Download SAT Tip #15 - Remainders

Name _______________________________________________________________ Date ___________________
SAT Tip of the Week: REMAINDERS
Remainders
Remainders are always whole numbers. When a number is divided
by another number, there is the number of times is goes in evenly
(the quotient) and the remainder.
For instance, when 12 is divided by 5, the remainder is 2.
2
5 12
10
2
And when 100 is divided by 3, the remainder is 1.
1. What is the remainder when 24 is divided by 5?
2. What is the remainder when 36 is divided by 5?
3. What is the remainder when 45 is divided by 5?
1. 4
2. 1
3. 0
Answers:
Name _______________________________________________________________ Date ___________________
SAT Tip of the Week: REMAINDERS
Due _________
Directions: For each problem, you must show your work or explain your answer for full credit.
Remember, calculators are allowed on the entire SAT Math test. You must use a pencil.
1. If n is divided by 9, the remainder is 5.
What is the remainder if 3n is divided by 9?
A.
B.
C.
D.
E.
4
5
6
7
8
3. When the positive integer m is divided by 5,
the remainder is 3. What is the remainder
when 20m is divided by 25?
2. The integer m is between 40 and 100.
When m is divided by 3, the remainder is 2.
When m is divided by 7, the remainder is 1.
What is one possible value of m?
4. When 25 is divided by 7, the remainder is
the same as when 49 is divided by which of
the following numbers?
A.
B.
C.
D.
E.
5. When a positive integer n is divided by 5,
the remainder is 4. Which of the following
expressions will yield a remainder of 2 when
it is divided by 5?
A.
B.
C.
D.
E.
n+1
n+2
n+3
n+4
n+5
3
4
5
6
7
6. For all possible integers j and k, let j ® k be
defined as the whole number remainder
when j is divided by k. If 13 ® k = 2, then
what is the value of k?
Name _______________________________________________________________ Date ___________________
SAT Tip of the Week: REMAINDERS
ANSWER KEY
Directions: For each problem, you must show your work or explain your answer for full credit.
Remember, calculators are allowed on the entire SAT Math test. You must use a pencil.
1. If n is divided by 9, the remainder is 5.
What is the remainder if 3n is divided by 9?
(C) 6
Try choosing a number for n – 14 is the lowest
positive choice since 9+5=14.
2. The integer m is between 40 and 100.
When m is divided by 3, the remainder is 2.
When m is divided by 7, the remainder is 1.
What is one possible value of m?
There are 3 possible answers: 50, 71, 92
14÷9 = REM of 5
3(14)÷9 = 42 ÷ 9 = REM of 6
3. When the positive integer m is divided by 5,
the remainder is 3. What is the remainder
when 20m is divided by 25?
REM of 10
Try numbers, n=8 is the smallest and
8÷5 = REM of 3
20(8) ÷ 25 = 160 ÷ 25 = REM of 10
5. When a positive integer n is divided by 5,
the remainder is 4. Which of the following
expressions will yield a remainder of 2 when
it is divided by 5? (C) n+3
Try a number for n that makes the first
statement true: n=9. 9 ÷ 5 = REM of 4
Now try each of the choices. C is the only one
that works.
4. When 25 is divided by 7, the remainder is
the same as when 49 is divided by which of
the following numbers? (C) 5
25 ÷ 7 = REM of 4. Try each of the answers – do
any of them give a remainder of 4 when
divided into 49? Yes, 49 ÷ 5 = REM of 4.
6. For all possible integers j and k, let j ® k be
defined as the whole number remainder
when j is divided by k. If 13 ® k = 2, then
what is the value of k?
k = 11
13 ÷ k = REM of 2
11 is the only integer that makes this statement
work.