remainder can be 0, 1, 2 or 3.

This is because the largest value for the remainder is 3, which's one less than 4.

We can write the number as n = 44k.

The remainder, where 44 is the product of 4 and 11.

To find the values of n we need to look at the valid values of the remainder for numbers that are less, than 100.

If the remainder is 0 the numbers would be 44, 88 which gives us 2 numbers.
If the remainder is 1 the numbers would be 1, 45 89 which gives us 3 numbers.
If the remainder is 2 the numbers would be 2, 46 90 which gives us 3 numbers.
If the remainder is 3 the numbers would be 3, 47, 91 which gives us 3 numbers.

Total 11 numbers

IMO Option D

GurpreetMahli

Joined: 06 Aug 2023

Last visit: 31 Aug 2026

Posts: 33

Own Kudos:

[1]

Given Kudos: 115

Location: United States

Products:

Posts: 33

Kudos: 12

[1]

13 Jul 2026, 15:15

Kudos

Bookmarks

Answer: D = 11

Step 1. LCM of 4 and 11 = 44

Step 2. Possible remainders 0 - 3 as 4 is the limiting integer

Step 3. Remainder (R) = 0

((Highest multiple of 44 - lowest multiple of 44) / 44 ) + 1

((88-44)/44) + 1 >> 2

0 is not included as lowest multiple of 44 since it is neither positive or negative and our set only includes positive integer less than 100

Step 4. R = 1

(( (88+1) - (1)) / 44) +1 >> 3

Step 5. R = 2 and 3

Same pattern holds as the highest multiple doesn't exceed 100, so 3 and 3 respectively

Total: 2(R=0) + 3(R=1) + 3(R=2) + 3(R=3) = 11

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

priyanka06

Joined: 10 Sep 2025

Last visit: 31 Aug 2026

Posts: 60

Own Kudos:

[1]

Given Kudos: 1

Products:

Posts: 60

Kudos: 35

[1]

13 Jul 2026, 16:29

Kudos

Bookmarks

4 and 11 have shared remainders=> 0,1,2,3

values for 44x + R, When remainder is 0 => 44, 88
when remainder is 1 => 1, 45, 89
when remainder is 2 => 2,46,90
when remainder is 3=> 3,47,91

total 11 positive integers less than 100.

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

alamin8

Joined: 24 May 2025

Last visit: 29 Aug 2026

Posts: 181

Own Kudos:

[1]

Given Kudos: 32

Location: Bangladesh

Concentration: Accounting, Technology

Schools: HEC Sept '27 INSEAD Aug '27 UNC '27

GPA: 3.89

Schools: HEC Sept '27 INSEAD Aug '27 UNC '27

Posts: 181

Kudos: 79

[1]

13 Jul 2026, 17:43

Kudos

Bookmarks

When we divide anything by 4, the reminder will be 0, 1, 2, 3
Therefore, when we divide anything by 11, the reminder must be 0, 1, 2, 3

Before finding the list, lets do an LCM of 4 and 11. It will be 44. Then, there will be no reminder.
Here is the list of positive integers less than 100
Reminder 0: 44, 88 (88/4 = 11) = 2
Reminder 1: 1, 45, 89 (11*4, reminder 1, 11*8, and 4*22, reminder 2) = 3
Reminder 2: 2, 46, 90 [11*4, reminder 2, 11*8, and 4*22, reminder 2] = 3
Reminder 3: 3, 47, 91 (11*4, reminder 3, 11*8, and 4*22, reminder 3) = 3

Total reminders =2+3+3+3 = 11

Answer: D

harshitaa45

Joined: 20 Feb 2021

Last visit: 29 Aug 2026

Posts: 49

Own Kudos:

[1]

Given Kudos: 8

Products:

Posts: 49

Kudos: 30

[1]

13 Jul 2026, 17:47

Kudos

Bookmarks

By brute force pattern
Any number less than both 4 and 11 will leave the same reminder:1,2 and 3
A number which is factor of both 4 and 11 will leave the same reminder:0: Possible nums:44,88
And when we add the first set of numbers to the multiples of 4 and 11 then also the same remainders are left:
SO the possible set of numbers:1,2,3,44,45,46,47,88,89,90,91=>11 nums possible

rockstar09rulez

Joined: 30 Sep 2023

Last visit: 26 Aug 2026

Posts: 43

Own Kudos:

[1]

Given Kudos: 74

Location: United States (CA)

Concentration: Technology, Finance

Products:

Posts: 43

Kudos: 25

[1]

13 Jul 2026, 19:14

Kudos

Bookmarks

N = 4a+r
N = 11b+r
equating we get a/b = 11/4;
Assume a = 11k, b = 4k
SO we get N = 44k + r
Now r can be 0,1,2,3 since it is has to leave same remainder as that when divided by 11
If r = 0
N = 44k so N can be 44,88
If r = 1
N = 44k+1 so N can be 1, 45, 89
similarly r=2 and r=3 give. 3 values each
So total values = 2+3+3+3 = 11 -> D

sunshineeee

Joined: 17 May 2020

Last visit: 30 Aug 2026

Posts: 174

Own Kudos:

