Algebra Gist for GMAT (Very Important) | Quantitative for GMAT PDF Download

Algebra holds a central place in the field of mathematics, and it is an integral part of the GMAT quant syllabus. Business schools actively seek candidates with a strong quantitative aptitude, a prerequisite for management programs. Proficiency in GMAT algebra is essential when tackling the quant section of the GMAT exam. Some candidates find GMAT algebra questions challenging due to a lack of sufficient understanding of algebraic concepts.

Why should you know GMAT algebra:

1. Approximately 15 algebra questions appear on the GMAT (and algebra skills tend to be useful on other types of questions as well).
2. Basic algebra on the GMAT is math that most test takers learned at age 13-14, so the knowledge is probably still there, but most students are “rusty” and need to re-familiarize themselves with the concepts.

Algebra Basics

Algebraic terms are vital for further understanding of the GMAT algebra concepts and a few important terms of GMAT algebra basics are:

• Variables: In GMAT algebra, they are the symbols that stand for numbers.
• Constants: In GMAT algebra, they are the values that are stagnant in certain problems.
• Terms: When constant and variable are singular or clubbed together, they form terms according to GMAT algebra concepts.
• Degree: Degree is the power of a variable in GMAT algebra.
• Algebraic expression: This is the assortment of terms mingled together by the involvement of addition or deduction and forms GMAT algebra formulas like (x + 2), (x – 3c), and (2x –3y).
• Coefficient: It is a number or symbol that caters as a measure of a property or characteristic.

Types of Expressions in Algebra

• Monomial: Contains only one term like 3x;
• Polynomial: It contains more than one term like a² – b²;
• Binomial: It is like a polynomial and contains two terms like a+b or 3a+6;

Algebra Concepts

Important Algebra Formulas

• The difference in Two Squares: a²–b²=(a−b)(a+b)
• Squaring a Binomial: (a±b)²=a²±2ab+b²
• The Discriminant: D=b²–4ac

Explanation

1V1E – 1 variable, 1 equation: I can solve it.

Questions with just 1 variable tend to be straight-forward math questions that count! Solve with basic algebra and arithmetic skills.

Be sure that you:
1. Write EVERYTHING DOWN (including when you translate sentences into math formulas).
2. Combine “like” terms.
3. Simplify expressions (reduce fractions, etc).

Example:

A museum plans to triple its collection of painting. After doing so, there will be a total of 426 paintings. How many paintings does the museum currently have?
A. 132
B. 138
C. 142
D. 146
E. 152

“In terms of” questions will usually include those 3 words. While they will appear to be TEST IT questions, they’re usually best solved with standard math approaches. They will ask you to solve for a variable (for example, “what is x in terms of y?”).

Example: 

If y = 3y+6/3x then what is x in terms of y?
(A) y+2/y
(B) y/y+2
(C) y+2/2y
(D) 2y/y+2
(E) y/2

Systems

“System” questions involve questions that have 2 or more variables and 2 or more equations for you to use. They’re traditional math questions (although they can sometimes be solved with TEST THE ANSWERS).
There are 2 math approaches to these types of questions: Substitution and Combination. On most System questions, the combination method is faster.  Be on the lookout to use the substitution method though; in subtle questions, it’s actually the faster method. 

2V2E – 2 Variables, 2 Equations…I can solve it!

The 2V2E is the standard in “System” questions. These questions usually appear as story problems and are worth points. 

Example: 

A class of boys and girls sells tickets for a school raffle. Each boy sells 2 tickets and each girl sells 3 tickets. If 52 total boys and girls were involved and a total of 118 tickets were sold, then how many more boys than girls were involved in the raffle?
(A) 6
(B) 14
(C) 18
(D) 20  
(E) 24

2V2E – Trap

Make sure the two equations are truly two DIFFERENT equations.

Example:

what is the value of 7A - 3B?
1) 14A  - 6B = 9
2) 7A + 3B = 4
2V2E – Time Shift

When a question involves a shift in time, that shift must apply to each character in the question.

Example: 

Alan is currently 15 Years older than Ben. In 4 Years, Alan will be exactly twice Ben`s age. How old is Alan now?
(A) 11
(b) 19
(c) 23
(D) 26            
(E) 37

Hint: In 4 Years: (A+4) = 2(B+4)

3V3E – 3 Variables, 3 Equations…I can solve it!

The 3V3E is a much rarer question type (so you might not see one). These questions can be solved with a LENGTHY series of calculations. However, there is usually a pattern (often involving the specific question that is asked) that can help you to answer the question in a much faster way.

Example:

Bob, Glen and Ed weigh a total of 280 pounds. If 4 times Bob's weight is equal to 660 pounds minus 4 times Ed's weight and Glen's weight is 70 pounds more than half of Ed's weight, then what is twice Glen's weight')
(A) 115
(B) 170
(C) 230 
(D) 235
(E) 290 

 3V2E – 3 Variables, 2 Equations… I can still solve it!

The 3V2E is also a much rarer question type (so you might not see one). These questions can be solved with a LENGTHY series of calculations. However, there is usually a pattern (often involving the specific question that is asked) that can help you to answer the question in a much faster way.

Example: 

Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mike's photos is 50 less than the sum of Mike and Norm's photos. If Norm's total photos is 10 more than twice the number of Lisa's photos, then how many photos did Norm take?
(A) 40
(B) 50
(C) 60
(D) 80
(E) 90 

Algebra Tips

• Utilize Numeric Examples: When dealing with intricate algebraic expressions on the GMAT, employ a straightforward numerical value to expedite your problem-solving process.
• Master GMAT Algebraic Formulas: Before delving into shortcuts, thoroughly grasp the theorems and comprehend their explanations. Regularly recall GMAT algebraic formulas, as solving algebraic problems without applying these formulas is not feasible.
• Prioritize Simple GMAT Algebra Questions: Allocate time for mastering the fundamental GMAT algebra formulas. Recognize that 20% of GMAT quant questions can be efficiently tackled by applying these formulas. Thus, balance your practice by dedicating time to both complex and straightforward questions, such as focusing on GMAT algebra word problems on one day and linear equations on the next.
• Daily Practice Routine: Devote 3-4 hours each day to practicing algebra. Utilize GMAT quant practice papers and allocate 1.5-2 minutes per equation for effective problem-solving. Consistent daily practice is imperative for maintaining proficiency in GMAT algebra and other quant sections.
• Embrace the Importance of Practice: Remember the adage that practice leads to perfection. In the GMAT quant section, neglecting regular practice can result in a loss of proficiency in GMAT algebra and other sections. Hence, prioritize consistent practice to secure a higher score on the GMAT.