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All You Wanted to Know About GRE Quant Algebra

Posted on October 19, 2017

In GRE Quant, Algebra can take up approximately 15to 20 % of the questions. That would be approximately six to eight questions, not including the experimental section.

 

Those who had problems with Algebra in school need not worry when it comes to the GRE because you can use alternatives like Plugging In and Back Solving to solve an Algebra question.

 

 

What is tested in Algebra?

 

What is tested in Algebra can be split into three broad buckets: 

   • Equations

   • Inequalities and Absolute Values

   • Functions

 

 

I) Equations

 

When it comes to Algebra in the GRE, what is tested is not more than what you learned at high school.

 

Algebra questions test your skills at:

   • Simplifying linear equation.

   • Quadratic equations – finding roots.

   • Factoring equation.

   • Polynomials – (very rarely tested. If tested, the questions will be more to do with logic than finding the x value).

   • Constructing word problems into mathematical equations.

 

Sample Question:

 

Sam is now 14 years older than Pam. If in 10 years Sam will be twice as old as Pam, how old will Sam be in 5 years?

   • 9

   • 18

   • 21

   • 23

   • 33

 

Explanation:

 

Now

In 5 years

In 10 years

Sam

X+14

X+19

X+24

Pam

X

X+5

X+10

 

Given X+24 = 2(X+10).

X+24 = 2X +20.

X =4.

In 5 years, Sam will be X+19 = 23.

So the answer is D.

We can also do back Solving to solve this question.

 

 

II) Inequalities and Absolute Values

 

This is where most of the GRE Students struggle. Students have to be very clear on the basics of Inequalities and Absolute values.

 

Inequalities and Absolute values questions test your skills at:

   • Basic rules of Inequalities and Absolute values (This also helps in solving the Quantity Comparison questions).

   • Properties of Inequalities and Absolute values

   • How to find Max – Min values in Inequalities.

 

We can make use of a few properties of inequalities while solving a Quantity comparison question.

   • Adding or subtracting the same expression to both sides of an inequality does not change the inequality

   • Multiplying or dividing the same positive number to both sides of an inequality does not change the inequality

   • Multiplying or dividing the same negative number to both sides of an inequality reverses the inequality, also called the flip rule of inequalities.

Knowing the above basic properties of inequalities helps to solve Quantity comparison questions.

 

Sample question

 

                                                                          Quantity A                                                                                       Quantity B

                                                                          b – 3a2 – 7                                                                                        6 + b – 3a2

 

Explanation

 

 

Quantity A

Quantity B

 

b – 3a2 – 7

6 + b – 3a2

Adding 3a2

b – 3a2 – 7 + 3a= b – 7

6 + b – 3a2 + 3a=6 + b

Subtracting b

b – 7 – b = – 7

6 + b – b = 6

 

Answer: B (Quantity B is greater)

 

 

III) Functions:

 

When you represent something in the form of f(x), you are saying that the value of function f is dependent on the value of the variable “x”. Whenever f(x)”and “g(y)” are used in the GRE, they do not represent products, but functions. Sometimes, functions can also be represented by a special character like #, $,*, etc.

 

Functions questions test your skills at:

   • Finding the input and output values when a function is given.

   • Comparing two functions.

   • Functions representing series and sequence.

 

Sample question

 

For which of the following functions g is g(x) = g(1-x) for all x?

   1. g(x) = 1-x

   2. g(x) = 1- (x^2)

   3. g(x) = (x^3) – (1-x)^3

   4. g(x) = (x^2)/(1-x)^2

   5. g(x) = x/(1-x)  +  (1-x)/x

 

Explanation

Instead of “X” substitute the answer option with (1-x) and check with option g(x) = g(1-x).

   1. g(x) = (1-x) g(1-x) = x , so not equal.

   2. g(x) = 1-(x^2) g(1-x) = 1 – (1-x)^2 = 1-1-x^2+2x = 2x-x^2, So not equal.

   3. g(x) = (x^3) – (1-x)^3 g(1-x) =(1-x)^3 – (x^3), So not equal.  

   4. g(x) = (x^2)/(1-x)^2 g(1-x) = (1-x)^2/ x^2, So not equal.

   5. g(x) = x1x + 1xx    g(1-x) = ((1-x) / x )+ (x / (1-x)) , So both are equal.

 

So the answer is E.

 

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