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Math Expert V
Joined: 02 Sep 2009
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GMAT Question Patterns: Remainders

We have gone through the GMAT Prep Tests and OG 13 and analyzed all of the questions to spot the most common patterns. This discussion is dedicated to the types of remainder problems that could appear on the test.

The idea behind this project is to find as many common question patterns as possible for 3 reasons:
1. Get a higher score - make sure you know how to answer every pattern and you don't miss one of these in your practice
2. Save Time - you don't need to solve hundreds of questions; you just need to solve a few questions from each pattern and if you answered them correctly, you can move on
3. Peace of Mind - know that you have covered all known question patterns

Background
• Most GMAT remainder problems are encountered in data sufficiency section.
• All GMAT remainder questions are limited to positive integers only.
• Both number plugging method and algebra are suitable to solve remainder questions.
• Some remainder questions can be disguised as word problems. See below.
• Usually you get 1, maximum 2 questions on remainders on the test (based on GMAT Prep CATs)

Typical questions:
NOTE: questions below are from OG13 and GMAT Prep. There are only 5 questions on remainders in OG13.

Pattern #1: Remainders & Ratios.

OG13 diagnostic test, question 13
If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45

Discussed HERE

OG13 Practice Questions, question 95
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Discussed HERE

Pattern #2: Division of a Variable

OG13 Practice Questions, question 26
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Discussed HERE

Pattern #3: Min/Max and Remainders

When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35.
A. 3
B. 4
C. 12
D. 32
E. 35

Discussed HERE

Other min/max DS questions: search.php?search_id=tag&tag_id=42
Other min/max PS questions: search.php?search_id=tag&tag_id=63

Pattern #4: Remainder Word Problem.

There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(A) 101
(B) 103
(C) 106
(D) 107
(E) 109

Discussed HERE

A person inherited few gold coins from his father. If he put 9 coins in each bag then 7 coins are left over. However if he puts 7 coins in each bag then 3 coins are left over. What is the number of coins he inherited from his father?
(1) The number of coins lies between 50 to 120.
(2) If he put 13 coins in one bag then no coin is left over and number of coins being lesser than 200.

Discussed HERE

Pattern #5: Find the Divisible Integer

OG13 Practice Questions, question 58
What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.

Discussed HERE

OG13 Practice Questions, question 83
If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.

Discussed HERE

Pattern #6: Find the Remainder Most common pattern.

What is the remainder when the positive integer n is divided by 6?
(1) n is multiple of 5
(2) n is a multiple of 12

Discussed HERE

If x and y are integer, what is the remainder when x^2 + y^2 is divided by 5?
(1) When x-y is divided by 5, the remainder is 1
(2) When x+y is divided by 5, the remainder is 2

Discussed HERE

If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?
(1) When t is divided by 7, the remainder is 6.
(2) When t^2 is divided by 7, the remainder is 1.

Discussed HERE

If p is a positive odd integer, what is the remainder when p is divided by 4 ?
(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.

Discussed HERE

If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?
(1) n is not divisible by 2
(2) n is not divisible by 3

Discussed HERE

If a and b are positive integers, what is the remainder when $$4^{2a+1+b}$$ is divided by 10?
(1) a = 1
(2) b = 2

Discussed HERE
C-Trap remainder problem. "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

Theory on remainders is HERE.
All OG13 questions with solutions are HERE.
PS questions on remainders are HERE.
DS questions on remainders are HERE.

_________________
Retired Moderator B
Joined: 27 Aug 2012
Posts: 1044
Re: GMAT Question Patterns: Remainders  [#permalink]

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Another GREAT analysis bunuel...Awesome man Kudos....

Just can't wait to see all of your analysis in each and every aspect of PS and DS.....Look forward to seeing those soon on the forum !

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Joined: 02 Jun 2011
Posts: 39
Schools: MIT Sloan (LGO)
Re: GMAT Question Patterns: Remainders  [#permalink]

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Dear Bunuel,

I haven't been able to find reviews like this one for other types of questions. I see this one is quite recent. Is this a one time review? Or maybe others are planned but not started/in the work?

Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 59712
Re: GMAT Question Patterns: Remainders  [#permalink]

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LGOdream wrote:
Dear Bunuel,

I haven't been able to find reviews like this one for other types of questions. I see this one is quite recent. Is this a one time review? Or maybe others are planned but not started/in the work?

Thanks!

We'll be covering one topic per week. Next topic will be ready in couple of days.
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59712
Re: GMAT Question Patterns: Remainders  [#permalink]

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Edited original post: named the patterns.
_________________
Intern  Joined: 17 Oct 2013
Posts: 37
Location: India
Concentration: Strategy, Statistics
Schools: ISB '17 (A)
GMAT 1: 730 Q49 V40 WE: Analyst (Computer Software)
Re: GMAT Question Patterns: Remainders  [#permalink]

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Bunuel wrote:
Edited original post: named the patterns.

Hello Bunnel
Is there a link to all the posts on Patterns?
Thank you!
Math Expert V
Joined: 02 Sep 2009
Posts: 59712
Re: GMAT Question Patterns: Remainders  [#permalink]

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Kconfused wrote:
Bunuel wrote:
Edited original post: named the patterns.

Hello Bunnel
Is there a link to all the posts on Patterns?
Thank you!

We only have two more:
gmat-question-patterns-arithmetic-146430.html (Arithmetic)
gmat-question-patterns-abolute-value-150327.html (Abolute Value)
_________________
Manager  Joined: 26 Feb 2015
Posts: 110
Re: GMAT Question Patterns: Remainders  [#permalink]

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Bunuel wrote:
Kconfused wrote:
Bunuel wrote:
Edited original post: named the patterns.

Hello Bunnel
Is there a link to all the posts on Patterns?
Thank you!

We only have two more:
gmat-question-patterns-arithmetic-146430.html (Arithmetic)
gmat-question-patterns-abolute-value-150327.html (Abolute Value)

Hey Bunuel,

I'd really like to see patterns on Fractions/Ratios/Decimals and on Equalities. I don't know if you decided to cancel this project, but I have really enjoyed all three topics done so far.
Intern  B
Joined: 19 Jan 2015
Posts: 7
Re: GMAT Question Patterns: Remainders  [#permalink]

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Hello Bunnel,

can you provide same analysis for other topics?

thanks
Non-Human User Joined: 09 Sep 2013
Posts: 13742
Re: GMAT Question Patterns: Remainders  [#permalink]

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________ Re: GMAT Question Patterns: Remainders   [#permalink] 10 May 2019, 15:18
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