## Remainders

When a number *n* is divided by 8, the remainder is 5. Which of the following could be the value of 2*n* - 3?

A. 3

B. 12

C. 19

D. 23

E. 37

## Knowsys Method

**Read the question carefully. ** Multiple numbers could be divided by 8 and produce a remainder of 5, but you are not asked to find every possible number. You are asked something entirely different.

**Identify the bottom line. **What is a possible value of 2*n* + 5?

**Assess your options. **You could work backwards from your answer choices, subtracting 5, dividing by 2, and then checking to see whether the resulting number produces a 5 when divided by 8, but that is a lot of steps. Instead of having to repeat these steps (possibly 5 times for each of your answer choices), work from the information that the problem gives you.

**Attack the problem. **Your Knowsys handbook has a specific method for finding a variable divided by a certain number and producing a certain remainder. First, write the problem out so that there is no confusion:

Next, add the divisor and the remainder to find one possible value of *n*:

*n* = 5 + 8 = 13

Your next step is to try out the number 13 by plugging it in the equation that you were given:

2(13) - 3 = 23

Does that match any of your answer choices? Yes!

**Loop back. ** You just proved that this answer can work, so you are finished! Select your answer.

The correct answer is (D).

This is a medium level question.

**Want some help reviewing the math concepts you need to master? **Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.