GMAT Question Patterns: RemaindersWe 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:

- Get a higher score - make sure you know how to answer every pattern and you don't miss one of these in your practice
- 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
- 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 13If 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

HEREOG13 Practice Questions, question 95When 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 VariableOG13 Practice Questions, question 26If 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 RemaindersWhen 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

HEREOther min/max DS questions:

search.php?search_id=tag&tag_id=42Other 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

HEREA 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 IntegerOG13 Practice Questions, question 58What 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

HEREOG13 Practice Questions, question 83If 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

HEREIf 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

HEREIf 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

HEREIf 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

HEREIf 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

HEREIf 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

HEREC-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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Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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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