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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:

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 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

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

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

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

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

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.

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.

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.

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

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.

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.

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

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.

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?

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.
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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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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.

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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