[1]

Given Kudos: 266

Location: Indonesia

Schools: Stern '26 (WL) Tepper '26 (WL) BU'26 (A) Ross '26 Johnson '26

Products:

Schools: Stern '26 (WL) Tepper '26 (WL) BU'26 (A) Ross '26 Johnson '26

Posts: 174

Kudos: 52

[1]

13 Jul 2026, 19:56

Kudos

Bookmarks

Question asked: positive integers < 100 have the SAME REMAINDER upon division 4 and 11

1. Upon Division 4 and 11 under 100 with remainder 0 -> 4x11 = 44, 88 (2)
2. with remainder 1: 1, 45, 89 (3)
3. with remainder 2: 2, 46, 90 (3)
4. with remainder 3: 3, 47, 91 (3)

1,2,3 are included since if divided by 4, will have reminder as above as well.

So, total 2+3+3+3 = 11 (Answer D).

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

kalkurd

Joined: 31 Oct 2025

Last visit: 25 Jul 2026

Posts: 28

Own Kudos:

[1]

Given Kudos: 1

Posts: 28

Kudos: 26

[1]

13 Jul 2026, 20:53

Kudos

Bookmarks

D 11.

Need n mod 4 = n mod 11 = r. Since r must be a valid mod-4 remainder, r is 0, 1, 2, or 3. Then n minus r is divisble by both 4 and 11, so by 44. Thus n = 44k + r

List 1 to 99

k = 0, 1, 2, 3 (drop 0, it's not positive) -> three
k = 1: 44, 45, 46, 47 -> four
k = 2: 88, 89, 90, 91 -> four

total 11.

Wrong ones
E - 12: Counted k=0, as four, forgetting that it's not positive
C - 10: Dropped a boundary value either 88 or 91, both under 100
B - 9: Kept the two full blocks, but missed the small three (1, 2, 3)
A - 8: Undercounted repeats across blocks.

SRIVISHUDDHA22

Joined: 08 Jan 2025

Last visit: 19 Aug 2026

Posts: 120

Own Kudos:

[1]

Given Kudos: 371

Location: India

Schools: ISB '26

GPA: 9

Products:

Schools: ISB '26

Posts: 120

Kudos: 80

[1]

13 Jul 2026, 21:19

Kudos

Bookmarks

Lets check small numbers like 1,2 and 3 (less than 4) when 1 is divided by 4 or 11 reminder is 1 , same is the case with 2 and 3 when divided by 11 or 4 leaves a reminder 2, 3
now if we check for larger number like 32 we see the reminder is 0 when divided by 11 the reminder is 10 so for 2 digit numbers less than 100 we need to find first the common multiples of 4 and 11
44, and 88 are the only common multiples .
Check
44 when divided by 4 / 11 leaves a reminder 0
44+1=45 when divided by 4/11 reminder is 1
44+2 =46 when divided by 4/11 reminder is 2
44+3 =47 when divided by 4/11 reminder is 3
44+4 =48 when divided by 4 leaves reminder 0 when divided by 11 leaves reminder 4 . STOP. So - 1,2,3 ,44,45,46 .47 when divided by 4 or 11 leaves same reminder

No check for 88

88 when divided by 4/11 leaves reminder 0
88+1=89 when divided by 4/11 leaves reminder 1
88+2=90 when divided by 4/11 leaves reminder 2
88+3 =91 when divided by 4/11 leaves reminder 3
88+4 =92 when divided by 4/11 leaves reminder 0 for 4 and reminder 4 for 11 . STOP!

So 1,2,3,44,45,46,47 ,88,89,90,91 leaves same reminder for 4 and 11
no of terms = 11

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

Aarushi100

Joined: 17 Jul 2024

Last visit: 28 Aug 2026

Posts: 70

Own Kudos:

Given Kudos: 98

Posts: 70

Kudos: 57

13 Jul 2026, 21:40

Kudos

Bookmarks

For 4 we can only have these remainders: 0,1,2,3
Let us consider the numbers when Remainder will be 0 : 44, 11
Remainder 1: 45,85
Remainder 2: 46, 86
Remainder 3: 47, 87

Apart from these 8 numbers, all other numbers have different remainders.
Eg: consider 34 => Remainder for 11 = 1
Remainder for 4 = 2.

ANSWER A

GreenPill

Joined: 13 Jun 2026

Last visit: 31 Aug 2026

Posts: 37

Own Kudos:

[1]

Products:

Posts: 37

Kudos: 25

[1]

13 Jul 2026, 22:06

Kudos

Bookmarks

Bunuel

How many positive integers less than 100 have the same remainder upon division by 4 as upon division by 11?

A. 8
B. 9
C. 10
D. 11
E. 12

This question was provided by GMAT Club
for the GMAT World Cup Competition

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

⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

OPTION D. 4 and 11 are co prime. from trial and error we know 22 gives remainder 0 with 11 and 2 with 4. for 33 its 0 and 1. then 44, both gives 0, as for 4 only 1,2,3 are possible remainders. 44,45,46,47 are nos. similarly 88,89,90,91. therefore 4+4 + 3(initial numbers 1,2,3) = 11