 Are you aware of the GMAT Maths PEMDAS and BODMAS rules? If you aren’t aware, then don’t worry! In this article,we will be talking about GMAT quant PEMDAS and BODMAS and hopefully by the end of it, you will have a clearer idea.

So, first let’s begin by understanding what is the order of operations for a mathematical expression.

Take a look at the sample question below.

What is the value of 15÷3(2+3)?

The above question involves very basic calculation, in your GMAT this could be a small part of your calculation or you could get a similar expression in terms of variables that is “x and y”.

Now, did you get confused while solving the above expression? Are you wondering whether you should do a multiplication first or a division first?

OR

Have you got the answer as “1” for the above expression? If yes, then, you should read  this article to understand the rules of “order of operations” because “1” is not the correct answer.

Before we discuss the answer for this question, let’s understand what is the “order of operations” for a mathematical expression.

We all know that the base of mathematics is constituted of four basic operations:

• Multiplication
• Division
• Subtraction

Any higher degree problem in the GMAT Quant section is just the complex version of these operations.

Now what is the issue? We all have studied the priority order of addressing a stream of expressions in our primary classes. Some might have studied as PEMDAS or some might have studied as BODMAS.

What are PEMDAS and BODMAS Rules?

First of all, do both have the same order of operations? The answer is NO. So, are they completely different and will  each give a different result?The answer is NO again.  Both have to give the same final result. Then what is the difference?

PEMDAS and BODMAS, these are two different problem-solving techniques based on the country you live. BODMAS is the UK/Australia/India based problem-solving technique, whereas PEMDAS is the US-based method.

BODMAS and PEMDAS, both give you a priority sequence of solving an expression. So, let’s check the order of operations for BODMAS and PEMDAS.

BODMAS stands for:

B 🡪  Brackets

O 🡪  Order(Index)

D 🡪  Division

M 🡪 Multiplication

S 🡪 Subtraction

Whereas, PEMDAS is the abbreviation for:

P 🡪 Parentheses

E 🡪 Exponents

M 🡪 Multiplication

D 🡪 Division

S 🡪 Subtraction

The only difference between these two methods is, in BODMAS we use ‘division’ prior to ‘multiplication’ in an equation. While in PEMDAS, we use ‘multiplication’ prior to ‘division’ in an equation. However, PEMDAS is the synonym of BODMAS.

PEMDAS and BODMAS are two similar rules and generate the same answer because division and multiplication hold the same weightage. Therefore, it doesn’t matter which method you follow to solve a question. But remember, the GMAT exam is administered by the GMAC,  which is a US based organization. Hence, test makers keep “PEMDAS” in mind while creating a question.

Now, let’s take you back to the question we asked you at the beginning of the article.

What is the value of 15÷3(2+3)?

• Using BODMAS:

Step 1:

Bracket first = (2+3) = 5

We will have, 15÷3*5

Step 2:

Division = 15 3 = 5

Step 3:

Finally, Multiplication = 5 * 5 = 25.

Hence, 25 is the correct answer.

• Using PEMDAS:

Step 1:

Parenthesis first = (2+3) = 5

We will have, 15÷3*5

Step 2:

Let say, if we do Multiplication next = 3 * 5 = 15

Step 3:

Then, Division = 15 15 = 1

Now, why is the result different? What is wrong here? As we discussed above, multiplication and division have equal priority.

Here the most important part is, we have to work from left to right. So, here division goes first, followed by multiplication.

Parenthesis first = (2+3) = 5

From left, it is Division first = 15 3 = 5

Then, Multiplication = 5 * 5 = 25

Hence the correct answer is 25.

What is the Conventional Order of Operation?

So, in general, to evaluate any mathematical sequence of operations whether we use BODMAS or PEMDAS, the conventional order of operation is as follows:

1. Evaluate the expressions in parenthesis (Brackets) first.

2. Then, evaluate exponents.

3. Next, comes multiplication and division, as discussed above, they are considered to have equal priority, and to avoid ambiguities, work from left to right.

4. Finally, comes addition and subtraction, which are also of equal priority, again to avoid ambiguities, work from left to right.

Some Examples

1. Find the value of 18*2+(19*30)?

Step 1:

Solve the innermost parentheses first,

19 * 30 = 570

So, we have 18*(2+570)

Step 2:

Then solve the outermost parentheses,

2 + 570 = 572

Step 3:

Finally, we have

18 * 572 = 10296

2. Evaluate 3*5+24-18-10÷5

Step 1: Parentheses first

24-18 = 6

We have, 3*5+6-10÷5

Step 2: Multiplication

3 * 5 = 15

We have, 15+6-10÷5

Step 3: Division

10÷5=2

We have, 15+6-2