# Number Properties

Arithmetic: Number Properties

Read the following SAT test question and then select the correct answer.

Every time you work a math problem, read the problem carefully.  Identify the bottom line and think about the most efficient method to solve for the bottom line.  Choose a method to solve the problem and attack the problem without hesitation.  When you think you have the answer, loop back to make sure that the answer addresses the bottom line because questions often require multiple steps to get to the answer.

When the positive integer n is divided by 5, the remainder is 0. What is the remainder when 3n is divided by 5?

Make a note that your bottom line is the remainder of 3n.  Then think carefully about the first portion of information that you are given.  Some number, n, is divided by 5 and there is no remainder.  That means that n must be a multiple of 5.  If you do not immediately see this, think about a concrete number that will not result in a remainder:

or    or
All of these values for n result in a whole number with no remainder.

If n is a multiple of 5, what will 3n be?  It will still be a multiple of 5!  It will still result in a remainder of 0.  If you cannot see this, look back at the examples above using 5 and 15.  If 5 is your n value, 3 times 5 is 15, and when you divide 15 by 5 the answer is 3 with a remainder of 0.  Now that you have found your bottom line, look down at your answer choices.

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

The correct answer is (A).

On sat.collegeboard.org, 70% of the responses were correct.

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