 # Algebra and arithmetic

Various types of algebra and arithmetic questions are a key part of the quantitative GMAT section. In fact, in any exam there will be 10-15 of these questions.

Which topics are covered?

• Equations
• Inequalities
• Absolute Value
• The Number Line
• Fractions
• Roots and powers

On this page you can view examples of these types of questions, and also login to our advanced on-line practice software to practice free arithmetic and algebra questions.

An example of this type of question on the GMAT quantitative section:

Which of the following fractions is equivalent to 0.4625?

• 18/37
• 16/33
• 21/45
• 37/80
• 5/11

Solution:

When tackling GMAT problems, it's important to know how to convert a decimal fraction into a simple fraction and vice versa. Having said that, there is no reason to do so in this case.
The question asks about a decimal with a finite number of digits. This is known as a terminating decimal. For example, 1/2 is a terminating decimal because if we convert it into a decimal fraction, we get 0.5. In comparison, 1/3 does not end when converted into a decimal fraction and is 0.333333… to infinity.

In order for a fraction to be converted into a terminating decimal, it must only contain (after reduction) powers of 2 or 5, or both. In the answer choices, all of the fractions are non-terminating decimals since they all have a prime factor in the denominator that isn't 2 or 5 or both. Only the fourth option has a denominator that contains only powers of 2 and 5 and is therefore definitely a terminating decimal.

Here's another example of an algebra and arithmetic question from the quantitative section of the GMAT. This time it's in the form of a Data Sufficiency Problem (Click here to read more about the DS format). (1) EDA>0
(2) ABC>0

A)   Statement (1) ALONE is sufficient to answer the question, but statement (2) ALONE is not
B)   Statement (2) ALONE is sufficient to answer the question, but statement (1) ALONE is not
C)   Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement alone is sufficient
D)   Either statement by itself is sufficient to answer the question
E)   Statements (1) and (2) taken together are not sufficient to answer the question, and additional data are needed to answer the question.

Solution:

We are asked if the product of ACE is positive. This will be so in one of two scenarios: Either all three numbers are positive or E is positive and A and C are negative.

The first statement tells us that the product of ADE is positive. That means that either all three numbers are positive (and then A, C, E are also positive and the answer to the question is "yes"), or A and B are negative and C is positive (and then E is also positive, so the product of ACE is negative and the answer to the question is "No").  So in both scenarios the answer to the question is yes, therefore, this statement is sufficient to answer the question.

The second statement tells us that ABC is positive meaning either all three numbers ar positive (and then ACE are also positive and the answer is "yes"), or A and B are both negative and C is positive (and then E is also positive, and product of ACE is negative and the answer is "no"). The two scenarios yield different answers, therefore this statement is insufficient to answer the question.