**By**: Apex GMAT

**Date:** 17 August 2021

While studying and preparing for the GMAT quant section, you might have come across some different types of GMAT arithmetic questions. These are actually quite common in the quantitative reasoning section and can be often intertwined with other GMAT algebra and GMAT geometry questions.

These usually come in 2 different formats: data sufficiency problems and problem-solving. The former have a very particular structure where you will have to determine whether the 2 statements are enough to come up with a solution. The latter type of problem requires you to actually solve the problem and derive a proper solution.

In this article, we’ll tell you more about how to go about solving these GMAT arithmetic questions, so keep on reading to find out more.

**Arithmetic Concepts you need to revise**

These are the arithmetic concepts you’ll need to know before you start practicing. Make sure to revise these fundamentals:

- Arithmetic Operations
- Number theory
- Divisibility
- Prime number properties
- Evens and odds
- Positives and negatives
- Fractions
- Decimals
- Real numbers
- Ratio and proportions
- Percents
- Powers and roots
- Statistics
- Sets
- Probability

**How to solve a GMAT arithmetic problem?**

The number 1 thing you need to keep in mind when dealing with GMAT arithmetic problems is that the concepts that you’ll come across are fairly simple. You can easily revise these concepts because they are all things we study in high-school-level math. But here’s the kicker: the way these concepts are incorporated into the GMAT problems makes them more challenging, especially when the GMAT arithmetic problems are intertwined with GMAT algebra problems or even GMAT geometry problems. That is where things get tricky, as you need to apply your knowledge in a much more complicated setting that incorporates more than one concept. However, it all comes down to knowing the basics of arithmetics, which we can also refer to as the mechanics of the problem.

In order to help you better understand how to go about a GMAT arithmetic question, we will discuss an arithmetic problem and its solution and solution paths. In this GMAT problem, we are going to see how even the simplest mathematical concepts can become more challenging given the way the problem is formulated and structured.

**Problem (GMAT Official Guide 2018) **

When positive integer x is divided by positive integer y, the remainder is 9.

If x/y = 96.12, what is the value of y?

(A) 96

(B) 75

(C) 48

(D) 25

(E) 12

Solution:

In this case, you will have to revise the properties of numbers in order to properly find a solution to the problem.

When x is divided by y, the remainder is 9. So x=yq + 9 for a random positive integer q.

After dividing both sides by y, we get: x/y = q + 9/y.

But, x/y= 96.12 = 96 + 0.12.

Equating the two expressions for x/y gives q + 9/y= 96+0.12.

Thus:

q=96 and 9/y= 0.12

9=0.12y

y=9/0.12

y=75

**The correct answer is B.**

Now that we went over the solution path for an arithmetic problem on the GMAT exam, you are ready to start your prep. Keep in mind that you should not overthink the questions. Some of them might really look challenging and complex. However, the solution paths can be fairly easy and it ultimately comes down to knowing the “mechanics” of the question.