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GMAT Question Patterns: Remainders

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GMAT Question Patterns: Remainders [#permalink] New post 07 Feb 2013, 04:23
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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.

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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: GMAT Question Patterns: Remainders [#permalink] New post 07 Feb 2013, 09:54
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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 !

P.S: BTW,have you added it to your sig ?
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Re: GMAT Question Patterns: Remainders [#permalink] New post 14 Feb 2013, 03:13
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!
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Re: GMAT Question Patterns: Remainders [#permalink] New post 14 Feb 2013, 03:15
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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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: GMAT Question Patterns: Remainders [#permalink] New post 14 Feb 2013, 04:55
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Re: GMAT Question Patterns: Remainders [#permalink] New post 07 Jul 2014, 09:01
Hello from the GMAT Club BumpBot!

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Re: GMAT Question Patterns: Remainders [#permalink] New post 19 Jul 2014, 23:38
Bunuel wrote:
Edited original post: named the patterns.



Hello Bunnel
Is there a link to all the posts on Patterns?
Thank you!
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Re: GMAT Question Patterns: Remainders [#permalink] New post 20 Jul 2014, 05:15
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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)
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: GMAT Question Patterns: Remainders   [#permalink] 20 Jul 2014, 05:15
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