# SAT Math: Arithmetic

## Remainders

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

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