Algebra Formulas for GMAT Quantitative Reasoning Section

GMAT (Graduate Management Admission Test) is a multiple-choice question, a computer-adaptive test which is designed to examine the student’s command of Geometry, Data Analysis, English Grammar, Basic Arithmetic, and Algebra. It evaluates the student’s ability to think critically, analyse and evaluate and solve problems. The GMAT Paper Pattern is divided into 4 sections- Analytical Writing Assessment, Integrated Reasoning, Quantitative Reasoning, and Verbal Reasoning. If you are preparing for this exam and are struggling to ace the Quant section because of the Algebra topic, we are here at your rescue! This blog aims to explain important algebra formulas and sample questions for the upcoming GMAT 2021 exam!

Understanding Algebra

Algebra is a branch of mathematics that deals with the study of operations, relations, geometry, polynomials and equations. It can be divided into two major categories that are, abstract and elementary algebra. Elementary Algebra is about basic concepts, which is mostly used in the field of Engineering, Science, Mathematics, Science, etc. Abstract algebra is more about the general study of numbers and equations. It also formulates a major section of quant in most of the competitive exams which can easily be cracked if one knows all the algebra formulas

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Algebra Formulas 

While dealing with algebra questions, students need to practice well in advance to solve the problems in less duration. For that, you need to remember the algebra formulas to go about solving questions in less time. Given below is a list of important formulas that students must know and practice before the examination:

Absolute Value

|x| depicts absolute value.
|x| = x
|-x| = x
|x| = |-x|
|x| ≥ 0
|x| + |y| ≥ |x+y|

Example: Solve for x, where x + 5- 10 = 0

Ans : x + 5- 10= 0
By adding 10 on both sides –
x + 5= 10
x + 5 = 10                          (By applying square on both sides)
x = 5

Without brackets, multiply the right side by -1 since the expression in the absolute value brackets could be negative due to the effect of the absolute value.
x + 5 = (10) (-1)
x + 5 = -10
So, therefore, the value of x is 5 or -15.

Quadratic Equations

a² + bx + c = 0
Quadratic Formula: X =-b b² – 4ac2a

Example: Find x, if x² + 6x + 6 = 0
Ans : Using the formula, x = -b b² – 4ac2a
x =-6 6² – 4(1)(6)2(1)
x =-6 36-242
x = -3 122
x = -3 232
x = – 33 (Ans)

Factoring Quadratic Equation

a² + b² = (a + b) (a- b)
a² + 2ab + b² = (a + b)²
a² – 2ab + b² = (a – b)²

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Interest 

Simple Interest = PRT/100
Where,
P = starting principle
R = annual interest rate
T = number of years

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Samples Questions Based on Algebra Formulas

For a better understanding of what type of questions are asked in the exam on algebra formulas, it is important for candidates must practise enough questions. Given below is a list of questions that can give you an idea of the type of questions of algebra, framed in the GMAT exam:

Question 1: If m +|m| = 0, which of the following must be true?

1. m>0
2. m0
3. m<0
4. m0
5. m=0

Answer – (5) m=0

Question 2: For what values of ‘k’ will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?

1. 9
2. 12
3. 3
4. 7.5
5. 2.5

Answer – (1) 9

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Question 3: Which of the following inequalities is equivalent to -2<a<4?

1. |a-2| < 4
2. |a -1| <3
3. |a+1|< 8
4. |a+2| < 4
5. |a+3| < 5

Answer – (2) |a -1| <3

Question 4: John gave his son Kenny a 5z number of coins in addition to what he already had. Kenny now has (y+10) times more coins than before. Express the number of coins he originally had in terms of z and y. 

1. 5z(y + 10)
2. (y + 10)/5z
3. (y + 9)/5z
4. 5z/( y + 9)
5. 5z/(y + 9)

Answer – (3) (y + 9)/5z

Question 5: If (x + 2)² = 9 and (y + 3)² = 25, then the maximum value of XY is?

1. 1/2
2. 5/2
3. -1/2
4. 1/8
5. 5/8

Answer – (5) 5/8

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FAQs

Learning and practising these algebra formulas for GMAT will help you in performing well in the quant section. If you need more help to crack this quintessential study abroad exam, let Leverage Edu help you. Get in touch with our experts to know about the tips and tricks to clear the GMAT in a single go with an excellent score!