SAT Math: Repeating Sequences and Remainders

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Author: Morris Goldstein

Description:

To solve problems using the remainder of integer division

In the refrigerator, left overs represent either an abundance of food...or the remains of a food that no one really liked in the first place. The math equivalent of left overs is the remainder of integer division which can be a useful tool in solving problems involving sequences.

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Tutorial

Introduction

Consider the following questions:

What is the remainder of 12581 when it is divided by 32?
What is the 100th letter in the repeating sequence: A, B, C, D, E, F...
For the repeating sequence of numbers: 1, -2, 3, -4, 5, -6, 1, -2, 3, -4, 5, -6, … what is the sum of the first 100 numbers?
179 people are seated in a room in rows of 17 seats per row. Each row is filled before starting the next row. How may people are in the last row.

Questions 2 - 4 involve repeating sequences and all of them involve the remainder of integer division.