Techniques to Solve Remainder Questions

Certain problems involving remainders can be solved easily by Plugging in numbers that fit the problem. For example: When positive integer x is divided by 5, the remainder is 3.…
by Talha Omer, M.Eng., Cornell Grad
in Math Concepts

Certain problems involving remainders can be solved easily by Plugging in numbers that fit the problem.

For example: When positive integer x is divided by 5, the remainder is 3. When the positive integer y is divided by 5, the remainder is 4. What is the remainder when x + y is divided by 5?

Plug-in numbers for x and y that fit the given conditions.

For instance, numbers that give a remainder of 3 when divided by 5 are 3, 8, 13, 18, 23,…

Similarly, the numbers that give a remainder of 4 when divided by 5 are 4, 9, 14, 19,….

Let’s select x = 3 and y = 4.

x + y = 7.

When 7 is divided by 5, the remainder is 2.

You don’t need to plug in a different set of numbers since the question is a numeric entry and can only have a single unique answer.

But just in case you want to check your working, you can try a different set of values.

Try x = 13 and y = 19.

x + y = 32

The remainder of 32 will still be 2 when divided by 5.

 

n is a positive integer that is divisible by 6. Find the remainder when n is divided by 12

  • 0
  • 2
  • 4
  • 6
  • 8
  • 10

Plug-in numbers for n that fit the given conditions.

Positive integers that are divisible by 6 are 6, 12, 18, 24, 30, 36,….

Let’s divide these numbers by 12.

6 ÷ 12, the remainder is 6 (quotient is 0)

12 ÷ 12, the remainder is 0 (quotient is 1)

18 ÷ 12, the remainder is 6 (quotient is 1)

24 ÷ 12, the remainder is 0 (quotient is 2)

We can clearly see a pattern here. But since this question can have multiple correct answers, we would advise to test out a few more numbers just to be sure.

So, to reassure that the pattern continues, you can check a couple of more values.

30 ÷ 12, the remainder is 6 (quotient is 2)

36 ÷ 12, the remainder is 0 (quotient is 3)

Hence, the remainder can be 0 or 6.

 

Integer x has a remainder of 5 when divided by 9, and integer y has a remainder of 7 when divided by 9. What is the remainder when y – 7x is divided by 9?

Plug-in numbers for x and y that fit the given conditions.

Numbers that give a remainder of 5 when divided by 9 are 5, 14, 23, 32, 41,…

Numbers that give a remainder of 7 when divided by 9 are 7, 16, 25, 34, 43,….

Let’s select x = 5 and y = 7. (selecting small numbers is time-efficient, although you can select any numbers of your choice)

y ? 7x = 7 ? 35 = ?28

When ?28 is divided by 9, the remainder is 8. (Quotient is ?4)

You don’t need to plug in a different set of numbers since the question is a numeric entry and can only have a single unique answer.

 

 

SEE ALSO

GRE Math: Fundamentals of a Triangle

Like most people who take the GRE, your Math knowledge might be a little rusty. The good news is that GRE only tests you on math that you have already learned in high school. If you are worried that you have forgotten most of what you learned in high school, you will...

read more

How do you Calculate Standard Deviation on the GRE?

Standard deviation is an important statistical term tested on the GRE. It gives you an insight into the deviation or dispersion of a set of numbers from its mean; therefore, a low standard deviation implies that the numbers are very close to the mean, and vice versa....

read more

What are Prime Factors?

Every integer greater than 1 either is a prime number or a composite number. All composite numbers can be expressed as a product of prime numbers. For example, 6 can be expressed as 2 × 3. The prime factors of 6 are 2 and 3. Whereas the expression 2 × 3 is called...

read more

How to calculate Factors of Perfect Squares

Let's see how we use the chart to deal with this question: How many positive factors does 100 have? Set up the chart: 100 Left Column Right Column 1 100 2 50 4 25 5 20 10 10   Remember the rule - once the factors repeat themselves, (i.e. 10 and 10), stop. Since...

read more

What are Factor Tables?

Some integer questions may require you to find the Factors of an integer. The factor table is a basic technique for finding all the factors of any integer. This technique can also be useful for questions asking how many factors a particular integer has. The technique...

read more

Basics of Prime Numbers

Primes play a central part in integer questions. Overconfidence is dangerous here: while almost everybody can recite the definition of a prime number at the drop of a hat, the field is actually rife with misconceptions. We are here to make sure you know everything...

read more

Rules of Operations for Odd and Even Numbers

Let's formulate rules for addition, subtraction, multiplication, and division of Even and Odd numbers. Here are the rules for adding / subtracting even and odd numbers: Even ± Even = Even (e.g. 2 + 2 = 4; -4 - 2 = -6) Odd ± Odd = Even (e.g. 1 + 1 = 2; -31 - 1 = -32)...

read more

Basics of Even & Odd numbers

We'll begin with the basic definitions: Even: any integer that is divisible by 2. Examples: 2, 4, 14. Odd: any integer that is not divisible by 2, i.e. leaves a remainder of 1 when divided by 2. Examples: 1, 3, 5, 7, 9 So far so good. Consider this potential...

read more

Shortcuts to find Remainders

Find the remainder when 5,142,376,298 is divided by 9?     The long division method will definitely tell you the remainder of dividing 5,142,376,298 by 9 but you can very well imagine how long would that take. The good news is that just like the divisibility...

read more